莱昂纳多
Leonardo
Roger F. Malina,建议编辑
Roger F. Malina, Advising Editor
肖恩·库比特,主编
Sean Cubitt, Editor-in-Chief
合成材料:1956-1975 年澳大利亚的艺术与技术方面,斯蒂芬·琼斯,2011 年
Synthetics: Aspects of Art & Technology in Australia, 1956–1975, Stephen Jones, 2011
混合文化:与西方对话的日本媒体艺术,伊冯娜·斯皮尔曼,2012
Hybrid Cultures: Japanese Media Arts in Dialogue with the West, Yvonne Spielmann, 2012
行走和制图:作为制图师的艺术家,Karen O'Rourke,2013
Walking and Mapping: Artists as Cartographers, Karen O’Rourke, 2013
现代艺术中的第四维和非欧几何,修订版,Linda Dalrymple Henderson,2013
The Fourth Dimension and Non-Euclidean Geometry in Modern Art, revised edition, Linda Dalrymple Henderson, 2013
运动中的幻觉:运动全景和相关景观的媒体考古学,Erkki Huhtamo,2013
Illusions in Motion: Media Archaeology of the Moving Panorama and Related Spectacles, Erkki Huhtamo, 2013
重温:媒体艺术史,由 Sean Cubitt 和 Paul Thomas 编辑,2013
Relive: Media Art Histories, edited by Sean Cubitt and Paul Thomas, 2013
重新收集:艺术、新媒体和社会记忆,Richard Rinehart 和 Jon Ippolito,2014
Re-collection: Art, New Media, and Social Memory, Richard Rinehart and Jon Ippolito, 2014
Biopolitical Screens: Image, Power, and the Neoliberal Brain , Pasi Väliaho, 2014
Biopolitical Screens: Image, Power, and the Neoliberal Brain, Pasi Väliaho, 2014
光的实践:从版画到像素的视觉技术谱系,肖恩·库比特,2014
The Practice of Light: A Genealogy of Visual Technologies from Prints to Pixels, Sean Cubitt, 2014
我们时代的基调:声音、感官、经济和生态,弗朗西丝·戴森,2014
The Tone of Our Times: Sound, Sense, Economy, and Ecology, Frances Dyson, 2014
体验机器:Stan VanDerBeek 的 Movie-Drome 和扩展影院,Gloria Sutton,2014
The Experience Machine: Stan VanDerBeek’s Movie-Drome and Expanded Cinema, Gloria Sutton, 2014
Hanan al-Cinema:对动态影像的热爱,Laura U. Marks,2015
Hanan al-Cinema: Affections for the Moving Image, Laura U. Marks, 2015
写作和不写作(媒体)艺术史:2048 年的 Erkki Kurenniemi,由 Joasia Krysa 和 Jussi Parikka 编辑,2015
Writing and Unwriting (Media) Art History: Erkki Kurenniemi in 2048, edited by Joasia Krysa and Jussi Parikka, 2015
控制:作为文化逻辑的数字化,Seb Franklin,2015
Control: Digitality as Cultural Logic, Seb Franklin, 2015
新趋势:信息革命门槛上的艺术(1961-1978),Armin Medosch,2016
New Tendencies: Art at the Threshold of the Information Revolution (1961–1978), Armin Medosch, 2016
屏幕生态学:亚太地区的艺术、媒体和环境,Larissa Hjorth、Sarah Pink、Kristen Sharp 和 Linda Williams,2016 年
Screen Ecologies: Art, Media, and the Environment in the Asia-Pacific Region, Larissa Hjorth, Sarah Pink, Kristen Sharp, and Linda Williams, 2016
海盗哲学:数字后人类,加里·霍尔,2016
Pirate Philosophy: For a Digital Posthumanities, Gary Hall, 2016
社交媒体考古学和诗学,朱迪·马洛伊编辑,2016
Social Media Archeology and Poetics, edited by Judy Malloy, 2016
实用:从参与到当代艺术互动, Samuel Bianchini 和 Erik Verhagen 编辑,2016
Practicable: From Participation to Interaction in Contemporary Art, edited by Samuel Bianchini and Erik Verhagen, 2016
二十世纪的机器艺术,安德烈亚斯·布罗克曼,2016
Machine Art in the Twentieth Century, Andreas Broeckmann, 2016
Here/There: Telepresence, Touch, and Art at the Interface , Kris Paulsen, 2017
Here/There: Telepresence, Touch, and Art at the Interface, Kris Paulsen, 2017
声轨:在媒体和艺术中调和声音,诺里纽马克,2017
Voicetracks: Attuning to Voice in Media and the Arts, Norie Neumark, 2017
欣喜若狂的世界:媒体、乌托邦、生态学,Janine Marchessault,2017
Ecstatic Worlds: Media, Utopias, Ecologies, Janine Marchessault, 2017
作为乌托邦的界面:弗雷德森林的媒体艺术和行动主义,迈克尔·F·勒鲁斯,2017
Interface as Utopia: The Media Art and Activism of Fred Forest, Michael F. Leruth, 2017
有意义:艺术、计算、认知和体现,Simon Penny,2017
Making Sense: Art, Computing, Cognition, and Embodiment, Simon Penny, 2017
天气作为媒介:迈向气象艺术,珍妮·兰德森,2018
Weather as Medium: Towards a Meteorological Art, Janine Randerson, 2018
实验室生活方式:科幻小说的构建,由 Sandra Kaji-O'Grady、Chris L. Smith 和 Russell Hughes 编辑,2018
Laboratory Lifestyles: The Construction of Scientific Fictions, edited by Sandra Kaji-O’Grady, Chris L. Smith, and Russell Hughes, 2018
看不见的颜色:原子时代的艺术,Gabrielle Decamous,2018
Invisible Colors: The Arts of the Atomic Age, Gabrielle Decamous, 2018
虚拟动物园:动物作为网络文化的中介,乔迪·伯兰德,2019
Virtual Menageries: Animals as Mediators in Network Cultures, Jody Berland, 2019
从手指到数字:人工美学,Ernest Edmonds 和 Margaret A. Boden,2019
From Fingers to Digits: An Artificial Aesthetic, Ernest Edmonds and Margaret A. Boden, 2019
材料证人:媒体、取证、证据,Susan Schuppli,2020
MATERIAL WITNESS: Media, Forensics, Evidence, Susan Schuppli, 2020
交互策略:对艺术和技术的编码影响,Ksenia Fedorova,2020
Tactics of Interfacing: Encoding Affect in Art and Technology, Ksenia Fedorova, 2020
让身体回归数据:磁共振技术中的图像制造者、拼凑和重塑,Silvia Casini,2021 年
Giving Bodies Back to Data: Image-Makers, Bricolage, and Reinvention in Magnetic Resonance Technology, Silvia Casini, 2021
像素传记,Alvy Ray Smith,2021
A Biography of the Pixel, Alvy Ray Smith, 2021
请参阅http://mitpress.mit.edu以获取本系列的完整标题列表。
See http://mitpress.mit.edu for a complete list of titles in this series.
阿尔维·雷·史密斯
Alvy Ray Smith
麻省理工学院出版社
The MIT Press
马萨诸塞州剑桥
Cambridge, Massachusetts
伦敦,英国
London, England
© 2021 麻省理工学院
© 2021 Massachusetts Institute of Technology
版权所有。未经出版商书面许可,不得以任何电子或机械方式(包括影印、录音或信息存储和检索)以任何形式复制本书的任何部分。
All rights reserved. No part of this book may be reproduced in any form by any electronic or mechanical means (including photocopying, recording, or information storage and retrieval) without permission in writing from the publisher.
麻省理工学院出版社要感谢对本书草稿提供意见的匿名同行审稿人。学术专家的慷慨工作对于确立我们出版物的权威性和质量至关重要。我们衷心感谢这些未经授权的读者的贡献。
The MIT Press would like to thank the anonymous peer reviewers who provided comments on drafts of this book. The generous work of academic experts is essential for establishing the authority and quality of our publications. We acknowledge with gratitude the contributions of these otherwise uncredited readers.
本书由 New Best-set Typesetters Ltd. 在 ITC Stone Serif Std 和 ITC Stone Sans Std 中设置。
This book was set in ITC Stone Serif Std and ITC Stone Sans Std by New Best-set Typesetters Ltd.
美国国会图书馆出版数据编目
Library of Congress Cataloging-in-Publication Data
姓名:Smith, Alvy Ray, 1943– 作者。
Names: Smith, Alvy Ray, 1943– author.
标题:像素传记 / Alvy Ray Smith。
Title: A biography of the pixel / Alvy Ray Smith.
描述:马萨诸塞州剑桥:麻省理工学院出版社,[2021] | 系列:莱昂纳多 | 包括参考书目和索引。
Description: Cambridge, Massachusetts : The MIT Press, [2021] | Series: Leonardo | Includes bibliographical references and index.
标识符:LCCN 2020029699 | ISBN 9780262542456(平装本)
Identifiers: LCCN 2020029699 | ISBN 9780262542456 (paperback)
科目: LCSH:电脑动画——历史。
Subjects: LCSH: Computer animation—History.
分类:LCC TR897.7 .S52 2021 | DDC 777/.7—dc23
Classification: LCC TR897.7 .S52 2021 | DDC 777/.7—dc23
LC 记录可在https://lccn.loc.gov/2020029699
LC record available at https://lccn.loc.gov/2020029699
10 9 8 7 6 5 4 3 2 1
10 9 8 7 6 5 4 3 2 1
d_r1
d_r1
至
To
艾莉森,我心爱的妻子
Alison, my beloved wife
山姆和杰西,我亲爱的儿子们
Sam and Jesse, my dear sons
和
and
Leo、Attie、Georgie、Augie 和 Evelyn,我受人爱戴又脾气暴躁的孙子们
Leo, Attie, Georgie, Augie, and Evelyn, my adored and ornery grandchildren
Foundations: Three Great Ideas
1 Fourier’s Frequencies: The Music of the World
2 Kotelnikov’s Samples: Something from Nothing
3 Turing’s Computations: Eleventy-Eleven Skydillion
Contributions: Two High Technologies
4 Dawn of Digital Light: The Quickening
5 Movies and Animation: Sampling Time
The Rise and Shine of Digital Light
8 The Millennium and The Movie
莱昂纳多,国际艺术、科学和技术协会,以及附属的法国组织莱昂纳多协会,有一些非常简单的目标:
Leonardo, the International Society for the Arts, Sciences, and Technology, and the affiliated French organization Association Leonardo, have some very simple goals:
当莱昂纳多杂志大约五十年前开始,这些创造性学科通常存在于隔离的机构和社会网络中,当时由 CP Snow 发起的“两种文化”辩论戏剧化了这种情况。今天,我们生活在一个由新的混合组织、新的资助者以及计算机和互联网的共享工具促成的跨学科发酵、协作和智力对抗的不同时代。有时在“STEM to STEAM”运动中被捕捉到,新的合作形式似乎将艺术、人文和设计与科学和工程实践相结合。最重要的是,新一代的艺术家研究人员和研究艺术家现在正在单独和协作地连接艺术、科学和技术学科。对于我们社会的一些难题,我们别无选择,只能找到将艺术与科学结合起来的新方法。也许在我们的有生之年,我们会看到“新莱昂纳多斯”的出现,这种混合创意的个人或团队不仅会为我们的时代开发出有意义的艺术,而且还会推动科学的新议程并刺激满足当今人类需求的技术创新。
When the journal Leonardo was started some fifty years ago, these creative disciplines usually existed in segregated institutional and social networks, a situation dramatized at that time by the “Two Cultures” debates initiated by C. P. Snow. Today we live in a different time of cross-disciplinary ferment, collaboration, and intellectual confrontation enabled by new hybrid organizations, new funding sponsors, and the shared tools of computers and the internet. Sometimes captured in the “STEM to STEAM” movement, new forms of collaboration seem to integrate the arts, humanities, and design with science and engineering practices. Above all, new generations of artist-researchers and researcher-artists are now at work individually and collaboratively bridging the art, science, and technology disciplines. For some of the hard problems in our society, we have no choice but to find new ways to couple the arts and sciences. Perhaps in our lifetime we will see the emergence of “new Leonardos,” hybrid creative individuals or teams that will not only develop a meaningful art for our times but also drive new agendas in science and stimulate technological innovation that addresses today’s human needs.
有关莱昂纳多组织和网络活动的更多信息,请访问我们的网站http://www.leonardo.info/和http://www.olats.org/。亚利桑那州立大学莱昂纳多知识企业为推进亚利桑那州立大学的跨学科艺术科学研究、创意实践和该领域的国际形象提供了领导力:https ://leonardo.asu.edu/ 。
For more information on the activities of the Leonardo organizations and networks, please visit our websites at http://www.leonardo.info/ and http://www.olats.org/. The Arizona State University–Leonardo knowledge enterprise provides leadership to advance ASU’s transdisciplinary art-science research, creative practice, and international profile in the field: https://leonardo.asu.edu/.
罗杰·F·马利纳
Roger F. Malina
建议编辑,莱昂纳多出版物
Advising Editor, Leonardo Publications
图 0.1
Figure 0.1
步行野猪,阿尔塔米拉,约公元前 20,000 年。
Walking boar, Altamira, ca. 20,000 BCE.
你不可为你雕刻任何偶像,或任何在天上,或在地下,或在地底下水中的任何东西的像。
Thou shalt not make unto thee any graven image, or any likeness of any thing that is in heaven above, or that is in the earth beneath, or that is in the water under the earth.
——出埃及记 20:4,詹姆士王版
—Exodus 20:4, King James Version
一开始——肯定早于圣经禁忌——一个被火焰点燃的雕刻图像似乎在移动。西班牙阿尔塔米拉洞穴墙壁上的一幅画是一只行走的野猪,以及一位古代艺术家在其上绘画的岩石以及使用的木炭和赭石颜料(图 0.1)。20 千年左右的时间里,世界上没有其他地方可以看到那只圣经前的猪。只有在旧石器时代电影院闪烁的火光中,你才能看到它的腿移动和头部摆动。1
In the beginning—predating scriptural taboo, surely—a flame-lit graven image appeared to move. A picture on the walls of Spain’s Altamira Cave was a walking boar AND the rock on which an ancient artist painted it AND the charcoal and ochre pigments used (figure 0.1). For 20 millennia or so there was no other place in the world to see that pre-biblical pig. Only there in the flickering firelight of a Paleolithic movie theater could you see its legs move and head bob.1
甚至直到 1800 年,也就是两个世纪前,一张拿破仑穿越阿尔卑斯山的照片和雅克-路易·大卫 (Jacques-Louis David) 画在上面的画布和他使用的油画颜料是一个不可或缺的单元。想象一下,您想与纽约的朋友分享拿破仑在欧洲令人愉快的传记照片(图 0.2)。那时还没有手机和摄像机,甚至连照片之类的东西都没有。在纽约展示他的唯一方法是将一幅实物画运送到那里——如果你敢的话。雕刻、蚀刻或素描可能会有所帮助,但这些只是更好或更差的副本——新图像永远不会完全忠实地捕捉原件。2
Even as late as 1800, just two centuries ago, a picture of Napoleon crossing the Alps AND the canvas on which Jacques-Louis David painted it AND the oil paints he used were an integral unit. Imagine that you wanted to share Napoleon’s delightfully hagiographic picture (figure 0.2) in Europe with a friend in New York. There were no cellphones or video cameras yet, not even such a thing as a photograph. The only way to display him in New York was to transport the one physical painting there—if you dared. An engraving, etching, or sketch might help, but those were only better or worse copies—new images that would never fully and faithfully capture the original.2
在那段时间里,一幅画和它的创作媒介是密不可分的。甚至没有人想过将两者分开。独立于媒介的图片会是什么?
Through all that time a painting and its medium of creation were inseparable. No one even conceived of separating the two. What could a picture be, independent of its medium?
然后在 19 世纪初发明了摄影,开创了我们现在所说的“媒体”世界。忠实的繁殖就在我们身上。电影出现在 19 世纪末,电视出现在 20 世纪初。那时所有的媒体都是模拟的——流畅和连续。一张图片可以从一种媒体转移到另一种媒体——这暗示着,一张图片毕竟是从它的媒体中分离出来的。
Then in the early nineteenth century photography was invented, ushering in the world of what we now call “the media.” Faithful reproduction was upon us. Movies followed in the late nineteenth century and television in the early twentieth. All media then were analog—smooth and continuous. And a picture could be transferred from one medium to another—a hint that something, after all, about a picture floats separate from its medium.
直到 1933 年,数字的概念——离散和尖峰——才完全存在。在 1950 年的世纪中叶,只有几张数字图片存在。少数了解它们的人实际上认为它们是对更严肃的数字计算机项目的无聊干扰。世界上所有其他图片都是用模拟方式制作和观看的——画布上的油、纸上的墨水和胶卷上的化学乳剂,仅举几例。
The notion of the digital—discrete and spiky—didn’t fully exist until 1933. At midcentury, 1950, there were only a couple of digital pictures in existence. The few people who knew about them actually thought they were frivolous distractions from the more serious projects of digital computers. All the other pictures in the world were made and viewed with analog means—oil on canvas, ink on paper, and chemical emulsion on photographic film, to name a few.
但在千禧年,即 2000 年,发生了一件鲜为人知的事件——大数字融合:一种新的数字媒体——无所不包的比特——几乎取代了所有的模拟媒体。比特成为了通用媒介,而像素——一种特殊的比特包装——征服了世界。可以说,从画布上移除一幅画成为可能。因此,世界上大多数图片现在都是数字的。与无处不在的数字图像相比,模拟图像几乎消失了。博物馆和幼儿园是为数不多的可以找到类似物的可靠场所。
But at the millennium, 2000, there was an unheralded event—the Great Digital Convergence: a single new digital medium—the all-encompassing bit—replaced nearly all analog media. The bit became the universal medium, and the pixel—a particular packaging of bits—conquered the world. It became possible to remove a painting, so to speak, from its canvas. As a consequence, most pictures in the world are now digital. Analog pictures have all but vanished relative to ubiquitous digital imagery. Museums and kindergartens are among the few reliable places to find the analog.
这本书通过庆祝数字光来预示着千禧年的事件——包括任何图片的广阔领域,用于任何目的,由像素制成。它从停车计时器延伸到虚拟现实,从仪表板到数字电影和电视,从 CAT 扫描到视频游戏再到手机显示屏,等等——任何以像素为媒介的事物。
This book heralds that signal millennial event by celebrating Digital Light—the vast realm that includes any picture, for any purpose, made from pixels. It extends from parking meters to virtual reality, from dashboards to digital movies and television, from CAT scans to videogames to cellphone displays, and many, many more—anything mediated by pixels.
新媒体令人困惑的是你看不到它。位和由位组成的像素是不可见的。不要像通常那样将像素与小像素混淆屏幕上的发光区域,称为显示元素。本书的技术核心是解释如何使由不可见的东西组成的图片可见——如何将数字像素转换为模拟显示元素。
What’s puzzling about the new medium is that you can’t see it. Bits, and pixels made of bits, are invisible. Pixels are not to be confused, as they often are, with the little glowing areas on a screen, called display elements. The technical heart of this book is the explanation of how to make pictures composed of invisible stuff visible—how to convert digital pixels to analog display elements.
图 0.2
Figure 0.2
雅克-路易·大卫,拿破仑穿越阿尔卑斯山,1801 年。
Jacques-Louis David, Napoleon Crossing the Alps, 1801.
千禧年发生的大数字融合只是一个巧合,而是一个方便的巧合。皮克斯于 1995 年发行了第一部数字电影《玩具总动员》。新的高清电视 (HDTV) 信号的首次播出是在 1998 年。1999 年,一款质量足以威胁胶片相机的数码相机震惊了市场。光盘或 DVD 于 2000 年首次亮相。Apple 于 2007 年推出了无处不在的 iPhone。曾经的墨水和纸张、照片、电影和电视在历史的一瞬间变成了比特。变化如此之快,以至于今天的年轻人可能从未体验过非数字媒体——除了那些模拟的最后堡垒:艺术博物馆和幼儿园。
That the Great Digital Convergence happened at the millennium was just a coincidence, but a convenient one. Pixar released the first digital movie, Toy Story, in 1995. The first broadcast of the new high-definition television (HDTV) signal was in 1998. A digital camera of sufficient quality to threaten film cameras astonished the market in 1999. The digital video disc, or DVD, debuted in 2000. Apple introduced the ubiquitous iPhone in 2007. What had been ink and paper, photographs, movies, and television became—in a blink of the historical eye—just bits. The change was so fast that young people today may have never experienced non-digital media—outside those last bastions of the analog: art museums and preschools.
我们现在都沉浸在像素的海洋中。我随身携带了数十亿个,我怀疑你也这样做了。但奇怪的是,我们日常经验中这种普遍的变化几乎没有引起人们的重视。也许这是因为大多数人还没有意识到 Digital Light 是一种单一的统一技术。这个概念是新的。讲清楚是本书的主要目的。
We are all now aswim in an ocean of pixels. I carry billions of them on my person, and I suspect that you do too. But curiously there’s been little serious notice taken of this pervasive change in our daily experience. Perhaps this is because most people haven’t realized that Digital Light is a single unified technology. The notion is new. Making it clear is a major purpose of this book.
只有三个想法——波、计算和像素——构成了数字光所有明显复杂性的基础。每个想法在直觉上都是简单、深刻和美丽的。这些是我们现代世界的技术基石,你不需要数学来理解它们。前三章(本书的第一部分)介绍了这些基本思想,以及使它们成为可能的人们的令人惊讶和引人入胜的故事。
Just three ideas—waves, computations, and pixels—underlie all the apparent complexity of Digital Light. Each idea is intuitively simple, profound, and beautiful. These are the technological cornerstones of our modern world, and you don’t need mathematics to understand them. The first three chapters (part I of this book) present these foundational ideas with the surprising and fascinating stories of the people who made them possible.
Waves 是一个模拟的想法。您可能知道音乐是由不同频率(音高)和幅度(响度)的同时声波组成的。两个世纪前,法国人约瑟夫·傅立叶将这一概念扩展到我们所有的感官体验。我们看到和听到的一切都是波的总和。都是音乐。在本书中,我将向您展示如何在视觉场景中观看音乐。
Waves are an analog idea. You probably know that music is made of simultaneous sound waves of different frequencies (pitches) and amplitudes (loudnesses). Two centuries ago the Frenchman Joseph Fourier extended that notion to all our sensory experience. Everything we see and hear is a sum of waves. It’s all music. In this book I show you how to see the music in a visual scene.
计算机是一种数字概念。使计算快速进行的机器是日常生活中数字化的典范。但是计算的概念只能追溯到 1936 年,当时英国人艾伦·图灵发明了它,以捕捉谨慎、精确过程的概念。这可能听起来乏味乏味,但后果绝不是这样。计算机是人类最具延展性的工具。还有他们惊人的速度是有史以来最重要的工程奇迹。以这样的速度,计算机将我们微不足道的人类可以做的事情放大到难以想象的程度。
Computers are a digital idea. Machines that make computations go fast are the very exemplars of the digital in ordinary life. But the idea of computation dates back only to 1936 when the Englishman Alan Turing invented it to capture the notion of a careful, precise process. That might sound plodding and boring, but the consequences are anything but. Computers are humankind’s most malleable tool. And their awesome speed is the most consequential engineering miracle of all time. With that speed, computers amplify what we puny humans can do by unimaginable amounts.
但是计算机的所有令人难以置信的、改变世界的能力实际上都归结为在两个状态之间小心翻转,通常被命名为 0 和 1。计算都是比特。这听起来可能微不足道,但我希望用计算中固有的意想不到的美丽和神秘来激发你的灵感。同样,不需要数学。
But all of the mind-boggling, world-changing power of computers really reduces to a careful flipping between two states, often named 0 and 1. Computation is all bits. That may sound trivial, but I hope to inspire you with the unexpected beauty—and mystery—inherent in computation. Again, no mathematics required.
三个基本思想中最重要但鲜为人知的是本书的基本主题:你可以在波和比特之间来回穿梭——在模拟世界和数字世界之间。这个想法只能追溯到 1933 年,当时俄罗斯人 Vladimir Kotelnikov 建立了我们今天所知的它。它的正式名称是采样定理。整本书——作为像素的传记,像素是我们对视觉世界样本的名称——都是关于采样的。像素是代表可见波的不可见位。我的热切意图是让您了解这件魔法,并对它的工作原理感到惊讶。这里也不需要数学。
The most important but least known of the three fundamental ideas is the underlying theme of this book: you can pass back and forth between waves and bits—between the analog and digital worlds. The idea dates back only to 1933 when the Russian Vladimir Kotelnikov established it as we know it today. Its formal name is the Sampling Theorem. This entire book—being a biography of the pixel, with pixel being our name for a sample of the visual world—is about sampling. Pixels are invisible bits that represent visible waves. My fervent intent is that you understand this piece of magic and be amazed by how it works. No mathematics is required here either.
既然我已经在两页中说过三次不需要数学,你可能会想:但是如果我们中的一些人关心数学怎么办?对于您——但实际上对于我所有的读者——我在http://alvyray.com/DigitalLight上提供了一个在线注释站点。在那里,您将找到有关人物、地点和事件的更多详细信息,这些细节会使这本书过于笨拙,无法在其物理封面之间进行放置——您还将找到支持 Digital Light 魔力的数学方程式和使之成为可能的像素. 3
Now that I’ve said no math required three times in two pages, you might be thinking: But what if some of us care about the math? For you—but really for all my readers—I provide an online annotations site at http://alvyray.com/DigitalLight. There you will find additional details about people, places, and events that would have made this book too unwieldy to fit between its physical covers—and you will find as well mathematical equations to support the magic of Digital Light and the pixels that make it possible.3
一个常见的误解是像素是一个小方块颜色。但事实上,像素是一个深刻而抽象的概念,将我们现代媒体世界联系在一起。这是Digital Light的组织原理。
There’s a common misconception that a pixel is a little square of color. But in fact, the pixel is a profound and abstract concept that binds our modern media world together. It’s the organizing principle of Digital Light.
一个视觉场景由无数个颜色点组成。根据定义,无限是太大而无法处理的。那么,我们如何才能用有限数量的离散位(像素)来替换平滑的视觉场景,而不会丢失它们之间的无限信息呢?采样定理告诉我们如何去做。这是使现代媒体世界运转的秘密。
A visual scene consists of an infinite number of points of color. Infinite is, by definition, too large to deal with. So how can we replace a smooth visual scene with only a finite number of discrete bits—the pixels—and not lose an infinity of information between them? The Sampling Theorem tells us how to do it. It’s the secret that makes the modern media world work.
依赖于傅立叶波的采样几乎是在 1930 年代中期与计算同时创建的。采样遇到了计算并孕育了一个孩子,Digital Light,这本书的主题。
Sampling, which depends on Fourier’s waves, was created almost simultaneously with computation in the mid-1930s. Sampling met computation and conceived a child, Digital Light, the subject of this book.
本书的第二部分专门介绍了塑造数码光的两项高科技的历史:计算机和电影。与第一部分一样,我直观地介绍了每项技术,并讲述其发明的历史——揭穿一些常见的神话。真实的故事总是比神话更有趣、更鼓舞人心、更复杂。
Part II of the book is devoted to the history of two high technologies that shaped Digital Light: computers and movies. As in part I, I present each technology intuitively and give the history of its invention—debunking some common myths. The true stories are invariably more intriguing, inspiring, and complicated than the myths.
在 Digital Light 中,我们可以从现实世界中获取像素——例如,从国际空间站上的摄像头跟踪最新的飓风。但更重要的是,对于这本书,我们还可以从头开始制作像素。这就是计算机的用武之地,也是我如此详细地介绍高科技发展的原因。
In Digital Light we can take pixels from the real world—from cameras on the International Space Station, say, tracking the latest hurricane. But more importantly for this book we can also make pixels from scratch. That’s where computers come in and why I present the development of that high technology in such detail.
我为这本书所做的研究中的许多惊喜之一是发现第一个像素出现在第一台计算机上。他们是一起出生的。因此,通过确定哪些计算机是世界上第一台计算机,我们还可以了解谁拥有世界上第一台像素。这就是为什么第二部分中关于计算机的章节被称为“数字光的黎明:加速”的原因。它展示了 1947 年用像素制作的第一张图片。它引入了一个巨大力量的驱动概念,称为摩尔定律:
One of many surprises from my research for this book was the discovery that the first pixels occurred on the first computers. They were born together. So by establishing which computers were the first in the world, we also learn who had the first pixels in the world. That’s why the chapter on computers in part II is called “Dawn of Digital Light: The Quickening.” It features the first picture made with pixels, in 1947. And it introduces a driving concept of enormous force, called Moore’s Law:
计算机的任何优点每五年就会提高一个数量级。
Anything good about computers gets better by an order of magnitude every five years.
尽管它很简单,但这种说法是革命性的。1965 年戈登摩尔宣布它时的 1 倍,现在约为 1000 亿,到 2025 年将达到 1 万亿。这是一颗爆炸的超新星。摩尔定律是 50 多年来所有计算机发展背后的强大动力,包括 Digital Light。
Despite its simplicity, that statement is revolutionary. What was a factor of 1 in 1965, when Gordon Moore announced it, is about 100 billion now, and will reach 1 trillion by 2025. It’s an exploding supernova. Moore’s Law is the astonishingly powerful dynamo behind every development of computers for over 50 years—including Digital Light.
Digital Light的数字电影部分来源于经典电影。标题为“电影和动画:采样时间”的章节回顾了这种前数字运动图像技术。它还有助于进一步说明采样:我们熟悉的闪烁胶片“帧”实际上是一个示例。
The digital movie part of Digital Light derives from classic film. The chapter titled “Movies and Animation: Sampling Time” reviews this pre-digital moving-image technology. It also helps to further illustrate sampling: the familiar “frame” of flickering film is actually a sample.
动词take和make 也适用于电影。我们用相机从现实世界的场景中拍摄经典电影。我们根据非现实世界的图画制作经典动画电影。这两种电影的核心奥秘在于它们为什么应该有效。一系列静止帧如何传递运动和情感?至少,采样定理有助于解释运动。第一部数字电影——例如皮克斯的《玩具总动员》 ——是经典动画电影的数字继承者。
The verbs take and make apply to film movies too. We take a classic film movie from real-world sets with a camera. We make a classic animated movie from drawings of a non-real world. The central mystery of both kinds of movies is why they should work at all. How does a sequence of still frames deliver both motion and emotion? The Sampling Theorem helps explain motion, at least. The first digital movies—such as Pixar’s Toy Story—are digital heirs to classic animated films.
Digital Light 的故事太大,无法在一本书中涵盖,因此必须重点关注这一点。它涵盖了从世纪中叶的第一个像素到千禧年的第一部数字电影的数字光。不出所料,我选择写我从个人经验中最了解的特定技术、人物和历史。我出生在计算机和像素之前,我的职业生涯主要致力于创造第一部数字电影。但是选择的路径可以帮助解释数字光是如何变得更普遍的。电子游戏和虚拟现实并没有那么遥远。
The Digital Light story is too large to cover in a single book, so this one necessarily has to focus. It covers Digital Light from the first pixels at midcentury to the first digital movies at the millennium. Unsurprisingly, I have chosen to write about the particular technologies, people, and history I know best from personal experience. I was born before computers—and pixels—and my career was principally devoted to creating the first digital movies. But that chosen path can help explain how Digital Light came to be more generally. Videogames and virtual reality aren’t that far removed.
第三部分的三章讲述了数码光在黎明后的故事(在第 4 章中讲述)和那些第一个世纪中叶的像素。1965 年的摩尔定律将它们清晰地分为摩尔定律之前的数字光时代 1 和之后的时代 2。标题为“即将到来的事物的形状”的章节专门介绍了第 1 纪元。另外两章“意义的阴影”和“千年与电影”涵盖了第 2 纪元中摩尔定律带来的巨大变化。
The three chapters of part III pick up the story of Digital Light after its dawn (told in chapter 4) and those first midcentury pixels. Moore’s Law of 1965 cleanly separates them into Epoch 1 of Digital Light, before Moore’s Law, and Epoch 2, after. The chapter titled “Shapes of Things to Come” is devoted to Epoch 1. The other two chapters, “Shades of Meaning” and “The Millennium and The Movie,” cover the massive changes wrought by Moore’s Law in Epoch 2.
时代 1 是计算机的巨大时代,但速度非常慢。一些幸运的人可以接触到那些昂贵的野兽。从这一时期开始出现计算机图形学的中心法则:在计算机内部使用三维欧几里得几何和牛顿物理学来描述一个虚构的世界。然后它被一个虚拟相机观察到,它把它的世界观渲染成文艺复兴视角的二维显示。
Epoch 1 was the era of monstrous, but ponderously slow, computers. A few lucky individuals got access to those expensive beasts. From this period came the Central Dogma of computer graphics: a fictitious world is described inside a computer with three-dimensional Euclidean geometry and Newtonian physics. Then it’s observed by a virtual camera that renders its view of the world into two dimensions in Renaissance perspective for display.
我或多或少地涵盖了 Epoch 2 直到 2000 年。千禧年的高潮是皮克斯、梦工厂和蓝天这三个伟大的数字电影工作室的崛起。他们的故事交织在一起。
I cover Epoch 2 until 2000, more or less. The culmination at the millennium was the rise of three great digital movie studios, Pixar, DreamWorks, and Blue Sky. Their stories are intertwined.
我不指望你在读完这本书后就能创作出一部数字电影,但我希望你能明白这是怎么可能的。这就像一堂音乐鉴赏课:学会了音乐原理后,你将无法自己为大提琴谱写巴赫组曲,但你会更好地理解这些组成部分,从而更爱巴赫。了解像《玩具总动员》这样的现代电影是如何制作的可以产生同样的效果。
I don’t expect you to be able to create a digital movie after reading this book, but I hope you might understand how it’s possible. It’s like a music-appreciation course: After you learn the principles of music, you won’t be able yourself to compose a Bach suite for cello, but you’ll better understand the components and so love Bach even more. Understanding just how a modern movie like Toy Story is made can have the same effect.
从我对本书技术史的研究中得出了几个共同的主题:
Several common themes emerged from my research on the technological histories in this book:
举一个例子,约瑟夫·傅立叶有一个伟大的想法,即一个连续统一体,比如一个视野,就是所有的音乐。这只是波的总和。法国大革命的混乱让他在巴黎登上了世界舞台,拿破仑的崛起给了他工作的机会。拿破仑本人就是将傅立叶流放到乡下的暴君让他远离巴黎。在这个受保护的地方很长一段时间,傅立叶将他的想法发展成波理论,最终他回到了巴黎。他的想法影响了所有随后的科学和技术——尤其是数字光。
To give just one example, Joseph Fourier had the great idea that a continuum, such as a visual field, is all music. It’s just a sum of waves. The chaos of the French Revolution ushered him onto the world stage in Paris, and the rise of Napoleon gave him his chance to work. Napoleon himself was the tyrant who exiled Fourier to the countryside to keep him out of Paris. In this protected place for a protracted time, Fourier developed his idea into the theory of waves that eventually returned him to Paris. His idea has influenced all subsequent science and technology—and Digital Light in particular.
为了避免这种简单化的叙述陷阱,我依靠家谱。对于每项技术的历史,我设计了一个家庭流程图——一种图形设备,看起来很合适——用于涉及的人、地点、想法和机器。该图表显示了谁从谁那里得到了什么(无论是不择手段还是不择手段)以及玩家阵容之间经常密集的相互作用。几乎没有一个人可以从一个人那里得到其他一切。从一个图表流向另一个图表,然后到另一个图表。我们看着不同的股线以不同的方式编织在一起以影响下一代。因此,每一章都成为其流程图的扩展标题,并通过相关人员的详细故事和他们想法的直观呈现来增强。
To avoid this simplistic narrative pitfall, I rely on genealogy. For the history of each technology, I’ve designed a family flow chart—a graphical device, which seems fitting—for the persons, places, ideas, and machines involved. The chart shows who got what from whom (whether by hook or by crook) and the often-dense interplay of the cast of players. There’s hardly ever a single person from whom all else derives. The flows from one chart proceed to another and then to another. We watch as the different strands braid together in different ways to influence the next generation. Each chapter thus becomes an extended caption for its flow chart, enhanced with detailed stories of the people involved and intuitive presentations of their ideas.
现在让我们开始我们的两个世纪之旅,大约在大卫的著名画作纪念的时候——但拿破仑的肖像画却远没有那么讨人喜欢。
Let’s now commence our two-century tour, at about the time commemorated by David’s famous painting—but with a substantially less flattering portrait of Napoleon.
科学院有一位著名的傅立叶,后人已经忘记了他。
There was a celebrated Fourier at the Academy of Science, whom posterity has forgotten.
——维克多·雨果,《悲惨世界》1
—Victor Hugo, Les Misérables1
你知道傅里叶吗?
Do you know Fourier?
答案使我们分裂。如果你说是,那么你可能在科学或技术领域。你今天可能已经使用了他的好主意。如果你从事艺术或人文学科,你可能从未听说过他。然而,他的想法是美丽、优雅和普遍的。它改变了我们的世界。2
The answer divides us. If you say yes, then you’re probably in the sciences or technologies. You might have used his great idea this very day. If you’re in the arts or humanities, you’ve probably never heard of him. Yet his idea is beautiful, elegant, and pervasive. And it changed our world.2
但是,即使您确实回答了“是”,您也可能对这个人本人一无所知。所以维克多雨果在这方面做得对。后人忘记了傅立叶。
But even if you did answer yes, you probably know nothing about the man himself. So Victor Hugo got it right in that regard. Posterity has forgotten Fourier.
例如,很少有人知道约瑟夫·傅立叶在法国大革命中几乎失去了理智。或者拿破仑波拿巴带他去埃及探险,发现了罗塞塔石碑。或者他在解密过程中指导了让-弗朗索瓦·商博良。或者说他介绍了地球温室效应的研究。或者,当女性不做数学时,他支持最早的女数学家之一索菲·热尔曼。
Few know, for example, that Joseph Fourier almost lost his head in the French Revolution. Or that Napoleon Bonaparte took him to Egypt on the expedition that discovered the Rosetta Stone. Or that he mentored Jean-François Champollion in its decryption. Or that he introduced the study of Earth’s greenhouse effect. Or that he championed one of the earliest women mathematicians, Sophie Germain, when women just didn’t do math.
正如我在引言中提到的,技术突破经常发生,当以下因素在某种程度上存在时:一个伟大的科学思想,某种混乱,以及一两个暴君。
Technological breakthroughs often occur, as I mentioned in the introduction, when the following ingredients are present in some degree: a great scientific idea, chaos of some sort, and a tyrant or two.
傅立叶在动荡的生活中提出了他的伟大想法。他的决定性暴君是拿破仑,他先提拔了他,然后放逐了他。这次升职让傅立叶有动力去思考他的好主意。Exile 给了他解决问题的空间。
Fourier formulated his great idea in a life of turmoil. His defining tyrant was Napoleon, who first promoted him and then exiled him. The promotion gave Fourier the incentive to think about his great idea. Exile gave him the space to work it out.
他的想法一开始是一个单一的科学种子,一个热理论。然后,它在随后的两个世纪中发展成为数千种技术解决方案。这是像素背后的中心思想。
His idea began as a single scientific seed, as a theory of heat. Then it blossomed during the subsequent two centuries into thousands of technological solutions. It’s the central idea behind the pixel.
傅立叶的伟大想法是:世界就是音乐。都是海浪。
Fourier’s great idea was this: The world is music. It’s all waves.
这种音乐洞察力导致了广播,这也许不足为奇。但它也导致了电视。事实上,在它的众多后代中,全是媒体技术——所有最近在大数字融合期间合并的各种媒体。简而言之,傅里叶的伟大思想风靡世界,催生了现代媒体的所有雷电。
This musical insight led to radio, which isn’t a surprise perhaps. But it also led to television. In fact, among its many progeny are all media technologies—all the varied media that recently coalesced during the Great Digital Convergence. In short, Fourier’s great idea stormed the world and fostered all the thunder and lightning of modern media.
但它比这更普遍,远远超出媒体。几乎没有一个科学和技术分支不受它的影响——电学和磁学、光学、X 射线衍射、概率论、地震分析和量子力学。名单还在继续。毫不夸张地说,傅立叶改变了我们对世界的理解。
But it’s even more pervasive than that, reaching far beyond just media. Hardly a branch of science and technology is untouched by it—electricity and magnetism, optics, X-ray diffraction, probability theory, earthquake analysis, and quantum mechanics. The list goes on and on. It’s no exaggeration to say that Fourier changed how we understand the world.
无论您坐在文化过道的哪一边,您都可能认识艾萨克·牛顿和阿尔伯特·爱因斯坦。世界在他们的有生之年认可了牛顿的万有引力理论和爱因斯坦的相对论。但在过去的 200 年里,只有物理学家和工程师才能让傅里叶的火焰保持活力。他们知道傅立叶是家长,并据此庆祝他。他们的工作,在许多不同的领域,展示了傅里叶波浪思想的伟大和普遍性。
Regardless of which side of the culture aisle you sit on, you probably know Isaac Newton and Albert Einstein. The world recognized Newton’s theory of gravitation and Einstein’s theory of relativity in their lifetimes. But for the past 200 years, only physicists and engineers have kept Fourier’s flame alive. They knew that Fourier was paterfamilias and celebrated him accordingly. And their work, in many diverse fields, demonstrated the greatness and universality of Fourier’s wave idea.
傅立叶本人只迈出了关键的第一步。他是第一个以数学方式提出这个想法并通过实验对其进行测试的人。尽管他提出了几乎所有科学领域都会产生数千种解决方案的解释,但他自己只培育了第一朵花,即他对固体热流的解决方案。
Fourier himself took only the crucial first step. He was the first to formulate the idea mathematically and test it experimentally. Although he planted the explanation from which thousands of solutions would grow in nearly all fields of science, he himself cultivated only the first flower, his solution to heat flow in solids.
这种不浪漫的专业是他延迟认可的一个很好的理由。他因其关于热如何流动的理论而成为“科学院著名的傅立叶”。它不像爱因斯坦关于引力是时空扭曲的概念那样充满诗意。
That unromantic specialty is a good reason for his delayed recognition. He was the “celebrated Fourier at the Academy of Science” for his theory of how heat flows. It doesn’t ring of poetry like Einstein’s concept that gravity is a warp in spacetime.
然而,傅立叶的伟大想法对于现代经验来说远比爱因斯坦的更重要。以它的音乐形式来说,它就像时空扭曲一样可爱——而且更直观。它没有理由隐藏在它通常难以理解的数学外衣后面。
Yet Fourier’s great idea is far more fundamental to the modern experience than Einstein’s. Stated in its musical form, it’s as lovely as spacetime warps—and more intuitive. There’s no reason for it to remain hidden behind its usual cloak of impenetrable mathematics.
是时候扭转雨果的评价,庆祝这个人和他的好主意了。无处不在的现代数字光技术是最终给予傅立叶应得的正确工具。
It’s high time to reverse Hugo’s assessment and celebrate both the man and his great idea. The ubiquitous modern technology of Digital Light is the right vehicle to finally give Fourier his due.
让·约瑟夫·傅立叶于 1768 年 3 月 21 日出生于巴黎东南约一百英里的古老省会欧塞尔。十年之内,他的父母死了,留下他和他的十四个兄弟姐妹成为孤儿。革命风起云涌。这个新的美国国家只有一岁,本杰明富兰克林在巴黎用他的浣熊皮帽和调情的方式吸引了他们。3
Jean Joseph Fourier was born on March 21, 1768, in Auxerre, an ancient provincial capital about a hundred miles southeast of Paris. Within ten years both his parents were dead, leaving him and his fourteen siblings orphaned. Revolution was in the air. The new American country was only a year old and Benjamin Franklin was charming them in Paris with his coonskin cap and flirtatious ways.3
孤儿傅立叶有一些特别之处,欧塞尔的好人确保这个有才华的孩子受到教育。他们把他安置在一所由约瑟夫·帕莱(Joseph Pallais)经营的学校里,帕莱以曾是让-雅克·卢梭的音乐老师而闻名。唉,没有证据表明发现世界音乐的人本身就是音乐家。
There was something special about the orphan Fourier, and the good people of Auxerre made sure that the talented child was educated. They placed him in a school run by Joseph Pallais, who was noted for having been Jean-Jacques Rousseau’s music teacher. Alas, there’s no evidence that the man who discovered the music of the world was musical himself.
傅立叶随后在他的家乡欧塞尔参加了皇家军事学院(法国全境有 11 个这样的学院分支机构)。当地支持者再次帮助资助了他。这些军校一致强调科学和数学,傅立叶尤其偏爱数学——疯狂地如此。
Fourier then attended the École royale militaire in his hometown Auxerre (there were 11 such branches of the école in all of France). Local supporters helped subsidize him again. These military schools uniformly stressed science and mathematics, and Fourier especially took to math—maniacally so.
13 岁时,他收集烛台点燃一个大“橱柜”,并将他的数学研究延伸到凌晨,直到“熄灯”。令人窒息的——而且肯定是冰冷的——橱柜损害了他余生的健康。也许那个橱柜首先让他对热产生了特殊的兴趣。
At 13 he collected candle stubs to light a large “cupboard” and extend his study of mathematics into the wee hours, past “lights out.” The suffocating—and surely cold—cupboard compromised his health for the rest of his life. Perhaps that cupboard first gave him his peculiar interest in heat.
但橱柜里的烛光课外训练很快就得到了回报。他获得了数学学生奖。这项技能开启了他的科学生涯,并最终使他不朽。然而,他还获得了修辞方面的一等奖,使他的政治生活成为可能,并直接导致他早日与死亡擦肩而过。在数学技能有机会发展之前,他的口语技巧几乎要了他的命。
But the candlelit extracurricular training in the cupboard soon paid off. He won a student prize in math. This skill launched his scientific career and ultimately made him immortal. And yet he also won a first prize in rhetoric, enabling his political life and leading directly to an early brush with mortality. His speaking skill almost killed him before the mathematical skill had a chance to develop.
危险一开始并不明显。进一步的军校训练可能直接将他带入了军队,但他肯定不是军人类型。一方面,他病得很重,而且是个数学怪胎。于是,在皇家军事学院完成学业后,他进入了教堂。他成为欧塞尔修道院的一名新手,并在那里向其他新手教授数学。大约在这个时候,他将自己的名字神圣化给了让·巴蒂斯特·约瑟夫·傅立叶,这是他此后使用的形式。
The danger wasn’t obvious at first. Further military school training might have led him directly to the army, but he certainly wasn’t the military type. He was sickly for one thing, and a math geek. So, after completing his studies at the École royale militaire, he entered the church. He became a novice at an abbey in Auxerre and taught mathematics to the other novices there. He sanctified his name at about this time to Jean Baptiste Joseph Fourier, the form that he used thereafter.
傅立叶在法国大革命前夕消失在修道院中。他幸存下来的几封信表明他隐约意识到这一点,但无动于衷。他更担心自己的名声和代数论文的状况,而不是法国的状况。“昨天是我的 21 岁生日。在那个年纪,”他在 1789 年 3 月的一封信中苦恼地说,“牛顿已经获得了许多不朽的主张。”
Fourier disappeared into the cloisters on the very eve of the French Revolution. The few letters of his that survive show he was vaguely aware of it, but indifferent. He was more worried about his fame and the state of an algebra paper than the state of France. “Yesterday was my 21st birthday. At that age,” he anguished in a March 1789 letter, “Newton had acquired many claims to immortality.”
9 月,他又写了一封信,哀叹代数论文的命运。在这两封信之间,革命已经开始。但 9 月的信中没有提到那些动荡的事件。
In September he wrote another letter, bemoaning the fate of his algebra paper. In the time between the two letters, the Revolution had begun. But the September letter said nothing about those tumultuous events.
然而,傅里叶的私人世界在那之后确实开始发生变化。他于 12 月在巴黎科学院提交了一篇关于“代数方程”的论文——大概是让他非常担心的那篇论文。
Nevertheless, Fourier’s private world did begin to change after that. He presented a paper on “algebraic equations”—presumably the paper that had worried him so much—before the Academy of Science in Paris in December.
他没有宣誓就离开了修道院。无论如何,革命政府很快就镇压了宗教秩序。
And he departed the abbey without taking his vows. The revolutionary government soon suppressed religious orders anyway.
然而,傅立叶在接下来的三年里并不是革命者。他改为在欧塞尔教数学。特别是,他没有签署欧塞尔革命人民协会向巴黎国民公会要求审判国王路易十六的请愿书。
Yet Fourier wasn’t a revolutionary for the next three long years. He taught math in Auxerre instead. In particular, he didn’t sign the petition from the revolutionary Popular Society of Auxerre to the National Convention in Paris demanding the trial of King Louis XVI.
但在 1793 年初,就在国王被斩首一个月后,我们开始听到公民傅立叶的来信。
But in early 1793, just a month after the king’s beheading, we begin to hear from Citizen Fourier.
在那个黎明活着是幸福的,
Bliss was it in that dawn to be alive,
但年轻就是天堂。
But to be young was very heaven.
——威廉·华兹华斯,前奏曲4
—William Wordsworth, The Prelude4
众所周知,法国大革命的黎明令华兹华斯着迷,而年轻的傅立叶在他迟来的拥抱它后,在同一个天堂中欢欣鼓舞。他的话比诗人的更笨拙:“可以设想在我们中间建立一个不受国王和教士影响的自由政府的崇高希望。” 但他同样充满热情:“我很容易就迷上了这项事业,在我看来,这是任何国家所从事的最伟大、最美丽的事业。” 5
The dawn of the French Revolution famously enthralled Wordsworth, and young Fourier exulted in that very same heaven once he belatedly embraced it. His words were clumsier than the poet’s: “It was possible to conceive the sublime hope of establishing among us a free government exempt from kings and priests.” But he was just as passionate: “I readily became enamored of this cause, in my opinion the greatest and the most beautiful which any nation has ever undertaken.”5
傅立叶不必从这些情绪跳到政治本身。1793 年 2 月,他在欧塞尔的革命公社发表了激动人心的首次演讲。他有一个为共和国军队招募当地新兵的计划。欧塞尔大众社会给他留下了深刻的印象,采纳了他的计划并邀请他加入。恐怖统治现在已经全面展开——最终有一万多人被斩首,被怀疑是国家的敌人。他明智地接受了“邀请”。
Fourier didn’t have to leap far from these sentiments to politics itself. He gave a rousing debut speech in February 1793 to the revolutionary commune in Auxerre. He had a plan for raising local recruits for the Army of the Republic. Favorably impressed, the Popular Society of Auxerre adopted his plan and invited him to join. The Reign of Terror was now in full play—with ultimately over ten thousand beheadings of suspected enemies of the state. He wisely accepted the “invitation.”
但天真的傅立叶——最近的新手——立刻就犯了错误,他的时机已经很糟糕了。他那受过修辞训练的舌头让他陷入了严重的麻烦。他不明智地用它来保护奥尔良的三个公民。不明智,因为他们已经在罗伯斯庇尔的敌人名单上,而罗伯斯庇尔是恐怖分子的“沙皇”。
But naive Fourier—the recent novice—immediately blundered, and his timing was about as bad as could be. That rhetoric-trained tongue of his got him into serious trouble. Unwisely he used it to defend three citizens of Orléans. Unwise because they were already on Robespierre’s enemies list, and Robespierre was the Terror’s “tsar.”
革命者迅速解除了傅立叶在欧塞尔以外的所有职责。由于无法进一步推进共和国,他苦苦挣扎,跋涉到巴黎,亲自会见罗伯斯庇尔为他的案子辩护。这种大胆的策略适得其反。他对奥尔良囚犯的支持使他在罗伯斯庇尔的敌人短名单上占有一席之地。由于革命的扭曲逻辑,尽管欧塞尔一直支持的公民提出抗议,但傅里叶所倡导的恐怖行动还是在 1794 年 7 月 17 日将他送进了监狱。这实际上是死刑。
The revolutionaries promptly relieved Fourier of all duties outside Auxerre. Miserable at not being able to further the Republic, he trekked to Paris and met with Robespierre himself to plead his case. This bold tactic seriously backfired. His support for the Orléans prisoners had earned him a spot on Robespierre’s short list of enemies. With the contorted logic of the Revolution, and despite protests from the always supportive citizens of Auxerre, the very Terror that Fourier had championed threw him into jail on July 17, 1794. It was effectively a death sentence.
“我经历了各种程度的迫害和不幸,”他说。“我的对手没有一个比这更危险,我是我们同胞中唯一被判处死刑的人。” 6
“I experienced every degree of persecution and misfortune,” he said. “None of my adversaries have run more dangers, and I am the only one of our compatriots who was condemned to death.”6
几天之内,下一站将是巴黎的革命法庭和断头台上的橡皮图章。他有理由感到害怕。他不可能知道仅仅十天之后——7 月 27 日,或者 9 日,法国大革命时间——罗伯斯庇尔会重重摔倒。那个叫人头倒地,从来没有受够——再次引导华兹华斯的人——亲自尝过断头台。幸运的是科学的未来,特别是像素,罗伯斯庇尔的脑袋拯救了傅里叶的脑袋。7
The next stop, within days, would’ve been the Revolutionary Tribunal in Paris and a rubberstamp to the guillotine. He was justifiably terrified. He couldn’t have known that just ten days later—July 27, or 9 Thermidor, French Revolutionary Time—Robespierre would fall hard. He who bade heads fall and never had enough—to channel Wordsworth again—tasted the guillotine himself. Lucky for the future of science, and the pixel in particular, Robespierre’s head saved Fourier’s.7
1789 年的那篇代数论文——将革命从傅立叶的脑海中推开的那篇论文——是这位伟大科学家的第一次公开瞥见吗?它是否包含他伟大想法的关键?正如数学家所说,这无疑提高了他的数学技能并提高了他的“数学成熟度”。但我们不知道里面有什么。
Was that algebra paper of 1789—the one that pushed the Revolution from Fourier’s mind—the first public glimpse of the great scientist? Did it contain keys to his great idea? Surely it sharpened his mathematical skills and increased his “mathematical maturity,” as mathematicians say. But we don’t know what was in it.
我们不知道,特别是傅立叶何时开始使用波,这是他伟大创意中的基本形状。但到了 1807 年,他已经公开了它。这是你通过展开一个完美的圆圈得到的形状,所以它是一种革命性的形式。它非常简单。像素具有崇高的传统。
We don’t know, in particular, when Fourier first began to use the wave, the fundamental shape in his great idea. But by 1807 he had gone public with it. It’s the shape you get by unwinding a perfect circle, so it’s a revolutionary form. And it’s elegantly simple. The pixel has a noble heritage.
要获得傅立叶波的图像,请从一个圆圈开始(图 1.1)。老式的模拟钟面可以达到目的。秒针的尖端围绕着那个圆圈稳定地移动,从一个分钟标记到下一个标记,一秒一秒。下图显示了三秒后的上表盘。
To get a picture of Fourier’s wave, start with a circle (figure 1.1). An old-fashioned analog clock face serves the purpose. The tip of its second hand moves steadily around that circle, from a single minute mark to the next one, second by second. The lower picture shows the upper clockface, three seconds later.
较大的红点描绘了波浪。动画电影在这里会特别有启发性,但如果没有这一点,请将时间的流逝想象为向右移动,如时间箭头所示。时钟边缘的每个刻度线都有一个沿着箭头的刻度线。想象一下,红点总是被一条拉紧的水平带拴在秒针的尖端。随着时间的推移,该带向右延长,那个红点所描绘的路径就是波。
The larger, red dot traces out the wave. An animated movie would be especially instructive here, but short of that, imagine the passage of time as movement to the right, as shown by time’s arrow. There’s a tick mark along the arrow for each tick mark along the edge of the clock. Imagine that the red dot is always tethered to the tip of the second hand by a taut horizontal band. The band lengthens toward the right as time passes, and the path traced by that red dot is the wave.
这里的重点是,简单地说,波浪看起来像什么,直观地说,它与圆密切相关。这种亲密关系的细节不如直觉重要,但更多的细节可能有助于更难忘地记录直觉。
The important points here are, simply, what the wave looks like and, intuitively, that it’s intimately related to the circle. The details of that intimate relation aren’t as important as the intuition, but a few more details might help to register the intuition more memorably.
考虑时钟的中心线——连接 9 点钟和 3 点钟的线。红点始终标记秒针尖端在该中心线上方或下方的当前高度。在为上图选择的(纯粹是任意的)时刻,自记录的第一个位置以来,红点已经追踪了 23 个位置,因为从那时起已经过去了 23 秒。在下一个滴答声中,红点将向右移动到波浪上的下一个点。之后再打两个刻度,得到下图。因此,当秒针在时钟上一次又一次地滴答作响时,它的尖端——实际上是附着在尖端的红点——描绘出所示的波浪形路径,上下,上下。. .
Consider the centerline of the clock—the line that connects 9 o’clock to 3 o’clock. The red dot always marks the current height of the tip of the second hand above or below that centerline. At the (purely arbitrary) moment chosen for the upper illustration, the red dot has traced through twenty-three positions since the first position recorded, because twenty-three seconds have elapsed since then. During the next tick the red dot will move right to the next dot on the wave. And two more ticks after that yields the lower illustration. So as the second hand ticks its way around the clock, again and again, its tip—actually the red dot attached to the tip—traces out the wavy path shown, up and down, up and down . . .
图 1.1
Figure 1.1
秒针每分钟转一圈,所以红点所描绘的波浪永远向右移动。它也永远向左延伸。图中的波浪似乎在中午后一分钟开始——另一个纯粹的任意选择——但显然时钟一直在滴答作响,直到你可能想追踪的时间。
The second hand makes one revolution after another every minute, so the wave traced by the red dot heads to the right forever. It extends to the left forever too. The wave in the figure appears to start one minute after noon—another purely arbitrary choice—but obviously the clock’s been ticking off the seconds as far back as you might care to trace.
图中的波是傅里叶波之一。他没有发明它们,但他深刻地利用了它们。这些是他音乐的组成部分。数学家将这种特别可爱的圆形波称为正弦波。由于这是我们需要的唯一一种 wave,我通常将其简称为wave。
The wave in the picture is one of Fourier’s waves. He didn’t invent them, but he made profound use of them. These are the components of his music. Mathematicians call this particularly lovely circle-made wave a sine wave. Since this is the only kind of wave we need, I’ll usually refer to it simply as a wave.
关于傅立叶波的一切都是简单、美丽、优美、完美的。科学家和工程师对傅立叶的热流解以及他伟大的音乐理念有一个正式的术语。他们将其描述为谐波。
Everything about Fourier’s wave is simple, beautiful, graceful, perfect. Scientists and engineers have a formal term for Fourier’s solution for heat flow, and for his great musical idea generally. They describe it as harmonic.
那个波浪形无处不在,并且一直伴随着你。从您家中或办公室的任何插座流出的电流电压都是波。由于其波动性,它被称为交流电,AC。它通常源于转子的转动,例如大坝后面的水。转子的圆圈展开成交流电或波电流。电机使转子向右转动。波形电流进入电机并将能量卷回圆形机械运动。电风扇吸进一波,又放出一个圆圈。
That wave shape is everywhere, and with you all the time. The voltage of the electrical current coming out of any outlet in your home or office is a wave. It’s called alternating current, AC, because of its wave nature. It often originates with the turning of a rotor, by water behind a dam for example. The circle of the rotor unfurls into AC, or wave, current. A motor turns that rotor right around. The wave-shaped current enters a motor and furls the energy back into circular mechanical motion. An electric fan takes a wave in and puts a circle out.
另一个熟悉的正弦波来自媒体世界。这是您最喜欢的 FM 广播电台的电话号码。我在旧金山地区的 KCSM 爵士乐是 91.1。数字 91.1 正式指定了当局分配给 KCSM 的波,仅用于广播。它描述了电台用来将音乐传递给听众的电磁波。
Another familiar sine wave comes from the media world. It’s the call number of your favorite FM radio station. Mine is 91.1 for KCSM jazz in the San Francisco area. The number 91.1 officially designates the wave assigned by authorities to KCSM for its sole use in broadcasting. It describes the electromagnetic wave that station uses to carry its music to listeners.
尽管所有的傅立叶波都具有相同的形状,但它们在两个方面有所不同——它们摆动的速度(称为频率)和波峰的高度(振幅)。在时钟图中,秒针波峰的频率是多少?它每分钟出现一次波峰,这就是它的自然频率——每分钟一个完整的波周期。循环是完全正确的词。当秒针绕钟面转一圈时,附在其尖端的红点会及时描绘出它的一个完整周期。绕圆周一圈产生一个波周期。
Although all Fourier’s waves have the same shape, they differ in two ways—how fast they wiggle (called frequency) and how high they crest (amplitude). In the clock figure, how frequently does the second-hand wave crest? It crests once every minute, so that’s its natural frequency—one complete wave cycle per minute. Cycle is exactly the right word. As the second hand cycles around the clock face once, the red dot attached to its tip paints out one complete cycle of its wave in time. One revolution around the circle yields one wave cycle.
时钟的分针尖端勾勒出一模一样的平滑曲线,但速度更慢。分针每小时只有一次波峰。它的频率是每小时一个周期,比秒针慢六十倍。第三个是时针波。它具有三者中最低的频率,每半天一个周期。
The tip of the clock’s minute hand traces out a curve of exactly the same smooth shape, but more slowly. The minute-hand wave crests only once per hour. Its frequency is one cycle per hour, sixty times slower than the second hand. A third one is the hour-hand wave. It has the lowest frequency of the three, one cycle per half day.
您在 KCSM 的电话号码中也遇到过频率;91.1 是该无线电台使用的波的频率(以每秒数百万个周期为单位)。那些无处不在的交流电源插座每个都以每秒 60 个周期的频率发出波(在美国)。
You’ve also met frequency in KCSM’s call number; 91.1 is the frequency (in millions of cycles per second) of the wave used by that radio station. And those ubiquitous AC electrical outlets each deliver a wave with a frequency of 60 cycles per second (in the US).
秒针、分针和时针波的幅度和频率各不相同。我把分针画得比秒针略短,所以分针的波峰略低。由于波峰的最大高度是其振幅,因此分针波的振幅低于秒针波的振幅。时针更短,所以时针波的振幅是三者中最低的。
The second-, minute-, and hour-hand waves differ in amplitude as well as frequency. I drew the minute hand slightly shorter than the second hand, so the wave crests for the minute hand are slightly lower. Since the maximum height of a wave’s crest is its amplitude, the amplitude of the minute-hand wave is lower than that of the second-hand wave. The hour hand is even shorter, so the hour-hand wave’s amplitude is the lowest of the three.
对于傅立叶的目的,波可以有任何频率和任何幅度,只要它是一个正弦波——一个展开的圆。时钟图(图 1.1)产生了三个这样的波,图 1.2 显示了另外三个,它们都具有优美的形状,并且仅在摆动速度和高度(频率和幅度)方面彼此不同。他们都有形状相同,意思是所有三角形都具有相同的形状。三角形只要有三个直边就可以成为三角形,而波浪只要是展开的圆形就可以成为波浪。
For Fourier’s purposes a wave can have any frequency and any amplitude so long as it’s a sine wave—an unfurled circle. The clock figure (figure 1.1) yielded three such waves, and figure 1.2 shows three more, all gracefully shaped and differing from one another only in wiggle speed and height—frequency and amplitude. They all have the same shape, in the sense that all triangles have the same shape. A triangle only has to have three straight sides to be a triangle, and a wave has only to be an unfurled circle to be a wave.
图 1.2
Figure 1.2
注意这张图片中波浪的另一件事:它们周期中的不同点与图片的左边缘对齐。顶部波的波峰与边缘对齐,中间的波谷,以及底部波之间的某个位置。如果你向左或向右滑动任何波,它的频率和幅度不会改变,但它相对于另一个波的位置会改变。这很重要,因为傅立叶让我们将波加在一起。如果波的排列方式不同,您会得到不同的总和。
Notice one other thing about the waves in this picture: different points in their cycles are aligned with the left edge of the picture. The crest of the top wave aligns with the edge, the trough of the middle one, and somewhere in between for the bottom wave. If you slide any wave left or right, its frequency and amplitude don’t change, but its position relative to another wave does. This is important because Fourier has us add waves together. You get different sums if the waves are aligned differently.
我们使用阶段这个词来描述波浪的位置。著名的月相告诉我们月亮在其周期中的位置。它是满月或新月,或者是在满月和新月之间的盈亏。波是循环的,所以它也有一个相位。在图 1.2 中,顶部的波浪在图片的左边缘处于波峰(满月),而中间的波在该处处于低谷(新月)。底部的刚刚开始从它的顶峰减弱到它的谷底。改变波的相位会使整个波向左或向右移动。但请注意,如果您将其移动一个完整的周期,则该波正是原始波。没有办法区分它们。因此,在单个周期中指定一个位置(即相位是什么)就足以指定整个波的位置。对于傅立叶的目的,波可以处于任何相位。
We use the word phase to describe the position of a wave. The moon’s phases famously tell us where the moon is in its cycle. It’s a full moon or a new one, or it’s waxing or waning between full and new. A wave is cyclic, so it has a phase too. In figure 1.2 the top wave is cresting (full moon) at the left edge of the picture, and the middle wave is troughing (new moon) there. The bottom one is just starting to wane from its full crest to its trough. Changing the phase of a wave shifts the entire wave left or right. But notice that if you shift it by an entire cycle, then the wave is exactly the original wave. There’s no way to tell them apart. So, specifying one place in a single cycle—which is what a phase is—is enough to specify the position of an entire wave. For Fourier’s purposes a wave can be in any phase.
傅立叶的伟大想法现在可以一瞥:世界的大量模式——包括我们能看到或听到的一切,还有很多很多——可以准确地描述为这种类型的波的总和,仅此而已. 傅立叶频率是这种描述中波的频率。他们的和谐是世界的音乐。这个想法是如此之大且违反直觉,以至于可能难以理解。所以让我们从音乐本身开始,这是一种熟悉的物理现实,有助于直观地理解傅立叶的深刻思想。
A first glimpse of Fourier’s great idea is now possible: a vast number of patterns of the world—including everything we can see or hear, but also many, many more—can be described exactly as a sum of waves of this type and nothing else. Fourier’s frequencies are the frequencies of the waves in such a description. Their harmony is the music of the world. This idea is so large and counterintuitive that it may be hard to grasp. So let’s start with music itself, a familiar physical reality that helps make intuitive sense of Fourier’s profound idea.
音乐是由——而且只是——不同频率的波组成,当然也称为声波。小提琴上的琴弦以不同的频率振动,钢琴也是如此。与时钟每分钟一个周期的秒针频率相比,钢琴的中间 C 是来自以每秒 262 个周期振动的弦的声波的速度恶魔。单簧管或长笛以特定频率共振,管风琴的每个管子也是如此。抒情的花腔女高音歌唱的频率比中音高,也比男中音或低音高得多。我们说女高音唱得更高而不是频率,指的是我们大脑对音乐的感知,而不是音乐创作的物理原理,但它等同于同一件事。正如我们所说,一个和弦本质上是几个波——比如三个或四个——同时演奏,或者加在一起。合唱团由许多不同音高的声音组成,管弦乐队由许多不同频率的乐器组成,从弦乐贝司到短笛。
Music is composed of—and only of—waves of different frequencies, called sound waves of course. The strings on a violin vibrate at different frequencies, and the same for a piano. Compared to a clock’s pokey second-hand frequency of one cycle per minute, a piano’s middle C is a speed demon of a sound wave from a string vibrating at 262 cycles per second. A clarinet or a flute resonates at certain frequencies, as does each of a pipe organ’s pipes. Lyric coloratura sopranos sing at a higher frequency than do altos and much higher than baritones or basses. We say sopranos sing at a higher pitch rather than frequency, referring to our brain’s perception of the music rather than to the physics of its creation, but it amounts to the same thing. A chord is essentially several waves—say three or four—played simultaneously, or added together, as we say. A choir consists of many voices at different pitches, and an orchestra comprises many instruments at different frequencies, from string basses to piccolos.
音乐的动态,从弱音到强音,反映了音乐中波的幅度。振幅越大,声音越大。巨大的双调音管风琴管——脚踏板最大限度地放在地板上——用全能者的可怕力量震撼着一座大教堂。用力敲击钢琴键或调高收音机的音量以增加波的幅度。毫无疑问,收音机或立体声系统的主要部件是其放大器。
The dynamics of music, from pianissimo to fortissimo, reflect the amplitudes of the waves in the music. The higher the amplitude, the louder the sound. The massive double diapason organ pipe—with the foot pedal maxed to the floor—shakes a cathedral with the awfulness of the Almighty. Strike the piano key harder or turn up the volume on a radio to increase the amplitude of the waves. It’s no surprise that the principal component of a radio or a stereo system is its amplifier.
当您描述音乐时,傅立叶的想法似乎很自然,但当您考虑到所有声音(不仅仅是音乐)都是由音频波组成时,他的想法的力量就会开始显现出来。我们谈论低频隆隆声和高音哨声。众所周知,狗能听到比我们更高的音调。我们对傅立叶大思想最本能的直觉是,任何声音或音乐都是由不同频率的声波组成的,它们全部叠加在一起,被我们的耳朵和大脑解读为斯特拉文斯基仪式、心爱的孩子的声音,甚至是建筑工地的噪音。
Fourier’s idea seems only natural when you’re describing music, but the power of his idea starts coming into focus when you consider that all sound—not just music—is composed of audio waves. We speak of low-frequency rumbles and high-pitched whistles. Dogs famously hear higher pitches than we do. Our most visceral intuition of Fourier’s big idea is that any sound or music is composed of audio waves of different frequencies all added together and interpreted by our ears and brain as a Stravinsky rite, a beloved child’s voice, or even construction site noise.
图 1.3 以不同频率和幅度的傅里叶波形式显示了单词yes(时间向右)。左边的“y”部分包含最低频率和最高振幅——它是单词的重音部分。中间的“e”部分具有最低幅度和混合频率。右边的“s”部分具有较低的幅度和最高的频率——“s”的嘶嘶声。
Figure 1.3 shows the word yes as Fourier waves of various frequencies and amplitudes (time proceeds to the right). The “y” part at the left contains the lowest frequencies and the highest amplitudes—it’s the accented part of the word. The “e” part in the middle has lowest amplitudes and mixed frequencies. The “s” part at the right has lower amplitudes and highest frequencies—the hiss of the “s.”
声波实际上是由——它们的“材料”是——空气的有节奏的压缩,或压力波。考虑一下扬声器系统中的低音扬声器——在响亮的低音音调下您实际上可以感觉到振动的大低音扬声器。很容易想象低音喇叭的快速移动膜在它面前晃动着空气。这种脉动的空气从低音扬声器的表面移动——可以说是被它推动的。更大的声音会在每个更大的振动中引起更高的空气压缩。
Sound waves are actually made of—their “stuff” is—rhythmic compressions of air, or pressure waves. Consider the woofer in your speaker system—the big one that you can actually feel vibrate on loud bass tones. It’s easy to imagine the woofer’s fast-moving membrane shaking the air in front of it. This pulsing air moves from the woofer’s surface—pushed along by it, so to speak. A louder sound causes higher compression of the air in each, larger vibration.
图 1.3
Figure 1.3
我们直接了解这些压力波。想想一个低速骑手在洛杉矶的克伦肖大道上慢慢地驼背,巨大的音箱摇晃着附近的窗玻璃。
We understand these pressure waves directly. Think of a lowrider humping slowly down Crenshaw Boulevard in Los Angeles with its massive boombox shaking nearby windowpanes.
一个非常响亮和低沉的声波将这些高压波转换为物理振动,似乎是地球本身的振动。但实际上,那些惊天动地的波浪,与进入我们耳朵,使我们的耳膜随着低音喇叭、音箱或双深管风琴一起振动的波浪完全一样。然后一个聪明的小骨头系统——令人愉快的名字是锤子、铁砧和马镫——将这些振动传递到内耳,在那里成千上万的微小毛细胞对不同的频率做出反应。它们将频率信息直接传递到大脑。
A very loud and low sound wave converts those high-pressure waves into physical vibrations, seemingly of the earth itself. But actually, those earth-shaking waves are exactly the same as the waves that enter our ears and make our eardrums vibrate in unison with the woofer, boombox, or double deep organ pipe. Then a clever system of little bones—the delightfully named hammer, anvil, and stirrup—pass these vibrations to the inner ear where thousands of tiny hair cells respond to the different frequencies. They pass the frequency information directly into the brain.
正常的年轻人耳可以听到每秒 20 次循环到每秒 2 万次循环之间的所有频率。现代用法将“每秒周期数”缩短为“赫兹”(缩写为 Hz),但我会坚持使用较长的短语以保持其直观性。还有人耳无法听到的其他声音,比如狗能听到但我们听不到的超声波哨子。
The normal young human ear can hear all frequencies between 20 cycles per second and 20 thousand cycles per second. Modern usage shortens “cycles per second” to “Hertz” (abbreviated Hz), but I’ll stick with the longer phrase to preserve its intuitiveness. There are other sounds outside the human ear’s capability, like the ultrasonic whistle the dog can hear but we cannot.
图 1.4
Figure 1.4
但是视觉中的波是什么——导致像素的波?视觉振动的频率是多少?
But what are the waves in vision—the ones that lead to pixels? At what frequencies does vision vibrate?
傅立叶出生仅一年多后,Nabolione Buonaparte 就出生在科西嘉岛,科西嘉岛与巴黎和欧塞尔接壤,但位于法国大陆东南约一百英里处(图 1.4)。科西嘉岛在这两个男孩出生的间隙已经成为法国人,所以波拿巴只是勉强是法国人。他的名字在他 20 多岁时才流行起来,当时他将其归结为拿破仑·波拿巴。8
Just over a year after Fourier’s birth, Nabolione Buonaparte was born on Corsica, an island in line with Paris and Auxerre but about a hundred miles southeast of mainland France (figure 1.4). Corsica had become French in the interval between the births of the two boys, so Buonaparte was just barely French. His name caught up only later, in his twenties, when he Frankified it to Napoleon Bonaparte.8
波拿巴参加了布赖耶纳城堡的皇家军事学院。这与傅立叶就读的学校系统相同,他在大约 60 英里外的欧塞尔就读。因此,波拿巴接受了与傅立叶基本相同的科学和数学训练。这足以让波拿巴对数学产生持久的兴趣。他他一生都与数学家互动,而不仅仅是傅立叶。甚至还有一个几何定理,拿破仑定理,以他的名字命名。
Bonaparte attended the École royale militaire in Brienne-le-Château. This was in the same system of schools attended by Fourier, who was at the one in Auxerre about 60 miles away. So Bonaparte received essentially the same training in science and mathematics as Fourier. It was enough to give Bonaparte an abiding interest in math. He was to interact with mathematicians all his life, and not just Fourier. There’s even a geometry theorem, Napoleon’s Theorem, named for him.
波拿巴在巴黎的精英军事学院继续深造,深入军事机构。他在那里的训练细节与我们无关,但他的期末考试却很重要。他的考官形容波拿巴“对数学有透彻的了解”。他是皮埃尔-西蒙·拉普拉斯,有时被称为法国的艾萨克·牛顿。
Bonaparte moved deeper into the military establishment with further schooling at the elite École militaire in Paris. Details of his training there don’t concern us, but his final exams do. His examiner described Bonaparte as having “a thorough knowledge of mathematics.” He was Pierre-Simon Laplace, sometimes called France’s Isaac Newton.
波拿巴后来让拉普拉斯成为法国参议院议员,此举令当代美国人感到难以置信。一位著名的数学家和物理学家担任参议员!
In a move that boggles the mind of a contemporary American, Bonaparte was later to make Laplace a member of the French Senate. A noted mathematician and physicist as senator!
罗伯斯庇尔倒台后,革命的法国政府不仅将傅立叶从监狱中释放出来,还授予他在新成立的巴黎综合理工学院(现为法国麻省理工学院和加州理工学院合并)的教授职位。最后,他在巴黎自称数学,并遇到了它的领军人物,比如拉普拉斯。这使他很好地吸引了雄心勃勃的波拿巴的注意,他正在寻找“专家”陪伴他去埃及旅行。并在身体上和政治上获得更多热量。
After Robespierre’s fall, the revolutionary French government not only freed Fourier from jail but awarded him a plum job as professor at the newly formed École polytechnique in Paris—now France’s MIT and Caltech combined. Finally, he was professing mathematics in Paris and meeting its leading lights, such as Laplace. This positioned him nicely to catch the eye of the ambitious Bonaparte who was looking for “savants” to accompany him on a trip to Egypt. And to catch a lot more heat—physically and politically.
波拿巴最近在与奥地利人的战斗中征服了意大利,并以英雄的身份回到了巴黎。有了这样的赞誉和一支军队,法国政府正确地将他视为威胁。看到他(更不用说他的军队)于 1798 年启程前往埃及并进行新的征服,他们并没有不高兴。这次离开最终使傅立叶和波拿巴走到了一起。
Bonaparte had recently conquered Italy in a fight against the Austrians and returned to Paris a hero. With such acclaim, and an army in tow, the French government rightly perceived him as a threat. They were not unhappy to see him (never mind his army) set off in 1798 for Egypt and a fresh conquest. This departure finally brought Fourier and Bonaparte together.
为了效仿他的英雄亚历山大大帝,波拿巴率领一队法国知识分子(他的学者)参加了入侵,其中包括来自巴黎综合理工学院的年轻教授傅立叶。同样,与我们时代的对比是惊人的。想象一下,在第一架飞往伊拉克或阿富汗的飞机上,一支由领先的数学家和考古学家组成的团队。
In emulation of his hero Alexander the Great, Bonaparte took a team of French intellectuals (his savants) on the invasion, including the young professor Fourier from the École polytechnique. Again, the contrast to our times is striking. Imagine a team of leading mathematicians and archaeologists on the first plane into Iraq or Afghanistan.
埃及探险队在军事上失败了,但在智力上却取得了飞速的成功。罗塞塔石碑的发现是一个著名的高点。埃及学就是从这些开始的。波拿巴本人在那里创立了埃及研究所并担任副校长。傅立叶很快就成为了它的常任秘书。在接下来的十年左右的时间里,他为埃及运动的持久学术声誉做出了贡献,他撰写了大量(20 多卷) 《埃及描述》的导言——对波拿巴过度赞扬。波拿巴甚至在这里和那里进行了一些编辑,以试图从军事失败中夺取知识分子的胜利。
The Egyptian expedition was a military flop, but a soaring intellectual success. The discovery of the Rosetta Stone was a famous high point. Egyptology sprang from those beginnings. Bonaparte himself founded the Institut d’Egypte while there and was its vice president. Fourier soon became its permanent secretary. He contributed to the lasting scholarly reputation of the Egyptian campaign by writing, over the next decade or so, the introduction to the massive (twenty-plus volumes) Déscription de l’Egypte—with overly fulsome praise for Bonaparte. Bonaparte even dropped in a few edits here and there in an effort to snatch an intellectual victory from the jaws of military defeat.
法国在亚历山大港、开罗和大金字塔取得了几次初步胜利后,纳尔逊海军上将和英国人在埃及港口摧毁了法国舰队。尽管英国控制了地中海,但波拿巴在埃及呆了一年多一点后,还是设法偷偷穿过它到达了法国,几乎把其他所有人——以及许多未完成的军事任务——都抛在了后面。
After several initial French victories—at Alexandria, Cairo, and the Great Pyramids—Admiral Nelson and the British destroyed the French fleet at harbor in Egypt. Despite British control of the Mediterranean, Bonaparte managed to sneak across it to France, after a little more than a year in Egypt, leaving nearly everybody else—and much unfinished military business—behind.
他的动机是尝试控制法国——他当然做到了。就在 18 世纪末,他成为了新政府的第一任执政官——这是他成为皇帝的第一步。
His motivation was to take a shot at controlling France—which of course he accomplished. He made himself First Consul of a new government just before the end of the eighteenth century—the first step on his march to become emperor.
当他的学者试图跟随他回家时,他们就没那么幸运了。英国人允许他们通过海上封锁,但保留了罗塞塔石碑。它仍然是大英博物馆中参观人数众多的珍品。
When his savants attempted to follow him home, they weren’t so lucky. The British allowed them through the naval blockade but kept the Rosetta Stone. It’s still a highly visited treasure in the British Museum.
波拿巴仓促而投机取巧地离开埃及,让让·巴蒂斯特·克莱伯 (Jean Baptiste Kléber) 陷入了军事混乱。波拿巴任命他为埃及军队的将军,并通过邮件将此事告知他,因此他无法拒绝。波拿巴用这个伎俩赢得了克莱贝尔的蔑视,后者被留下来收拾残局。
Bonaparte’s hasty and opportunistic departure from Egypt left Jean Baptiste Kléber in the lurch with a military mess. Bonaparte made him general in charge of the army in Egypt, informing him of this via mail so he couldn’t refuse. With this trick Bonaparte gained the scorn of Kléber, who was left to mop up.
现在傅立叶犯了他的第二个重大政治错误。他变得与这位不幸的将军过于亲近了。Kléber 任命他为埃及的分局局长。然后,当一名学生在开罗暗杀克莱伯时,傅立叶为这位将军发表了悼词。那个有天赋但很麻烦的舌头再次摇摆不定:首先他得罪了罗伯斯庇尔,现在得罪了波拿巴。
Now Fourier made his second major political mistake. He became too closely identified with the unhappy general. Kléber made him a bureau director in Egypt. Then when a student assassinated Kléber in Cairo, Fourier gave the general’s eulogy. That gifted, but troublesome, tongue was wagging again: first he’d offended Robespierre, now Bonaparte.
波拿巴显然不希望傅立叶在首都提出克莱伯的观点。他不想让法国知道他在埃及战役中不那么高尚的军事细节。傅立叶曾希望,在埃及之后,他可以在巴黎恢复他的声望地位,成为知识分子行动的中心。相反,波拿巴将直言不讳的傅立叶流放到格勒诺布尔。
Bonaparte clearly didn’t want Fourier propounding Kléber’s views in the capital. He didn’t want France to know the less-than-noble military details of his Egyptian campaign. Fourier had hoped that after Egypt he could resume his prestigious position in Paris, at the center of the intellectual action. Instead, Bonaparte exiled the outspoken Fourier to Grenoble.
但在这样做时,他委婉地选择了他的话,“要求”傅立叶担任伊泽尔省的省长,该省由格勒诺布尔管辖。换句话说,波拿巴“要求”他成为一个比巴黎更靠近科西嘉的省的省长(省长)——距离行动还有很长的路要走。
But in doing so, he chose his words euphemistically, “requesting” that Fourier take the job as prefect of the Isère department, governed from Grenoble. In other words, Bonaparte “asked” him to become the provincial governor (prefect) of a province that was closer to Corsica than Paris—a long way from the action.
傅立叶接受了。波拿巴现在是法国最有权势的人。然而,这是流放,这就是傅立叶的看法。在埃及之后的十年里,他是法国唯一一位不在巴黎的领先数学家和物理学家。
Fourier accepted. Bonaparte was now the most powerful man in France. It was exile, however, and that’s how Fourier perceived it. He was the only leading mathematician and physicist in France who wasn’t in Paris in the decade after Egypt.
您可能很乐意将您听到的内容视为波的总和,但您不会以这种方式思考您看到的内容。那么,下一步将需要一些时间更多解释。傅立叶的伟大想法是视觉世界,就像音乐一样,是由波的总和构成的。但就视觉而言,波是空间波。它们是二维的。看到它们需要一点练习,但是一旦你养成了寻找它们的习惯,这一点也不难。我们会习惯于看到它们,然后实现傅里叶所做的飞跃。
You are probably comfortable thinking about what you hear as a sum of waves, but you don’t think about what you see that way. This next step, then, is going to take a bit more explaining. Fourier’s great idea is that the visual world, just like music, is made of a summation of waves. But in the case of vision, the waves are space waves. They’re two-dimensional. It takes a little practice to see them, but once you get in the habit of looking for them, it’s not hard at all. We’ll get used to seeing them, and then make the leap that Fourier did.
时钟图中的二手波(图 1.1)实际上描绘了一种空间波。它代表了一个沿着时间箭头前进的时间波,但我实际上画的是一个左右延伸的空间波。傅立叶的伟大思想涵盖了空间和时间。波的种类取决于物理过程。如果它通过时间传播,如声音、光或二手波,那么这些波就是时间波,频率就是每秒的周期数。图片_二手波的频率是空间波,它的频率以每英寸的周期数表示,如图所示,大约每 3 英寸一个周期。如果我要以相同的比例绘制分针波,它的频率将减少 60 倍,或大约每 180 英寸一个周期。时针空间波大约每 2,160 英寸有一个周期,比分针波少十二倍。
The second-hand wave in the clock diagram (figure 1.1) actually depicts a space wave. It represents a time wave proceeding along time’s arrow, but what I’ve actually drawn is a space wave extending left and right. Fourier’s great idea covers both space and time. The kind of wave depends on the physical process. If it proceeds through time, like sound, light, or the second-hand wave, then the waves are time waves and the frequencies are cycles per second. The picture of the second-hand wave is a space wave, and its frequency is expressed in cycles per inch, roughly one cycle per 3 inches as drawn. If I were to draw a picture of the minute-hand wave at the same scale, its frequency would be sixty times less, or roughly one cycle per 180 inches. The hour-hand space wave would have roughly one cycle per 2,160 inches, twelve times less than the minute-hand wave.
我称之为视觉波的波不要与光波混淆。光波是一种激发我们眼睛的视杆和视锥细胞的机制,以便我们可以看到。它是一种以极高频率随时间变化的波,例如每秒 500 万亿个周期。所以光波是观看的手段,但视觉波是我们所看到的。光波随时间变化,视觉波随空间变化。
The waves I’m calling vision waves are not to be confused with light waves. A light wave is a mechanism for exciting the rods and cones of our eyes so that we can see. It’s a wave that varies in time at extremely high frequencies, such as 500 trillion cycles per second. So light waves are the means of seeing, but vision waves are what we see. Light waves vary in time, vision waves in space.
视觉空间波的证据无处不在。看看你正在阅读的页面。字母,包括作为字符的空格,似乎或多或少均匀地放置在页面的水平尺寸上。在frequencyspeak中,它们在页面上以或多或少的恒定频率出现,并且文本行在页面下方以绝对恒定的频率出现。您可以将文本视为波峰,将线条之间的空间视为某种“波浪”的波谷。书架上的书籍在水平方向上以相当恒定的速度重复。货架本身以相当可预测的频率垂直重复。这些都不是傅里叶的美丽平滑波,但它们都暗示了视野中空间波的概念。
Evidence of visual space waves is everywhere. Just look at the page you’re reading. The letters, including the spaces as characters, appear more-or-less uniformly placed across the horizontal dimension of the page. In frequencyspeak, they appear at a more-or-less constant frequency across the page, and the lines of text appear at a definitely constant frequency down the page. You can think of the text as the crests and the space between the lines as the troughs of some kind of “wave.” Books on a bookshelf repeat at a fairly constant rate horizontally. And the shelves themselves repeat at a fairly predictable frequency vertically. None of these is a beautiful smooth wave à la Fourier, but they all hint at the notion of spatial waves in the visual field.
事实上,如果你能在你的视觉世界中感知到某个频率的“波”,那么傅里叶版本的它就会以那个频率的波为特征。我刚刚测量了我正在阅读的书中一行文本的底部与下一行底部之间的距离为四分之一英寸。所以那个页面的音乐版本,如果你想它是一张图片,一定有一个频率相同的傅立叶空间波,每英寸四个周期。
In fact, if you can perceive a “wave” of some frequency in your visual world then the Fourier version of it will feature a wave of that frequency. I just measured the distance between the bottom of one line of text in a book I’m reading to the bottom of the next line to be a quarter inch. So the musical version of that page, which is a picture if you think about it, must have a Fourier space wave of that frequency, four cycles per inch.
屋顶梁以恒定的节拍“涟漪”穿过天花板,硬木地板的木板在一维中以熟悉的频率重复。瓷砖地板有重复的瓷砖在两个维度的平铺频率上,平铺屋顶也是如此。Alhambra(图 1.5)将瓷砖——地板、墙壁、天花板——带到了令人惊叹的愉悦高度。
Roof beams “ripple” across the ceiling at a constant beat, and a hardwood floor has boards repeating at a familiar frequency in one dimension. A tiled floor has tiles repeating at the tiling frequency in both dimensions, and a tiled roof does too. The Alhambra (figure 1.5) takes tiling—of floors, walls, ceilings—to stunning heights of delight.
图 1.5
Figure 1.5
妙语是,您可以仅用傅立叶波来表示所有这些空间节奏。所有视觉图案,无论多么明显不规则,都可以描述为傅立叶美丽规则波的组合、总和。
The punch line is that you can represent all these spatial rhythms with Fourier’s waves alone. All visual patterns, no matter how apparently irregular, can be described as a combination, a sum, of Fourier’s beautiful regular waves.
但是自然界呢?那里也是如此,尽管不太明显——除了海浪。草坪或草地上的草叶以特征频率重复。树的叶子也是如此,尽管叶子之间的粗略间距取决于树的种类。森林中树木的间距具有特征频率,也取决于物种。山脉以某种频率达到顶峰。大自然母亲的频率远不如我们的那么均匀。她的重复模式更具随机性。然而,山峰不会出现在例如每英寸两个山峰或每百万英里两个山峰处。有一个频率范围,这或多或少是我们对山脉的期望,更像是每十英里有两个山峰。再一次,所有这些视觉节奏都符合傅立叶的节奏。
But what about the natural world? The same is true there, although less obvious—except for ocean waves. The blades of grass in a lawn or meadow repeat at a characteristic frequency. The leaves of a tree do too, although the rough spacing between leaves depends on the species of tree. The spacing of trees in a forest has a characteristic frequency, also dependent on species. Mountain ranges peak in a sort of frequency. Mother Nature’s frequencies are much less uniform than ours. She has more randomness in her repeating patterns. Yet mountain peaks don’t occur at, say, two crests per inch or at two crests per million miles. There is a range of frequencies, which is more-or-less what we expect of mountain ranges, more like two peaks per ten miles. Again, all these visual rhythms beat to Fourier’s tune.
图 1.6 的目的是向您展示如何在世界上寻找空间频率——作为查看它的另一种方式。这是我多肉花园的照片加利福尼亚州伯克利。到处都有空间频率。一旦你开始在这里或任何地方看到它们,那么实现傅立叶所做出的飞跃并不难——波和它们的各种频率是你完全描述视觉场景所需要的。
The purpose of figure 1.6 is to show you how to look for spatial frequencies in the world—as an alternative way to view it. It’s a picture of my succulent garden in Berkeley, California. There are spatial frequencies everywhere in it. Once you begin to see them, here or anywhere, then it isn’t so difficult to make the leap that Fourier made—that waves and their various frequencies are all you need to completely describe a visual scene.
图 1.6
Figure 1.6
考虑一下陶罐,这是这个场景的一些人造成分。观察它们在松散的网格上的情况。它们的间距不规则,但它们确实有一个松散规则的重复模式——比如每隔一英寸左右就有一个锅。在这部分图片的傅里叶等效项中,有一组与底池放置频率略有偏离的波浪,以解释与严格规律性的轻微偏离。
Consider the terracotta pots, some of the manmade constituents of this scene. Observe how they are on a loose grid. They aren’t regularly spaced exactly, but they do have a repeat pattern that’s loosely regular—say a pot every one inch or so. In the Fourier equivalent of this part of the picture there is a group of waves with slight departures from that frequency of pot placement to account for the slight departures from strict regularity.
花盆上的图案也很规则。只考虑一条穿过图片的线,比如一条与罐子对齐的线,由下方的一对箭头表示,线 a。换句话说,一次只将注意力集中在一条线上的规则频率上——就好像沿着那条线的光强度是一段音乐中的声音幅度一样。你能想象你花园的光强度会说“是”吗?
The patterning on the pots is regular too. Consider only a single line through the picture, say a line aligned with the pots and indicated by the lower pair of arrows, line a. In other words, constrain your attention to the regular frequencies along one line at a time—as if the light intensities along that line were the sound amplitudes in a passage of music. Can you imagine a yes spoken by your garden’s light intensities?
从a线上的左边开始,详细地,那里是锅上螺旋凹槽的中频,然后是锅之间的高频(但幅度很小)污垢,然后是第二个锅上的凹槽的中频,然后是定义最大电位器曲线的波的低频,然后是其他两个电位器的两个稍高的频率,依此类推。
Starting from the left on line a, in detail, there is the medium frequency of the spiraling grooves on the pot there, then the high frequency (but low amplitude) dirt between the pots, then a medium frequency of the grooves on the second pot, then the low frequency of the wave defining the curve of the largest pot, then two slightly higher frequencies for the two other pots, and so forth.
植物也有频率。不同的仙人掌和多肉植物具有不同的分枝或叶子放置频率。要看到这一点,请将您的注意力集中在沿线 b 的位置处几乎规则的频率上。这条线穿过(图像)两个星爆状结构的仙人掌。沿着这条线,每个物种的“叶子”以几乎规律的频率出现。(仙人掌的刺实际上是它的叶子。“叶子”是它的树枝。)
The plants too have frequencies. The different cactus and succulent species have various frequencies of branch or leaf placement. To see this, constrain your attention to the almost regular frequencies at places along the line b. The line cuts through (the image of) two cacti of starburst-like structure. Along that line the “leaves” of each species occur at an almost regular frequency. (The cactus spines are actually its leaves. The “leaves” are its branches.)
下一条线,c 线,与绣球花的大球相交,每个球由数百个小花组成。小花以比任何其他尚未讨论的植物更高的频率与线相交。下一行(d 行)与绣球花的叶子相交。它们沿着这条线出现的频率低于小花沿着c线出现的频率。也就是说,同一个空间里大约有两个叶宽,相当于有几十个小花宽。小花比叶子更密集,或者,在频率峰值中,它们以更高的空间频率出现。
The next line up, line c, intersects the large balls of hydrangea flowers, each composed of hundreds of tiny florets. The florets intersect the line at a higher frequency than any other plant yet discussed. The next line up (line d) intersects the leaves of the hydrangea. They occur along that line at a lower frequency than the florets do along line c. That’s to say, there are about two leaf widths in the same space as there are dozens of floret widths. The florets are denser than the leaves or, stated in frequencyspeak, they occur at a higher spatial frequency.
穿过图片的四行显示为彼此平行,但傅立叶并不要求这样做。您可以通过在图片中以其他角度(甚至垂直于所示角度)寻找重复的图案来锻炼您的直觉。例如,您可能会看到大扁平椭圆上的凸起的规则结构照片中央附近的仙人掌仙人掌的“叶子”。那些颠簸是它的刺所在的地方。您可以通过二维中的凸块绘制两个或多或少相互垂直的波。这或多或少是二维傅里叶思想的作用。
The four lines through the picture are shown parallel to one another, but Fourier doesn’t require that. You might exercise your intuition by looking for repeating patterns in lines through the picture at other angles, even perpendicular to the ones shown. For example, you can probably see the regular structure of the bumps on the large flat oval “leaf” of the prickly pear cactus near the center of the photo. Those bumps are where its spines are located. You could draw two waves more or less perpendicular to one another through the bumps in the two dimensions. That’s more or less what the two-dimensional Fourier idea does.
回到人造部分:砖天井在宽度和宽度上有重复频率。背景中的栅栏(很难看到)有它的板重复频率,在它上面编织的格子也是如此。
Back to the manmade parts: The brick patio has repeat frequencies in width and breadth. The fence in the background (difficult to see) has its frequency of board repeats, and so does the trellis weaving above it.
我们可以继续对照片的每个部分进行这种分析。由于粗糙,穿过树皮的线会产生具有高频细节的波。盆中的豌豆砾石以非常高的空间频率出现。等等。花园是空间音乐的交响曲。
We could continue this analysis for every part of the photograph. A line through the tree bark would produce a wave with high frequency detail because of the roughness. The pea gravel in the pots occurs at very high spatial frequency. And so forth. Gardens are symphonies of spatial music.
傅立叶的遗产是我们所看到的一切——呈现给我们视网膜的视觉世界,无论它是否看起来有重复的模式——都是空间音乐的交响乐。它可以用所有频率和幅度的二维空间波来表示。都是音乐。它就像音乐一样工作,但对我们的眼睛来说是二维的,而不是对我们的耳朵来说的。我们需要这种关于可见世界波动性质的直觉,以便在下一章解释像素。
Fourier’s legacy is that everything we see—the visual world presented to our retinas, whether it appears to have repeated patterns or not—is a symphony of spatial music. It can be represented with two-dimensional space waves of all frequencies and amplitudes. It’s all music. It works just like music but in two dimensions for our eyes instead of one for our ears. We need this intuition about the wave nature of the visible world in order to explain pixels in the next chapter.
让-弗朗索瓦·商博良是格勒诺布尔的公民,而傅立叶则应波拿巴的“要求”在那里担任省长。傅立叶向年轻的商博良介绍了罗塞塔石碑(图 1.7)以及占据其前三分之一的古埃及象形文字的奥秘。在接下来的二十年里,商博良使用石头底部三分之一处的古希腊对应物作为重要来源,破译了象形文字。
Jean-François Champollion was a citizen of Grenoble while Fourier was prefect there, at Bonaparte’s “request.” Fourier introduced young Champollion to the Rosetta Stone (figure 1.7) and the mystery of the ancient Egyptian hieroglyphs that occupy its top third. Over the next two decades Champollion deciphered the hieroglyphs using the ancient Greek equivalent in the bottom third of the stone as an important source.
傅立叶与第一领事的特殊关系使这成为可能。商博良多次被征召入伍,但每次傅立叶都成功地直接向当时的首席埃及亲信者波拿巴提出了豁免这个年轻人的请求。如此自由地追求他的激情,商博良破解了罗塞塔石碑的密码并建立了埃及学领域。9
Fourier’s special relationship with the First Consul made this possible. Champollion was drafted several times, but in every case Fourier successfully appealed directly to the chief Egyptophile at the time—Bonaparte—to exempt the young man. Thus free to pursue his passion, Champollion cracked the Rosetta Stone’s code and established the field of Egyptology.9
傅立叶的伟大想法——世界就是音乐,一切都是波——是科学的罗塞塔石碑,而傅立叶是它的商博良。今天,所有同类的科学家、工程师和技术人员都在使用傅里叶频率语言。它是声音、图像、视频等等的通用语言——包括许多最常见的物理过程,尤其是媒体技术。傅立叶展示了如何在他的频率语言和普通语言之间来回翻译,比如跨越空间的颜色或跨越时间的声音振幅。
Fourier’s great idea—the world is music, it’s all waves—is the Rosetta Stone of science, and Fourier was its Champollion. Scientists, engineers, and technologists of all ilk speak Fourier’s frequency language today. It’s the lingua franca of sound, image, video, and on and on—including many of the most common physical processes, and particularly the media technologies. Fourier showed how to translate back and forth between his frequency language and the ordinary languages of, say, colors across space or sound amplitudes through time.
图 1.7
Figure 1.7
照片由克劳迪奥·迪维齐亚拍摄。
Photo by Claudio Divizia.
您可能在随意的谈话中听到有人说“我没有足够的带宽”。如果您是技术人员,您将立即知道这意味着什么。如果你不是,你可能已经推断出它的意思是“容量”,但你不知道为什么。这是一个傅立叶频率词,这就是原因。
You’ve perhaps heard someone say, “I haven’t got enough bandwidth,” in casual conversation. If you’re technical, you’ll immediately know what it means. If you’re not, you’ve probably deduced that it means something like “capacity,” but you don’t have a clue why. It’s a Fourier frequency word, that’s why.
从技术上讲,带宽是衡量通信信道容量的指标。例如,年轻的人耳可以听到每秒 20,000 次循环到每秒 20 次循环的声音。所以它的带宽是两者之差,即对耳朵有意义的频带宽度。在随意的演讲中,带宽被用来比喻你处理信息的能力。
Bandwidth is, technically, a measure of the capacity of a communications channel. The young human ear, for example, can hear sounds of 20,000 cycles per second down to 20 cycles per second. So its bandwidth is the difference of the two, the width of the band of frequencies that are meaningful to the ear. In casual speech bandwidth is used metaphorically to mean something like your capacity to process information.
像这样的频率说话是两种文化的分隔符之一。它对艺术来说是希腊语,所以通过罗塞塔石碑的比喻,频率说话(傅立叶的波浪语言)必须是象形文字。现在让我们看看傅立叶的象形文字——他的二维形式的波——如何代表图片。
Frequencyspeak like this is one of the separators of the two cultures. It’s Greek to the arts, so by the Rosetta Stone metaphor, frequencyspeak (Fourier’s wave language) must be the hieroglyphs. Now let’s see how Fourier’s hieroglyphs—his waves in two-dimensional form—can represent pictures.
究竟什么是二维波?到目前为止,我们只看到了一维波,比如用于声音的波。傅立叶应用于视觉世界的想法需要他的波的二维版本。
What exactly is a two-dimensional wave? We’ve only looked so far at one-dimensional waves, like those used for sound. Fourier’s idea applied to the visual world needs a two-dimensional version of his wave.
一维波是一个展开的圆。二维波是一个展开的圆柱体。要在二维中可视化波浪,请想象时钟的二手波浪垂直于页面挤出。你得到的是一个波纹状的表面,就像一个有沟的田野。波纹金属建筑由二维空间波片组成。一些门廊屋顶由波纹塑料板制成(图 1.8)。某些褶边薯片是波纹状的。我们称之为瓦楞纸板的平面之间的波浪层是另一种空间波。地中海风格的红瓦屋顶是另一个。
A one-dimensional wave is an unwound circle. A two-dimensional wave is an unwound cylinder. To visualize a wave in two dimensions, imagine the clock’s second-hand wave extruded perpendicular to the page. What you get is a corrugated surface, like a furrowed field. A corrugated metal building is composed of sheets of two-dimensional space waves. Some porch roofs are made from corrugated plastic panels (figure 1.8). Certain ruffled potato chips are corrugated. The wavy layer between the flat surfaces of what we call corrugated cardboard is another space wave. A Mediterranean-style red tiled roof is another.
因此,波纹是二维空间波。查看它的边缘(横截面)以查看一维波。事实上,它的任何直截面也是一维波。
So, a corrugation is a two-dimensional space wave. Look at its edge—a cross-section—to see a one-dimensional wave. In fact, any straight cross-section of it is also a one-dimensional wave.
傅立叶的大思想是,所有的视觉世界都可以表示为所有频率和幅度的波纹空间波的总和。为了处理第二维,唯一增加的扭曲是波可以旋转到任何方向。犁沟可以向南北向,或东向西,或东北向西南,或以任何其他角度延伸,这对自然界尤其重要。空间波的“材料”可能是镀锌铁,或者,正如图中所示,塑料。工程师们使用傅立叶的想法来描述现实和人造世界中的所有复杂模式——由世界构成的所有材料构成。
Fourier’s big idea is that all of the visual world can be represented as a sum of—only—corrugated space waves of all frequencies and amplitudes. The only added twist, to handle the second dimension, is that the waves can be rotated to any degree of orientation. The furrows can run north and south, or east and west, or northeast by southwest, or at any other angle, especially important for the natural world. The “stuff” of the space waves might be galvanized iron or, as the figure here suggests, plastic. Engineers use Fourier’s idea to describe all the complex patterns in the real and manmade world—made of all the stuff the world is made of.
图 1.8
Figure 1.8
但是要理解像素,我们需要考虑某人看待那个世界的观点。世界可能是由铁、塑料和土豆构成的,但我们看到的是一种色彩亮度的图案——一个由明暗色调和形状组成的领域。我们所看到的世界的傅里叶波的东西是光的强度,因为它在视野中变化。
But to understand the pixel we need to consider the point of view of someone looking at that world. The world may be made of iron and plastic and potatoes, but what we see is a pattern of colored brightnesses—a field of light and dark hues and shapes. The stuff of Fourier’s waves for the world we see is the intensity of light as it varies across the visual field.
我们怎么能想象这样一个领域呢?解释呈现给眼睛的世界的一种明显方法是描述视野中每个点的光强度。但这意味着视野中的每个点。视野是一个连续的东西——每一个可能的点都被光着色。这些点之间没有中断。无论我们选择的两个点有多接近,中间总会有另一个点。有无数个点,需要指定很多点。
How might we even imagine such a field? One obvious way to explain the world that’s presented to the eye would be to describe the light intensity at every point of the visual field. But this means every point in the visual field. A visual field is a continuous thing—every possible point is colored with light. There are no breaks between these points. No matter how close together the two points we choose, there’s always another one in between. There’s an infinite number of points and that’s a lot of points to specify.
傅里叶为我们提供了另一种方式:将视觉世界视为空间波的总和,这些空间波加起来与逐点描述相同。例如,图 1.9 顶行中的图片可以通过给出每个点的灰度值以显而易见的方式描述,或者可以通过仅指定一个波等效地描述为傅里叶方式。“加起来”到这张图片中的一个空间波的频率约为每英寸两个周期,其亮度水平在明暗之间摆动。只有少数几个值指定了整个图片——一个频率和一个最大幅度——而不是大量的灰度,一个对应图片中的每个点。
Fourier offers us an alternative way: to think of the visual world as a sum of spatial waves that add up to be the same as the point-by-point description. The picture in the top row of figure 1.9, for instance, could be described in the obvious way by giving its gray value at every point, or it could equivalently be described the Fourier way by specifying just one wave. The one space wave that “adds up” to this picture has a frequency of, say, about two cycles per inch, and its brightnesses wiggle between dark and light horizontally. Just a handful of values specifies this entire picture—one frequency and one maximum amplitude—instead of an extremely large number of grays, one for each point in the picture.
图 1.9
Figure 1.9
顺便说一句,最上面的图片显示了从上面看到的傅里叶波纹之一(部分)。因此,毫不奇怪,那个波浪就是这张图像的完整描述。请注意,您可以看到构成视野的波的振动,就像您可以听到构成声音的波的振动一样。该图中波的“成分”是光强度(或亮度)——被认为是灰色阴影。波浪的高部分是浅灰色,低部分是较暗的。(该图是图 1.2 中波浪线的二维对应物。)
By the way, that top-row picture shows (part of) one of Fourier’s corrugated waves seen from above. So, not too surprisingly, that very wave is the complete description à la Fourier of this image. Notice that you can see the vibrations of the waves that make up the visual field, just as you can hear the vibrations of those that make up sound. The “stuff” of the wave in this figure is light intensity (or brightness)—perceived as a shade of gray. High parts of the wave are lighter grays, and low parts are darker. (This figure is a two-dimensional counterpart of the wavy lines in figure 1.2.)
幅度对应于视觉场景的亮度,就像它对应于声音的响度一样。频率对应于场景中细节的数量,人们在谈论高分辨率图片或高清视频时所指的那种东西。高振幅意味着明亮,高频意味着细节。
Amplitude corresponds to the brightness of a visual scene, just as it corresponds to loudness in the case of sound. Frequency corresponds to the amount of detail in a scene, the sort of thing people refer to when they talk about a high-resolution picture or a high-definition video. High amplitude means bright, and high frequency implies detail.
当颜色可用时,颜色信息也在那里。我们的眼睛有三种颜色感受器——视锥细胞——红、绿、蓝光强度各有一种。如果一个手机或电视屏幕上的点会显示红、绿、蓝光强度,然后我们的大脑会从我们的视锥细胞中接收这三种信号的相对强度,并从中感知颜色。来自电子显示器的发射光混合颜色的方式与来自油画(比方说)或彩色墨水印刷页面的反射光不同。为了使发射的光呈现黄色,我们必须打开红色和绿色部分并关闭蓝色部分。但是,为了让白色页面反射的光呈现黄色,我们必须阻挡白光的蓝色部分,只让红色和绿色通过。无论采用何种显示技术,在视觉上都是一样的。我几乎总是使用发射(非反射)光术语。
Color information is there too, when color is available. Our eyes have three types of color receptors—the cones—one type each for red, green, and blue light intensities. If a point on a cellphone or television screen displays red, green, and blue light intensities, then our brain takes in the relative strengths of these three signals from our cones and perceives a color from them. Emitted light from electronic displays mixes colors in a different way than does reflected light from an oil painting, let’s say, or a printed page of colored inks. For emitted light to appear yellow, we must turn on the red and green parts and turn off the blue part. But for light reflected off a white page to appear yellow, we must block the blue part of the white light and let only the red and green through. Regardless of the display technology, it all amounts to the same thing at the eye. I’ll nearly always use emitted (not reflected) light terminology.
因此,将图 1.9 顶行中的灰度波想象成一种颜色波——比如说黄色波。所显示的波峰是介于中灰和全白之间的灰色,而我们的彩色波峰是介于中黄和全黄之间的黄色。您可以将彩色波想象成三个频率相同但幅度不同的波,每个用于我们的红色、绿色和蓝色受体。所以我们的黄色波由三个波组成,一个类似于上面显示的红色受体的灰度波,另一个与绿色受体类似(相同幅度),第三个与蓝色受体类似但幅度为零。红色和绿色相等,没有蓝色,我们的大脑看到黄色波。
So imagine the grayscale wave in the top row of figure 1.9 as a wave of color instead—say a yellow wave. Where the crest of the wave shown is a gray somewhere between mid-gray and full white, the crest of our colored wave is a yellow somewhere between mid-yellow and full yellow. You can think of a colored wave as three waves at the same frequency but of different amplitudes, one each for our red, green, and blue receptors. So our yellow wave consists of three waves, one like the grayscale wave shown above for the red receptor, another just like it (at the same amplitude) for the green receptor, and a third like it but with zero amplitude for the blue receptor. With equal parts red and green and no blue, our brain sees a yellow wave.
图 1.9 中下两行的图片显示了额外的二维波浪,以使您熟悉它们的外观。就像一维的情况一样,三个波处于三个不同的频率和三个不同的幅度。对于所示的波,最高频率波(底行)具有最低振幅(中灰色),而最低频率波(顶行)具有最高振幅(接近白色)。但事实并非如此。波可以具有任何幅度的任何频率。
The pictures in the middle and bottom rows of figure 1.9 show additional two-dimensional waves to familiarize you with what they look like. Just as for the one-dimensional case, the three waves are at three different frequencies with three different amplitudes. For the waves shown, the highest frequency wave (bottom row) has the lowest amplitude (mid-gray), and the lowest frequency wave (top row) has the highest amplitude (near white). But that doesn’t have to be the case. A wave can have any frequency at any amplitude.
这是从这些数字中得出的直觉:图片中的精细细节必须来自其傅里叶描述中的高频波。它们是唯一变化得足够快的波浪。计算机图形学高手会说诸如“那个场景中有很多高频”之类的东西,这意味着——当然没有解释——它有很多微小的细节和锐利的边缘。
Here’s the intuition to take away from these figures: the fine detail in a picture must come from the high-frequency waves in its Fourier description. They are the only waves that change fast enough. Computer graphics whizzes say things in frequencyspeak like, “There are lots of high frequencies in that scene,” meaning—without explanation, of course—that it has many tiny details and sharp edges.
后面关于边缘的评论指的是你应该知道的一个方便的事实。这当然不直观。这是傅里叶数学的直接结果:在锐边的突然转变需要傅里叶世界中非常高的频率;一个非常突然的变化需要非常高的频率。
The latter remark about edges refers to a handy fact you should know. It’s certainly not intuitive. It’s a direct consequence of Fourier’s math: the sudden transition at a sharp edge requires very high frequencies in Fourier’s world; a really sudden change requires a really high frequency.
这是我对傅里叶妙语的再次表述:
Here’s my formulation of Fourier’s punch line again:
任何视野——让我们称之为图片或图案——都是优雅起伏的波浪的总和,并且只是这些波浪的总和,所有这些都是完美圆柱体的展开。
Any visual field—let’s call it a picture or a pattern—is a sum of, and only of, gracefully undulating waves such as those shown, all unfurlings of perfect cylinders.
作为波浪的视觉世界并不比声音更神秘——或者我们可以说它同样非常神秘。葛底斯堡演说可以用林肯演讲时每一刻的声压强度来描述,也可以用不同频率和振幅的声波叠加在一起来描述。傅立叶告诉我们两种描述是等价的。
The visual world as waves is no more mysterious than sound—or let’s say it’s just as wonderfully mysterious. The Gettysburg Address can be described by the intensity of sound pressure at each moment during Lincoln’s speech or it can be described as the sum of the sound waves of various frequencies and amplitudes that add up to the same thing. Fourier taught us that both descriptions are equivalent.
科学家和工程师喜欢傅立叶的版本,因为通过使用非显而易见的频率描述,他们可以解决现实世界中无法通过明显的、等效的逐点描述解决的问题。
Scientists and engineers love Fourier’s version because, by using the nonobvious frequency description, they can solve problems in the real world that resist solution in the obvious, equivalent point-by-point description.
我们不是在谈论一千个光点,而是在频率上谈论叠加到这些点的光强度波的频率和幅度。傅立叶的变革性教导是这两种描述是等价的。逐点视野是希腊文。傅立叶波音乐等价物是象形文字。对于极客来说,象形文字比希腊文更容易阅读。罗塞塔石碑是傅立叶证明两者相同的证据。
Instead of talking about a thousand points of light, we talk in frequencyspeak about the frequencies and amplitudes of the waves of light intensity that add up to the points. Fourier’s transformative teaching is that these two descriptions are equivalent. The point-by-point visual field is the Greek text. The Fourier wave musical equivalent is the hieroglyphs. For a geek, hieroglyphs are easier to read than Greek. The Rosetta Stone is Fourier’s proof that the two are the same.
傅立叶的批评者不相信他是对的,但数学表明这是对的。这就是这个想法的魔力——以及数学令人敬畏的、打破直觉的力量。把不同频率的波加起来真的会给你一张图片。. . 任何事物!例如,关于我多汁的花园,或者你正在阅读的页面,或者你的孩子。这是傅立叶伟大而宏大的想法。
Fourier’s critics didn’t believe he was right, but the math said it was true. That’s the magic of the idea—and the awesome, intuition-breaking power of math. Adding up waves of different frequencies really will give you a picture of . . . anything! Of my succulent garden, or the page you’re reading, or of your child, for instance. That’s Fourier’s great and very large idea.
傅立叶在恐怖袭击中幸存下来,他甚至在法国统治——如果只是作为省长——多亏了波拿巴。但是,当国王重新掌权时,无论是他早期的反贵族立场还是他与皇帝的关系,都不是方便的凭据——两次。尽管如此,傅立叶还是在这场摄政和帝国之舞中的幸存者,就像他在恐怖中一样。他以相当高的政治技巧成功地在伊泽尔省担任了近十三年的省长,只有最后一年是冒险的。
Fourier survived the Terror, and he even came to rule in France—if only as a provincial governor—thanks to Bonaparte. But neither his early anti-aristocratic stance nor his association with the emperor were handy credentials when the king returned to power—twice. Nevertheless, Fourier was a survivor in this dance of regency and empire, as he had been in the Terror. He managed, with considerable political skill, to remain prefect of the Isère department for almost thirteen years, and only the last year was dicey.
在 1802 年 4 月至 1814 年 4 月的 12 年中,傅立叶作为一名出色的格勒诺布尔总督充分利用了他的流放生涯。他与40个公社谈判达成了一项协议,以排干伊泽尔 (Isère) 布尔干 (Bourgoin) 的大沼泽地,这是一场巨大的政变,因为之前的所有谈判尝试都失败了。他穿过一条从格勒诺布尔到都灵的新路。他为图书馆购买书籍,支持他所在部门的年轻人——最著名的是商博良——并参与了《埃及的描述》 ,最终于 1810 年出版。在此期间,傅立叶以某种方式找到了发展他的波动理论的时间。他不是通过听莫扎特或观察阿尔罕布拉宫到达那里的,而是通过考虑热量波的条款。也许他的théorie de la chaleur(他的热理论)——以及他伟大的和谐思想——是他重新进入巴黎的总体计划。
For 12 years, April 1802 to April 1814, Fourier made the best of his exile as an accomplished governor in Grenoble. He negotiated an agreement with 40 communes to drain the massive swamp of Bourgoin in Isère, quite a coup since all previous attempts at negotiation had failed. He pushed through a new road from Grenoble to Turin. He purchased books for the library, championed young men of his department—most notably Champollion—and worked on Déscription de l’Egypte, finally published in 1810. During this interval Fourier somehow found time to develop his wave theory. He didn’t get there from listening to Mozart or observing the Alhambra but by thinking of heat in terms of waves. Perhaps his théorie de la chaleur (his theory of heat)—and with it his great harmonic idea—was his master plan for readmission to Paris.
傅立叶本人谈到他对热的非凡兴趣时说:“在我看来,地球温度问题一直是宇宙学研究的最重要对象之一,而我在建立热的数学理论时主要考虑了这个主题。” 他正在寻找一个和牛顿一样大的想法。
Fourier himself said about his extraordinary interest in heat, “The question of terrestrial temperatures has always appeared to me to be one of the greatest objects of cosmological studies, and I have had this subject principally in view in establishing the mathematical theory of heat.” He was looking for an idea as big as Newton’s.
Victor Cousin 是一个认识傅立叶的人,他对他的动机有不同的看法。他写道,当傅立叶从埃及回到格勒诺布尔时,即使在最热的天气里,他也从不出门,没有一件大衣和另一件备用。他已经产生了对热量的身体需求,这听起来充其量是古怪的,但这相当于一种疾病。
Victor Cousin, a man who knew Fourier, had a different take on his motivation. He wrote that when Fourier came back to Grenoble from Egypt, he never went outside, even in the hottest weather, without an overcoat and another in reserve. He’d developed a physical need for heat that sounds eccentric at best, but which amounted to a disease.
法国人对他有一个我们在英语中缺乏的词:傅立叶是frileux。他感到非常寒冷。他对寒冷非常敏感,也许很痛苦。这个词还带有他无法个人温暖的内涵。人们可能认为傅立叶的冷酷程度不止一种。
The French have a word for him that we lack in English: Fourier was frileux. He felt the cold terribly. He was very sensitive to cold, perhaps painfully so. The word also carries the connotation that he was incapable of personal warmth. People may have thought that Fourier was chilly in more ways than one.
没有人知道傅立叶是什么时候开始研究热力的,但他在格勒诺布尔时就全神贯注于这个理论,就在埃及之后几年。可能在 1804 年或 1805 年完成的有缺陷的草稿版本包含他的波浪的第一次已知外观。他在 1807 年末的一本名为“固体中的热传播理论”的“回忆录”中向学术公众展示了该手稿的一个大大改进的版本,现在被认为是确立他的想法的论文。在编写这两个版本之间的时间里,他已经熟悉了热的实际物理学,并进行了实验来测试和验证他的数学结果。
Nobody knows when Fourier first started his work on heat, but he was engrossed in the theory while in Grenoble, just a couple years after Egypt. A flawed draft version probably completed in 1804 or 1805 contains the first known appearance of his waves. He presented an enormously improved version of that manuscript to the academic public in a late 1807 “memoir” called Theory of Propagation of Heat in Solids, now considered to be the paper that established his idea. During the time between writing the two versions, he had become familiar with the actual physics of heat and performed experiments to test and verify his mathematical results.
用傅立叶的话说,整个过程“有助于赋予该理论一种权威,在一个仍然晦涩难懂且显然存在许多不确定性的问题上,人们可能倾向于拒绝这种权威。” 这就是经典科学。使用理论进行假设。用实验来验证。这证明傅里叶既是数学家又是实验物理学家。他不怕弄脏自己的手。
In Fourier’s words, the whole process “contributed to give the theory an authority which one might have been inclined to refuse in a matter still obscure and apparently subject to so many uncertainties.” That’s classic science. Use theory to hypothesize. Use experiment to verify. It proves that Fourier was both a mathematician and an experimental physicist. He wasn’t afraid to get his hands dirty.
傅立叶意识到他可以将流经固体物体的复杂热量模式描述为他的波的总和。这意味着他可以预测热量将如何(以及多长时间)从大炮的接触点流到嘴巴。
Fourier realized that he could describe the complex pattern of heat flowing through a solid object as a sum of his waves. That meant that he could predict how (and how long) heat would flow from, say, the touchpoint of a cannon to its mouth.
因此,从长远来看,在 1803 年至 1807 年期间,他在完善热理论和进行支持性实验的同时,也在谈判沼泽排水合同、修路、指导部门中的年轻人,并为埃及出版物工作. 傅里叶从哪里获得带宽?
So, for perspective, between 1803 and 1807, while he was perfecting his theory of heat and performing the supporting experiments, he was also negotiating the swamp-draining contracts, building roads, mentoring young men in his department, and working on the Egypt publication. Where did Fourier get the bandwidth?
傅立叶驾驭了帝国和革命的政治。他利用自己对拿破仑(皇帝被称为波拿巴的称呼)的个人知识,根据一页纸的提案获得了大型公路项目的批准,拿破仑在两天内就批准了。但傅立叶在学术界更加激烈的政治中度过了一段艰难的时光,也许是因为流亡中的傅立叶与巴黎喧嚣的学术活动疏远了。
Fourier navigated the politics of empire and revolution. He used his personal knowledge of Napoleon—as Bonaparte the emperor was called—to get the big road project approved based on a one-page proposal, which Napoleon granted in two days. But Fourier had a harder time with the even fiercer politics of academia, perhaps because Fourier in exile was alienated from the hurly-burly of academic goings on in Paris.
在 1807 年“回忆录”的科学院官方读者中,有拉普拉斯,他是拿破仑的参议员任命者,他从傅立叶在巴黎综合理工学院的时候就认识了他。拉普拉斯对傅立叶伟大想法的数学运算感到不舒服。对它的第一次公开攻击来自拉普拉斯的门徒西蒙·丹尼斯·泊松,当傅立叶成为伊泽尔省长时,他在巴黎综合理工学院担任傅立叶的主席。长期而激烈的争论的结果是,这本回忆录从未出版过。最终,拉普拉斯开始支持傅立叶,但傅立叶的死敌泊松从来没有这样做过。
Among the official Academy of Science readers of the 1807 “memoir” was Laplace, Napoleon’s senatorial appointee, who had known Fourier since his days at the École polytechnique. Laplace was uncomfortable with the mathematics of Fourier’s great idea. The first public attack on it came from Laplace’s protégé, Simeon Denis Poisson, who assumed Fourier’s chair at the École polytechnique when Fourier became prefect of Isère. The outcome of the long and acrimonious controversy was that the memoir was never published. Eventually, Laplace came to support Fourier, but Poisson—Fourier’s implacable enemy—never did.
在后人看来,傅立叶在他 1807 年的回忆录中确立了这一理论——使 2007 年成为这个想法不为人知的 200 周年——但在它被真正接受之前,他必须经历另一个挑战。可能是因为长期的争论,学院宣布将在 1811 年颁发数学大奖,主题是 . . . 热在固体中的传播。厚脸皮!傅立叶以他的论文奖作为回应,这是 1807 年论文的扩展版本,保留了早期回忆录的主要贡献。10
To posterity’s mind, Fourier had established the theory in his memoir of 1807—making 2007 the idea’s uncelebrated bicentennial—but he had to pass through another gauntlet before it was truly accepted. Probably because of the prolonged controversy, the academy announced that it would award a grand prize in mathematics in 1811 on the subject of . . . the propagation of heat in solid bodies. Cheeky! Fourier responded with what is known as his Prize Essay, the extended version of the 1807 paper that kept the principal contributions of the earlier memoir in place.10
因此,让我们总结一下傅立叶在准备获奖论文时所做的事情:沼泽。道路。指导。描述 de l'Egypte。同样,他从哪里获得带宽?
So let’s summarize what Fourier did while he was preparing the Prize Essay: Swamps. Roads. Mentoring. Déscription de l’Egypte. Again, where did he get the bandwidth?
1807 年回忆录之外的获奖论文的延伸之一讲述了傅立叶的牛顿野心。他将他的热流理论应用于一个球体——一个行星大小的球体——因此是第一个研究现在被称为温室效应的陆地现象的人。穿过地球大气层的阳光加热地球表面,而大气层在附近保存了一些热量。这是一个不完美的比喻,但大气就像温室的玻璃,它可以让阳光进入,但不会让所有的热量散发出去。自然温室效应的热量使地球变暖,并使其成为我们所知的生命之地。尽管傅立叶才华横溢,但他无法预见目前威胁地球生命的非自然温室效应热量。11
One of the extensions of the Prize Essay beyond the 1807 memoir speaks to Fourier’s Newtonian ambitions. He applied his theory of heat flow to a sphere—a planet-sized one—and so was the first to study the terrestrial phenomenon now known as the greenhouse effect. Sunlight that passes through Earth’s atmosphere heats the Earth’s surface, and the atmosphere holds some of the heat nearby. It’s an imperfect metaphor but the atmosphere resembles the glass of a greenhouse, which allows sunlight in but doesn’t let all the heat out. The heat of the natural greenhouse-effect warms the Earth and makes it the place for life as we know it. Fourier, despite his brilliance, couldn’t have foreseen the unnatural greenhouse-effect heat that currently threatens life on Earth.11
尽管有学院派的恶作剧,傅立叶还是凭借他的论文奖获得了奖项。但同样,他没有得到阅读它的学院委员会的全力支持。特别是,拉普拉斯投了反对票。
Despite the academy shenanigans, Fourier won the prize with his Prize Essay. But again, he didn’t get the full support of the academy commission who read it. In particular, Laplace voted against it.
“作者得出这些方程式的方式并非没有困难,”委员会在其报告中说。“他整合它们的分析在一般性甚至严谨性方面仍有待改进。”
“The manner in which the author arrives at these equations is not exempt of difficulties,” the commission said in its report. “His analysis to integrate them still leaves something to be desired on the score of generality and even rigor.”
数学上缺乏严谨性是最大的侮辱。学院在出版有奖论文方面拖了后腿,就像它为回忆录所做的那样。12
Lacking rigor in math is the ultimate insult. The academy dragged its heels in publishing the Prize Essay as it had for the memoir.12
直到 1815 年拿破仑最后一次流放至圣赫勒拿,傅立叶返回巴黎后,他才成功发表了他的获奖论文。它仍然受到无情的泊松的猛烈抨击。但是傅立叶在泊松的著作中发现了一个基本错误,并且在他的竞争热理论中发现了一个错误的主张。傅立叶在给拉普拉斯的一封信中摧毁了两者。这是他的对手的致命一击,最终拉普拉斯站在了他的一边。
It wasn’t until after Napoleon’s final exile, to Saint Helena in 1815, and Fourier’s return to Paris, that he managed to get his Prize Essay published. It still came under withering fire from the implacable Poisson. But Fourier found an elementary error in Poisson’s writings and a false claim in his competing theory of heat. Fourier demolished both in a letter to Laplace. That was the coup de grâce to his opposition, finally bringing Laplace to his side.
胜利的科学进步并没有与光荣的政治成功相匹敌。傅立叶继续与拿破仑共舞,这让他作为伊泽尔省长的第十三年也是最后一年感到不安。拿破仑于 1814 年 4 月退位,路易十八恢复为国王。这位前皇帝前往厄尔巴岛进行他的第一次流放,厄尔巴岛位于科西嘉岛以东约 30 英里处,位于巴黎东南部。他在去格勒诺布尔的路上自然会经过格勒诺布尔。在正常情况下,傅立叶也很自然地会向“给他”工作的人打招呼。知府必须迎接前皇帝。但时代几乎不正常。这注定是一次尴尬的相遇。
Triumphant scientific progress wasn’t matched by glorious political success. Fourier’s continuing dance with Napoleon upset his thirteenth and final year as prefect of Isère. Napoleon abdicated in April 1814, and Louis XVIII was restored as king. The ex-emperor headed for his first exile in Elba, an island about thirty miles straight east of Corsica and southeast of Paris. It was natural that he would pass through Grenoble on his way there. Under normal circumstances it would also be natural for Fourier to greet the man who had “given” him the job. The prefect would have to greet the ex-emperor. But the times were hardly normal. It promised to be an embarrassing encounter.
国王的复辟使傅立叶的地位暂时保持不变,但拿破仑会认为他向摄政的鞠躬是一张变脸吗?傅立叶不打算四处寻找。在幕后,他在拿破仑的旅行路线上绕道绕过格勒诺布尔,理由是对前皇帝的潜在伤害。有效。拿破仑回避了傅立叶,新的王室政府着手确认傅立叶为省长。国王的兄弟,即后来的查理十世,拜访了他,完成了交易。
The restoration of the king had left Fourier’s position provisionally intact, but would Napoleon consider his bow to regency a volte face? Fourier wasn’t about to hang around to find out. Behind the scenes he engineered a detour in Napoleon’s travel route to bypass Grenoble, citing potential harm to the ex-emperor. It worked. Napoleon sidestepped Fourier, and the new royal government proceeded to confirm Fourier as prefect. The king’s brother, who would become Charles X, paid him a visit, consummating the deal.
但这并不是与拿破仑共舞的结束。1815 年 3 月 2 日,傅立叶收到了来自邻近省长的这封可怕的信:
But that wasn’t the end of the dance with Napoleon. On March 2, 1815, Fourier received this frightening letter from a neighboring prefect:
我荣幸地通知您,波拿巴率领 1,700 人昨天在胡安湾登陆。. . [并且] 将由圣瓦利耶、迪涅和格勒诺布尔前往里昂。不管这个消息在你看来多么不同寻常,它都是真实的。13
I have the honor to inform you that Bonaparte at the head of 1,700 men disembarked yesterday at Gulf Juan . . . [and] is heading for Lyon by Saint-Vallier, Digne, and Grenoble. No matter how extraordinary this news may seem to you it is entirely true.13
拿破仑从厄尔巴岛回来了他最后的百日权力,再次取代了国王。他沿着连接厄尔巴岛和科西嘉岛到格勒诺布尔、欧塞尔和巴黎的那条决定性的东南西北走廊返回。傅立叶将不得不再次与拿破仑打交道,而此时他已经设法伪装成忠诚的保皇党人。
Napoleon returned from Elba for his final Hundred Days of power, displacing the king again. He returned along that fateful southeast-northwest corridor joining Elba and Corsica to Grenoble, Auxerre, and Paris. Fourier was going to have to deal with Napoleon again, just when he had managed to pass himself off as a loyal royalist.
他准备了府邸,供归来的皇帝居住。他在那里给他留下了一张漂亮的字条,给予他个人的欢迎。在其中,他清楚地表明了他对国王的新忠诚并解释了他的冲突。但是当拿破仑进入城市的前门时,他正在从格勒诺布尔的后门到里昂。
He prepared the prefectural residence for occupancy by the returning emperor. He left a nice note there for him, giving him a personal welcome. In it he stated clearly his new loyalty to the king and explained his conflict. But he was hightailing it out the back gate of Grenoble to Lyon as Napoleon entered the front gate of the city.
拿破仑非常不满,解雇了傅立叶。一个篡位者——傅立叶自己对拿破仑的评价——怎么可能解雇任何人?他不仅这样做了,而且傅立叶和格勒诺布尔的市民都认为他有权这样做,这是衡量这个人权力的标准。
Highly displeased, Napoleon fired Fourier. How could a usurper—Fourier’s own word for Napoleon—fire anybody? It’s a measure of the man’s power that he not only did so, but that Fourier and the citizens of Grenoble perceived he had the authority to do so.
顾问们通过向拿破仑展示傅立叶对Déscription de l'Egypte的赞誉“历史导论”来安抚拿破仑。他的怒火冷却下来,他要求见傅立叶。他们在布尔根相遇,傅里叶在那里排干了沼泽。很难理解这个删除的动态:数学家的软肋?老埃及同志?但是拿破仑不仅原谅了傅立叶,还让他成为了里昂的罗纳省长官!
Advisers mollified Napoleon by showing him Fourier’s laudatory “Historical Introduction” to Déscription de l’Egypte. His anger cooled, and he asked to see Fourier. They met in Bourgoin, where Fourier had drained the swamps. It’s difficult to understand the dynamics at this remove: A soft spot for mathematicians? Old Egyptian comrades? But Napoleon not only forgave Fourier, he made him prefect of Rhône, governed from Lyon!
罗讷河谷的任命发生在 1815 年 3 月 12 日,就在宣布拿破仑从厄尔巴岛返回的信之后十天。事情发生得非常快。拿破仑的滑铁卢是 6 月 18 日,路易十八的第二次复辟是 7 月 8 日。
The Rhône appointment occurred on March 12, 1815, just ten days after the letter announcing Napoleon’s return from Elba. Things were happening very fast. Napoleon’s Waterloo was June 18, and the second restoration of Louis XVIII was July 8.
拿破仑的第二次帝制只持续了著名的百日,而傅立叶的第二府更短,大约六十天。拿破仑作为皇帝的最后一项行为是在滑铁卢前两周授予傅立叶退休金,并在两周后生效。当然,这笔养老金从未兑现。因此,当拿破仑最终被流放到圣赫勒拿岛时,傅立叶既没有工作,也没有退休金,而且政治声誉也很差。
Napoleon’s second imperial effort lasted only the famous Hundred Days, but Fourier’s second prefecture was even shorter, about sixty days. One of Napoleon’s last acts as emperor was to grant Fourier a retirement pension just two weeks before Waterloo, to go into effect two weeks after it. Of course, that pension was never honored. So, when Napoleon was finally exiled to Saint Helena, Fourier was left without a job or pension and with a soiled political reputation.
但至少他的流放终于结束了。他可以回到巴黎并建立他的热音乐理论。
But at least his exile was finally over. He could return to Paris and establish his musical theory of heat.
傅立叶有生命吗?也许不在格勒诺布尔省,但肯定会回到首都?我们可以希望世界音乐概念之父有一部戏剧性的浪漫故事,就像大约十年前本杰明富兰克林与一家著名法国沙龙的寡妇的故事一样。
Did Fourier have a life? Perhaps not in provincial Grenoble but surely back in the capital? We could wish for the father of the world-as-music concept a dramatic romance, like Benjamin Franklin’s about a decade earlier with the widowed hôtesse of a renowned French salon.
也许又是那些奇怪的痛苦,但傅里叶没有赫尔维修斯夫人。事实上,可悲的是,似乎根本没有任何浪漫的兴趣。我们对亲密关系的唯一暗示——这肯定是柏拉图式的——是他与著名数学家玛丽-索菲·热尔曼的深厚友谊。她赢得了科学院奖,是第一位获得该奖项的女性,但她没有出席领奖,这让“一大群无疑被渴望看到一种新的精湛技艺的人所吸引”感到失望。但这还不足以让她获得参加会议的邀请。在傅立叶成为常任秘书七年后,她才收到参加学院降神会或会议的长期邀请。傅立叶做到了。
Perhaps it was those strange afflictions again, but there was no Madame Helvétius for Fourier. In fact, sadly, there seems never to have been any romantic interest at all. The only hint we have of an intimate relationship—and it was surely platonic—was his deep friendship with the noted mathematician Marie-Sophie Germain. She had won an Academy of Science prize, the first woman to do so, and had disappointed “a very large crowd that doubtlessly had been attracted by a desire to see a new kind of virtuosity,” by not showing up to receive the prize. But that hadn’t sufficed to get her an invitation to meetings. She only received a standing invitation to attend séances, or meetings, of the academy seven years later after Fourier became permanent secretary. Fourier made it happen.
从傅立叶写给玛丽-索菲的信件中,仅存一份。所有的都是正式的,除了一个,可能是在他晚年写的,因为字迹残缺,写给“Ch。S”(Chère Sophie)并签名“Jh”(约瑟夫)。但傅立叶给一位医生写了一封信,为一位身患疾病的亲爱但未透露姓名的朋友寻求他的秘密帮助:
There is one surviving cache of letters from Fourier to Marie-Sophie. All are formal except one, probably written in his last years, given the broken handwriting, addressed to “Ch. S” (Chère Sophie) and signed “Jh” (Joseph). But Fourier wrote a letter to a doctor seeking his confidential help for a dear but unnamed friend in medical trouble:
由于最稀有和最美丽的品质,她值得你所有的兴趣。对于温柔地爱着她的我自己,尽管这完全无法预料的事件可能会使我对她的感情化为乌有,但我非常感谢您为她和我所做的一切。14
She is worthy of all your interest by reason of the rarest and most beautiful qualities. For myself, who love her tenderly, in so much as this entirely unforeseen event may bring to nothing the feelings which I have had for her, I would be most deeply grateful for anything you could do for her and for me.14
我们不确定这个女人是谁,但杰曼确实死于乳腺癌。如果她真的是苏菲,他对她的感情会带来什么?15
We don’t know for sure who this woman was, but Germain did die of breast cancer. What something might the feelings he’d had for her, if indeed she was Sophie, have brought?15
巴黎科学院最终让傅立叶成为成员(图 1.10)。拿破仑于 1821 年去世后不久,他的理论的完整版本最终以《热分析理论》的形式出版。荣誉开始累积。学院选举他为常任秘书,牛顿皇家学会于 1823 年 11 月任命让·巴蒂斯特·约瑟夫·傅立叶为外国会员。他在 21 岁时非常羡慕牛顿,但在 55 岁时,他终于在他生命的最后十年中踏上了永生之路自己。1826 年,他成为法兰西学院的官方常任理事,1889 年,古斯塔夫·埃菲尔将他的名字命名在这座著名的塔楼上。 16
The Academy of Science in Paris finally made Fourier a member (figure 1.10). Shortly after Napoleon’s death in 1821, the full version of his theory was finally published as the Analytical Theory of Heat. The accolades began to accumulate. The academy elected him permanent secretary, and Newton’s Royal Society made Jean Baptiste Joseph Fourier a Foreign Member in November 1823. He had so envied Newton at age 21, but at 55 he was at last, in his final decade, treading the road to immortality himself. He became an official immortel of the Académie française in 1826, and Gustave Eiffel placed his name on the famous tower in 1889.16
拿破仑的死也最终使养老金成为可能。起初,国王政府对傅立叶接受拿破仑在最后百日里担任罗讷省的任命并不高兴。在拿破仑流放圣赫勒拿岛后,他第一次尝试从君主制中获得养老金。他的请求被拒绝了。他在 1816 年、1818 年和 1821 年再次尝试,每次都被拒绝。只有在拿破仑死后,他的下一次尝试才成功。
Napoleon’s death also finally made a pension possible. At first, the king’s government wasn’t happy that Fourier had accepted Napoleon’s appointment to the prefecture of Rhône in the last Hundred Days. He first tried for a pension from the monarchy just after Napoleon’s exile to Saint Helena. His request was rejected. He tried again in 1816, 1818, and 1821, each time rejected. Only his next attempt, after Napoleon had died, was successful.
政治斗争已经结束,但与健康有关的斗争还没有结束。他从来没有摆脱某种身体上的瘟疫。作为一个上了年纪的人,他被呼吸问题所困扰,以至于他为自己制造了一个特殊的盒子,可以在他写作或说话时——或睡觉时——让他保持直立!——只有他的头和手臂伸出。呼吸困难可能要追溯到他十几岁时令人窒息的橱柜,或者可能是充血性心力衰竭。
The political battles were over, but not the ones related to health. He was never free from some physical plague or another. As an aging man he was so bothered with breathing problems that he had a special box built for himself to hold him upright when he was writing or speaking—or sleeping!—with only his head and arms protruding. The breathlessness might have dated back to the asphyxiating cupboard of his teenage years, or it might have been congestive heart failure.
傅立叶于 1830 年死于心脏病,仅比拿破仑晚了几年。他在巴黎著名的 Pére Lachaise 公墓的坟墓以波浪和埃及图案为特色(图 1.11)。他半身像的两侧是一朵百合花,茎很长,是波浪的轴心。每朵百合花的顶部都有一条戴着太阳圆盘的饲养眼镜蛇。如果埃及确实引起了傅立叶对热的痴迷,那么他的纪念碑的象征意义就是庆祝因果关系。
Fourier died of a heart attack in 1830, having outlasted Napoleon by only a few years. His grave in Paris’s famed Pére Lachaise Cemetery features the wave and Egyptian motifs (figure 1.11). To either side of his bust is a lily with a very long stem that is the axis of a wave. Each of the lilies is topped by a rearing cobra crowned with a solar disk. If Egypt did induce Fourier’s obsession with heat, then his monument’s symbology celebrates both the cause and effect.
图 1.10
Figure 1.10
Julien-Léopold Boilly,傅立叶院士,1820 年。
Julien-Léopold Boilly, Academician Fourier, 1820.
两年后,年轻的格勒诺布洛瓦兹、埃及学的第一位教授让-弗朗索瓦·商博良跟随傅立叶来到拉雪兹神父。他的兄弟雅克-约瑟夫·商博良-菲雅克撰写了最早的傅立叶传记之一。傅立叶的挚友索菲·杰曼(Sophie Germain)——在谈到她时,他几乎不像是弗莱克斯——在他之后不久也被安葬在拉雪兹神父。
The younger Grenobloise, Jean-François Champollion, the first professor of Egyptology, followed Fourier to Pére Lachaise only two years later. His brother, Jacques-Joseph Champollion-Figeac, wrote one of the earliest biographies of Fourier. And Fourier’s dear friend Sophie Germain—he hardly seems frileux when it comes to her—was also buried in Pére Lachaise shortly after him.
日耳曼的最后一幕是为傅立叶的拉雪兹佩尔纪念碑捐款。泊松,他们俩的敌人,一直顽固不化,没有做出贡献。17
One of Germain’s final acts was contributing to the fund for Fourier’s Pére Lachaise monument. Poisson, enemy of them both and recalcitrant to the end, did not contribute.17
傅立叶的烦恼反映在他 1807 年的原创杰作的命运中,这本“回忆录”首先宣布了他的伟大成果。这份手稿消失了 160 多年,终于在国立桥梁和道路学院的图书馆中重新发现。这并不像最初看起来那么奇怪。这所学校是世界上最古老的土木工程学校,比傅立叶还要古老。18
Fourier’s troubles are reflected in the fate of his original 1807 masterpiece, the “memoir” that first announced his great result. The manuscript disappeared for over 160 years, finally rediscovered lying in the library of the École nationale des ponts et chaussées, the National School of Bridges and Roads. This is not as strange as it may first seem. The school is the oldest civil engineering school in the world, older than Fourier.18
图 1.11
Figure 1.11
为什么傅立叶的好主意会遇到这样的阻力?正如他的批评者所看到的那样,问题在于:一个高度不规则的模式——比如一首任意的歌曲或绘画——怎么可能等同于高度规则的波的总和?
Why did Fourier’s great idea meet with such resistance? The problem, as his critics saw it, was this: How could a highly irregular pattern—like an arbitrary song or painting—be equivalent to a sum of highly regular waves?
在数学中,某些东西被证明或未被证明,或者它被证明是不可证明的。傅立叶本人的理论并没有达到这个真理的顶峰,尽管他的直觉非常合理。它落到了年轻的 Peter Gustav Lejeune Dirichlet 来填补剩余的数学空白。他于 1826 年来到巴黎,结识并钦佩傅立叶。在老人的指导下,狄利克雷坚定地确立了这一理论——十分严谨——并于 1829 年发表,也就是傅里叶生命的最后一年。19
In mathematics something is proved or it’s not, or it’s provably unprovable. Fourier himself didn’t attain this pinnacle of truth for his theory, although his intuition was remarkably sound. It fell to young Peter Gustav Lejeune Dirichlet to close the remaining mathematical gaps. He came to Paris in 1826 and met and admired Fourier. With the older man’s guidance, Dirichlet firmly established the theory—with full rigor—and published it in 1829, the last year of Fourier’s life.19
尽管如此,一些数学家仍然为傅里叶数学深奥的死水困扰。但工程师不是。在 1960 年代后期,我参加了斯坦福大学 Ron Bracewell 的一门非常有影响力的傅立叶技术基础课程。他特别努力强调傅里叶理论边缘的数学困难,并教导其适用性的严格限制。但他也强调了这些数学细节如何不适用于对现实世界现象的分析。或者更确切地说,他明确表示,现实世界属于狄利克雷等数学家所建立的界限。
Nevertheless, some mathematicians are still troubled by the esoteric backwaters of Fourier’s math. But engineers aren’t. In the late 1960s I took a remarkably influential foundation course on Fourier techniques from Ron Bracewell at Stanford. He took special pains to emphasize the mathematical difficulties at the edges of Fourier theory and to teach the strict limits of its applicability. But he also emphasized how those mathematical niceties don’t apply to analyses of real-world phenomena. Or rather he made clear that the real world falls within the limits established by mathematicians like Dirichlet.
数学家必须处理所有可能的模式,而不仅仅是我们在现实世界中实际发现的模式。数学家处理抽象,但工程师处理物理现实——热、光、声音、道路和桥梁以及图像。对于工程师来说,傅立叶的频率和幅度与他们描述的物理世界一样“物理”。如果大自然产生了一种模式,那么傅立叶的伟大想法几乎总是可以用来描述它。20
Mathematicians must deal with all possible patterns, not just the patterns we actually find in the real world. Mathematicians deal in abstracts, but engineers deal in physical realities—heat, light, sound, roads and bridges, and images. To engineers Fourier’s frequencies and amplitudes are as “physical” as the physical world they describe. If Mother Nature produces a pattern, then Fourier’s great idea almost always works to describe it.20
牛顿和爱因斯坦知道他们在谈论宇宙,他们的崇拜者也是如此。傅立叶没有或无法预见他伟大的音乐理念有多么普遍——当时其他人也没有。我们没有关于通过时间积累的天才或通过分支产生的天才的词。我们通常对天才的概念是终生的——无论是在成就方面还是在认可方面。
Newton and Einstein knew that they were addressing the universe, and so did their admirers. Fourier didn’t or couldn’t foresee how universal his great musical idea was—nor did others at the time. We don’t have a word for genius accumulated through time, or genius by ramification. Our usual notion of genius is local to a lifetime—both in accomplishment and in recognition.
然而,两个世纪以来,工程师们已经成功地大量使用了他的谐波理念,让我们感到舒适和享受。所有现代媒体都依赖于它。Digital Light 的像素和故事只是最新的例子之一。
Yet for two centuries engineers have made successful and massive use of his harmonic idea for our comfort and enjoyment. All of modern media depends on it. The pixel and the story of Digital Light is just one of the latest examples.
毫无疑问,傅立叶现在已经达到了他应得的位置,无论我们是否选择称其为天才。只剩下跨越两种文化的过道,让他在双方都知道和尊重。
Surely Fourier has now arrived at his deserved position, whether we choose to call it genius or not. It only remains to reach across the aisle separating the two cultures and make him known and respected on both sides.
有一个模糊的、未经证实的、未经任何人证实的传说,你仍然可能在营地里听到:这个群岛的某个地方是天堂般的小岛。. . 唯一的工作就是脑力劳动——而且所有这些都是超级超级秘密的。因此,我亲自到了那些天堂岛(在罪犯行话中,它们被称为“sharashkas”)并在他们身上花了一半的刑期。我的生存归功于他们。
There was a vague, unverified legend, unconfirmed by anybody, that you might nevertheless hear in camp: that somewhere in this Archipelago were tiny paradise islands . . . and the only work was mental work—and all of it super-supersecret. And so it was that I got to those paradise islands myself (in convict lingo they are called “sharashkas”) and spent half my sentence on them. It’s to them I owe my survival.
——亚历山大·索尔仁尼琴,古拉格群岛1
—Aleksandr Solzhenitsyn, The Gulag Archipelago1
发明像素并开始数字革命的人是俄罗斯最高苏维埃主席。然而,不是同时,而是同一个人。他的名字是弗拉基米尔·科捷尔尼科夫。2003 年,当他 95 岁时,另一位弗拉基米尔——普京——在克里姆林宫封他为爵士。到那时,他佩戴了苏维埃俄罗斯的大部分功勋勋章,包括两次斯大林奖和六次列宁勋章,并两次获得社会主义劳动英雄称号。他在 1917 年十月革命以及此后定义现代俄罗斯的所有清洗和战争中幸存下来。他几乎没有避开古拉格——索尔仁尼琴曾在其中辛勤劳作的那个岛屿——受到斯大林最血腥心腹之一的强大妻子的保护。他警告美国人不要使用人造卫星,并用数字图像(来自太空的像素)绘制金星图。
The man who invented the pixel and started the digital revolution was Chairman of the Supreme Soviet of Russia. Not at the same time but the same man, nevertheless. His name was Vladimir Kotelnikov. In 2003, when he was 95, another Vladimir—Putin—knighted him in the Kremlin. By then he sported most of the merit badges of Soviet Russia, including two Stalin Prizes and six Orders of Lenin, and was twice a Hero of Socialist Labor. He had survived the 1917 October Revolution and all the purges and wars that since define modern Russia. He had barely avoided the Gulag—the very island in it where Solzhenitsyn had toiled—protected by the powerful wife of one of Stalin’s bloodiest henchmen. He warned Americans about Sputnik and mapped Venus with digital images—pixels from space.
Kotelnikov 在美国也获得了荣誉,在 2000 年获得了亚历山大·格雷厄姆·贝尔奖章——恰如其分地发生了大数字融合。然而,他在美国基本上不为人知。他很少因为他最伟大的发现——采样定理——而得到赞誉,这个想法是整个数字媒体世界的核心。这顶皇冠通常属于美国著名工程师和数学家克劳德·香农,尽管香农从未声称过它。
Kotelnikov was honored in America too, with the Alexander Graham Bell Medal in 2000—befittingly as the Great Digital Convergence transpired. Yet he’s largely unknown in the States. He rarely gets credit for his greatest discovery—the Sampling Theorem—the idea that lies at the heart of the entire digital media world. That crown usually goes to Claude Shannon, a famous American engineer and mathematician, even though Shannon never claimed it.
与傅立叶的故事一样,科捷利尼科夫的故事也具有技术突破的三个驱动力:伟大的科学理念、将其变成必要发明的革命和战争的混乱,以及保护科学家和推广他们的技术的暴君。Kotelnikov 的伟大想法——直接导致了像素——与默默无闻的 Kotelnikov 和著名的 Shannon 极其平行的生活故事交织在一起。
Like Fourier’s story, Kotelnikov’s features three drivers of technological breakthrough: a great scientific idea, the chaos of revolution and war that turns it into a necessary invention, and tyrants who protect the scientists and promote their technology. Kotelnikov’s great idea—which led directly to the pixel—is intertwined in the remarkably parallel life stories of obscure Kotelnikov and famous Shannon.
图 2.1
Figure 2.1
想法是这样的:数字可以忠实地代表模拟。离散的、分离的、尖的可以准确地表示光滑的、连接的和弯曲的。断续可以真实地代表未断续。如果现在这不让你感到惊讶,那么我希望很快就会引起你的惊讶,因为看起来我们可以丢弃大量的信息——实际上是无限的——而不会丢失任何东西。这是使数字光(以及数字声音)成为可能的关键思想。这是促成大数字融合以及现代世界的基本真理。
Here’s the idea: digital can faithfully represent analog. The discrete and separated and spiky can accurately represent the smooth and joined and curved. The broken continual can truthfully represent the unbroken continuous. If this doesn’t surprise you now then I hope to provoke your amazement soon, because it appears that we can throw away an astounding amount of information—an infinite amount, in fact—without losing anything. This is the key idea that makes Digital Light (as well as Digital Sound) possible. It’s the fundamental truth that enabled the Great Digital Convergence and hence the modern world.
正如波是代表傅立叶频率的形状一样,也有一个形状代表 Kotelnikov 的样本(见图 2.1)。我们很快就会发现它与像素的“形状”密切相关。数学家称其为sinc,而工程师则称其为重构滤波器。因为这两个名字都不直观,所以我把这个可爱的形状称为吊具。你很快就会明白为什么。
Just as the wave is the shape that represents Fourier’s frequencies, there’s a shape that signifies Kotelnikov’s samples (see figure 2.1). We’ll soon see that it’s intimately related to the “shape” of a pixel. Mathematicians call it a sinc, and engineers a reconstruction filter. Because both those names are nonintuitive, I call this lovely shape a spreader. You’ll see why shortly.
请注意,散布器类似于傅里叶波的波峰和波谷,它们逐渐被挤压,直到它们最终在任一方向上都消失。事实上,这正是它的本质。相关波在任何地方都有一个与中央驼峰一样高的振幅,其频率与吊具的上下摆动频率相同(图 2.2)。
Notice that a spreader resembles one of Fourier’s waves with its crests and troughs progressively squeezed until they’re ultimately reduced to nothing in either direction. In fact, that’s exactly what it is. The associated wave has an amplitude everywhere as high as the central hump, and a frequency the same as the spreader’s frequency of up and down wiggles (figure 2.2).
吊具来自数学,而不是现实世界,但它可能会让你想起一颗落在静水中的鹅卵石,涟漪向外辐射,它们的高度随着距离的增加而降低。像波浪一样,吊具永远在各个方向摆动。但是距中央驼峰一定距离的波峰是如此之低,以至于它们无关紧要。正如我们将看到的,这在现实世界中很重要。最早的图片我在正确的上下文中发现的吊具出现在 Vladimir Kotelnikov 1933 年的经典俄罗斯论文中(图 2.3)。2
The spreader comes from mathematics, not the real world, but it might remind you of a pebble dropped in still water, with ripples radiating outward, their height decreasing with increasing distance. Like a wave, a spreader continues to wiggle in each direction forever. But the crests at some distance from the central hump are so low that they don’t matter. That’s important in the real world, as we’ll see. The earliest picture of the spreader that I’ve found, in correct context, appears in the classic 1933 Russian paper by Vladimir Kotelnikov (figure 2.3).2
图 2.2
Figure 2.2
图 2.3
Figure 2.3
1960 年代初,我在电气工程系第一次了解到本章的好主意。我们听说它来自美国电气工程师的英雄 Harry Nyquist。他在 AT&T 传说中的贝尔实验室工作——我们都梦想有一天能成为那里。但是在 1960 年代后期,当计算机科学最终成为一门独立的学科时,就我而言,在斯坦福大学,这个伟大的想法变成了克劳德·香农的想法。当谈到所有数字化事物时,香农是我们的新英雄。他是第一个在印刷品中使用比特这个词的人。作为奈奎斯特的年轻同事,他也在贝尔实验室工作。3
I first learned this chapter’s great idea in the early 1960s in an electrical engineering department. We heard that it came from Harry Nyquist, an American hero to us electrical engineers. He worked in the fabled Bell Labs at AT&T—where we all dreamed to be someday. But in the late 1960s, when computer science finally emerged as a separate discipline, at Stanford in my case, the great idea became Claude Shannon’s. Shannon was our new hero when it came to all things digital. He was the guy who had first used the word bit in print. And he worked at Bell Labs too, as Nyquist’s younger colleague.3
但这只是美国版本,这就是斯蒂格勒的地名法则发挥作用的地方:“没有科学发现以其最初的发现者命名。” (顺便说一句,这条定律并不是由斯蒂格勒发现的。)所以在俄罗斯,毫不犹豫地,这个想法的全部功劳总是归科捷利尼科夫所有。在日本,功劳归功于染谷功。在英格兰,致埃德蒙·惠特克爵士。在德国,赫伯特·拉贝。想来想去,奈奎斯特出生在瑞典。只有香农是一个真正的蓝色,出生于密歇根州的美国人。香农标签只是粗暴的民族主义吗?所有这些人都击败了香农,除了染谷之外,他只遵循了几个月的想法。大概保留给第一个发现者的命名荣誉几乎是最后一个发现者——不管怎样,在美国。4
But that’s just the American version, and here’s where Stigler’s Law of Eponymy comes into play: “No scientific discovery is named after its original discoverer.” (This law, by the way, was not discovered by Stigler.) So in Russia, with no hesitation, full credit for the idea always goes to Kotelnikov. In Japan, credit goes to Isao Someya. In England, to Sir Edmund Whittaker. In Germany, Herbert Raabe. Come to think of it, Nyquist was born in Sweden. Only Shannon was a true-blue, Michigan-born American. Is the Shannon tag just crude nationalism? All these men beat Shannon to a version of the idea except for Someya, and he followed by only a few months. The naming honor presumably reserved for the first discoverer went instead to almost the last—in the United States anyway.4
尽管存在归属问题,但事实很清楚:这个伟大的想法——正如它在 Digital Light 中所使用的——首先由 Kotelnikov 在 1933 年清楚、清晰、完整地陈述和证明。西方人可能很难相信这样一个基本的想法是在斯大林的俄罗斯最糟糕的日子里发明的。在冷战期间,我们被教导说,俄罗斯科学即使不像李森科的生物学那样虚假,充其量只是一种衍生品或只是宣传。是时候热身一下 Kotelnikov 值得称赞的事实了。5
Despite the attribution tangle, the facts are clear: the great idea—as it’s used in Digital Light—was first clearly, cleanly, and completely stated and proved by Kotelnikov in 1933. Westerners may find it hard to believe that such a fundamental idea was invented during the worst days of Stalin’s Russia. We were taught during the Cold War that Russian science was, if not bogus like Lysenko’s biology, at best derivative or just propaganda. It’s time to warm up to the fact that Kotelnikov deserves the credit.5
Vladimir Aleksandrovich Kotelnikov 于 1908 年出生在喀山,一座位于莫斯科以东约 500 英里的伏尔加河畔古城。很难想象还有一位科学家拥有如此完美的数学血统。他的曾曾曾曾祖父谢苗·科捷尔尼科夫是莱昂哈德·欧拉的学生,他是有史以来最伟大的数学家之一。傅里叶使用的一些数学可能来自欧拉。1757 年,谢苗成为圣彼得堡科学院的早期院士,该科学院由彼得大帝创立,现称为俄罗斯科学院。6
Vladimir Aleksandrovich Kotelnikov was born in 1908 in Kazan, an ancient city on the Volga about 500 miles straight east of Moscow. It’s difficult to think of another scientist with such an impeccable mathematical pedigree. His great-great-great-grandfather, Semyon Kotelnikov, was a student of Leonhard Euler, one of the greatest mathematicians who ever lived. Some of the mathematics that Fourier used might have come from Euler. In 1757 Semyon became an early academician of the St. Petersburg Academy of Sciences, founded by Peter the Great and now called the Russian Academy of Sciences.6
Vladimir 的祖父 Petr Kotelnikov 是喀山大学的数学家。列宁和托尔斯泰是那里最著名的两个学生,但列宁被开除,托尔斯泰也退学了。留下来的人中有著名的几何学家尼古拉·罗巴切夫斯基(Nikolai Lobachevsky)。他挑战了古希腊的欧几里得几何,提出它关于平行线的第五个假设不一定是正确的——当时这个惊人的想法最终在爱因斯坦的广义相对论中找到了归属。祖父彼得是罗巴切夫斯基的助手,然后是冠军。
Vladimir’s grandfather, Petr Kotelnikov, was a mathematician at the University of Kazan. Lenin and Tolstoy were two of the most famous students there, but Lenin was expelled, and Tolstoy quit. Among those who stayed the course was the famed geometer Nikolai Lobachevsky. He challenged the ancient Greek geometry of Euclid by suggesting that its fifth postulate about parallel lines was not necessarily true—a startling idea at the time that eventually found a home in Einstein’s general theory of relativity. Grandfather Petr was Lobachevsky’s assistant and then champion.
毫不奇怪,弗拉基米尔的父亲亚历山大·科捷尔尼科夫也是喀山大学的数学家。但当亚历山大决定离开喀山并举家搬到基辅担任新的教学职位时,弗拉基米尔的故事才真正开始。
Not surprisingly, Vladimir’s father Aleksandr Kotelnikov was also a mathematician at the University of Kazan. But when Aleksandr decided to leave Kazan and move his family to Kiev for a new teaching position, Vladimir’s story really began.
1914 年 8 月,当德国军队突破该市的防御工事时,Kotelnikovs 和 6 岁的弗拉基米尔抵达基辅。民众惊慌失措,从城里冲了出来,带着新来的人一起扫荡。他们以巨大的困难设法忍受了 850 英里的撤退到喀山。这个家庭已经卷入了第一次世界大战的第一次爆炸。这是决定弗拉基米尔生活和事业的许多战争中的第一场。7
The Kotelnikovs, with six-year-old Vladimir, arrived in Kiev on the very day in August 1914 when the German army broke through that city’s defenses. The population panicked and rushed from the city, sweeping the new arrivals with them. With enormous difficulty they managed to endure the 850-mile retreat to Kazan. The family had ridden right into the first blasts of World War I. It was the first of many wars that would define Vladimir’s life and career.7
他接下来的两场战争是 1917 年的十月革命和随后的红军和白人之间的内战。俄罗斯发生了翻天覆地的变化。年轻的弗拉基米尔也是——但改变他的并不是战争。在一片混乱中,他第一次听到了无线电广播。
His next two wars were the October Revolution of 1917 and the subsequent civil war between Reds and Whites. Russia was transformed. Young Vladimir was too—but it wasn’t the wars that changed him. In the midst of the chaos he heard, for the first time, a radio broadcast.
“它是如何工作的?” 他问父亲。
“How does it work?” he asked his father.
“这是你还无法理解的东西。”
“It’s something you can’t understand yet.”
这一挑战使他在 10 岁时专注于广播生活。在接下来的九个十年里,他大部分时间都在无线电和通信工程上度过,这一职业与苏联的兴衰相吻合。8
That challenge focused him, at age 10, on a life in radio. He would spend most of the next nine decades in radio and communications engineering, a career coincident with the rise, turmoil, and fall of the Soviet Union.8
“伟大的一年,可怕的一年,我们的主 1918 年,革命开始以来的第二年。” 米哈伊尔·布尔加科夫的《白卫队》就这样开始了,他对基辅可怕的、破坏性的、无政府主义的世界的描述。在第二次时机不佳的情况下,Kotelnikovs 恰好选择了这个不幸的时刻再次搬到基辅并亲身体验布尔加科夫的噩梦。教授煮肥皂,孩子们揭开窗帘缝线——任何可以用来驱走饥饿的东西。9
“Great was the year and terrible the Year of Our Lord 1918, the second since the Revolution had begun.” So begins Mikhail Bulgakov’s White Guard, his account of the terrible, destructive, anarchical world of Kiev. In their second case of bad timing, the Kotelnikovs picked exactly this unfortunate moment to move to Kiev again and experience Bulgakov’s nightmare firsthand. The professor boiled soap, and the children unraveled curtains for the thread—anything to sell to drive away the hunger.9
1924 年,亚历山大再次举家搬家,这次是搬到莫斯科。他在莫斯科高等技术学校获得了一个新职位。学校的一部分将很快变身为莫斯科动力工程学院(俄语为MEI),并成为世界领先的技术大学之一。把它想象成莫斯科理工学院。10
In 1924 Aleksandr moved his family yet again, this time to Moscow. He took a new position at the Moscow Higher Technical School. Part of the school would soon metamorphose into the Moscow Power Engineering Institute (MEI in Russian) and become one of the leading technical universities in the world. Think of it as the Moscow Institute of Technology.10
Vladimir,我们的 Kotelnikov,是 MEI 的第一批毕业生之一。他们最初不会接受他,因为他的知识渊源——他不是工人或农民的血统——但幸运的规则改变允许他进入,他从未离开过。他 1931 年的文凭是电气工程专业,专攻无线电。他将在该机构工作 75 年。
Vladimir, our Kotelnikov, was one of MEI’s first graduates. They wouldn’t accept him initially because of his intellectual pedigree—he wasn’t of worker or peasant stock—but a fortunate rule change allowed him to enter, and he never left. His 1931 diploma was in electrical engineering, with a specialty in radio. He would be with the institution for 75 years.
然后它发生了——他的奇迹年。1932 年,科捷尔尼科夫在没有明显监督的情况下独自创作了两篇论文,每篇论文都将让他永远载入工程史册。其中之一是“非线性滤波器理论”,我们不再关注。但另一个包含了他的好主意,即采样定理。他在 11 月提交了它,并于次年以没有希望的标题“论电子通信中的‘以太’和电线的传输能力”出版。
Then it happened—his annus mirabilis. The year 1932 saw Kotelnikov create two papers on his own, with no apparent supervision, each of which would have established him in the annals of engineering forever. One of them was “The Theory of Non-Linear Filters” and won’t further concern us. But the other contained his great idea, the Sampling Theorem. He submitted it in November, and it was published the next year with the unpromising title, “On the Transmission Capacity of ‘Ether’ and Wire in Electric Communications.”
当他把它提交给 MEI 的教员时,其中一位说:“看起来很正确,但听起来更像科幻小说。” 从无到有。尽管如此,他们还是批准了它,使他走上了通往 MEI 院长的学术轨道。11
When he submitted it to the MEI faculty, one of them said, “It appears correct, but sounds more like science fiction.” Something from nothing. Nevertheless, they approved it, launching him on an academic trajectory toward a deanship at MEI.11
1933 年,在 MEI 担任讲师后,科捷尔尼科夫还开始为人民通讯委员会(俄语为 NKS)工作。沟通是最重要的在战争中的重要性,因此布尔什维克在 1917 年 10 月红色夺取政权的那天创建了 NKS 也就不足为奇了。科捷利尼科夫在那里成为了一名通信工程师,并最终领导了自己的研究所。他总是一只脚在象牙塔里,另一只脚在现实世界的政治和战争中。12
In 1933, with a lectureship at MEI, Kotelnikov also began working for the People’s Commissariat for Communications (NKS in Russian). Communications are of utmost importance in war, so it’s no surprise that the Bolsheviks had created NKS on the very day they seized power in Red October 1917. Kotelnikov became a communications engineer there and eventually headed his own institute. He would always have one foot in the ivory tower and the other in the real world of politics and war.12
图 2.4
Figure 2.4
他正在路上,在两个著名的组织中拥有两篇重要的论文和职位。他准备在学术界和政府中迅速发展。在两条道路上,科捷尔尼科夫都必须像傅立叶那样与暴君共舞。
He was on his way, with two important papers and positions in two prestigious organizations. He was poised for rapid advancement in both academia and government. On both paths Kotelnikov would have to dance with tyrants, as Fourier had.
让我们不要对无限这个词感到害羞。实际上有许多不同类型的无穷大,但我们这里需要的只有两种是数字类型和模拟类型。熟悉的时钟秒针波图(图 2.4)将有助于清楚区分。
Let’s not be shy about the word infinite. There are actually many different kinds of infinity, but the only two we need here are the digital kind and the analog kind. The familiar diagram (figure 2.4) of the clock’s second-hand wave will help make the difference clear.
您会记得,在秒针绕表盘转动的每一个周期中,钟面上的每分钟标记都会在波浪上出现一个圆形黑点。随着秒针在表盘周围移动,圆点永远向右展开。他们有多少人?好吧,你可以数一数——一、二、三,等等——但你必须永远数数。那就是数字无限。总是有另一个。出于显而易见的原因,数学家称其为可数无穷大。
You’ll recall that there’s one round black dot on the wave for every minute mark on the clock’s face during each and every cycle the second hand makes around the dial. As the second hand progresses around and around the dial, the dots unfurl to the right forever. How many of them are there? Well, you can count them—one, two, three, and so forth—but you’ll have to count forever. That’s digital infinity. There’s always another one. Mathematicians call it countable infinity, for the obvious reason.
第二种无限,模拟无限,并不那么容易。考虑波浪上的两个连续点。点之间的波上有多少点?答:有很多你都数不过来。模拟无穷远大于数字无穷——听起来很奇怪。数学家 Georg Cantor 证明了这是真的,这就是他的意思:
The second kind of infinity, analog infinity, isn’t so easy. Consider two successive dots on the wave. How many points are there on the wave between the dots? Answer: there are so many you can’t even count them. Analog infinity is larger than digital infinity—as strange as that sounds. The mathematician Georg Cantor proved it was true, and here’s what he meant:
在波浪的任意两点之间,总会有另一点。例如,有一点——在波浪上——在两点之间。现在想想那个中点和左边的两个原点。他们之间有道理吗?是的,总是——例如,它们之间的中间点。现在重复这个四分之一点和两个原始点的左边。以此类推,无穷无尽,正如表达式所说的那样。困难在于您永远无法将其划分得足够细以结束划分过程。换句话说,你永远无法到达一个甚至可以开始数数的地方。数学家喜欢称它为不可数无穷大,但我会坚持使用模拟无穷大。两者都有效:平滑的事物具有模拟或不可数的无限部分。离散事物具有数字或可数无穷大的部分。从深刻的意义上说,数字小于模拟——即使你使用很多点来表示平滑的东西。
Between any two points on the wave, there’s always another point on it. For example, there’s the point—on the wave—halfway between the two points. Now think of that midpoint and the left of the two original points. Is there a point between them? Yes, always—for example, the point halfway between them. Now repeat for this one-quarter point and the left of the two original points. And so on, ad infinitum, as the expression goes. The difficulty is that you can never divide finely enough to reach an end to the dividing process. In other words, you can never get to a place where you can even start counting. Mathematicians like to call it uncountable infinity, but I’ll stick with analog infinity. Both work: Smooth things have an analog or uncountable infinity of parts. Discrete things have a digital or countable infinity of parts. In a profound way, digital is lesser than analog—even if you use lots of dots to represent the smooth thing.
图 2.5
Figure 2.5
但 Kotelnikov 的好主意似乎是——令人惊讶的是——数字等同于模拟。数字化不会丢失任何东西。一个离散的数字事物可以忠实地代表一个平滑的模拟事物。图 2.5 显示了一段声音片段,或者说是沿着一条水平线穿过它的视觉场景的片段。Kotelnikov 的想法在这两种情况下都有效。底部的直线是零响度或零亮度级别——完全无声或完全黑暗。曲线是声音随着时间的推移而变化的响度,或者是当你沿着一条线向右移动时视觉场景的亮度变化。在任何一种情况下,大点都会突出显示片段中等距的点。我们将通过这个一维示例建立直觉,
But Kotelnikov’s great idea appears to be—and here’s the surprise—that digital is equivalent to analog. Nothing is lost by going digital. A discrete digital thing can faithfully represent a smooth analog thing. Figure 2.5 shows a snippet of sound, say, or of a visual scene along a horizontal line through it. Kotelnikov’s idea works in either case. The straight line along the bottom is the zero loudness or zero brightness level—completely silent or completely dark. The curve is the changing loudness of the sound as time passes, or the changing brightness of the visual scene as you move to the right along one line through it. In either case the big dots highlight equally spaced points along the snippet. We’ll build intuition with this one-dimensional example, then gradually extend to the two dimensions that a full visual scene actually requires—just as we did for Fourier waves in the first chapter.
图 2.6 是如果你忽略平滑曲线上的所有点,除了大点处的点。在这些点之间,我们现在只有一条直线,即零响度或零亮度级别。不难想象二维版本会是什么样子。想想水平和垂直间隔相等的不平整的钉床。它们的高度会根据作为视觉场景的相应光滑表面上的亮度而变化。钉床将是一个“表面”,除了钉子外,其他地方都为零。
Figure 2.6 is what you get if you omit all the points on the smooth curve except the ones at the big dots. Between these points all we have now is the straight line, the zero loudness or zero brightness level. It’s not hard to imagine what the two-dimensional version would look like. Think of an uneven bed of nails, equally spaced horizontally and vertically. Their heights would vary according to the brightnesses on a corresponding smooth surface that was a visual scene. And the bed of nails would be a “surface” that is zero everywhere except at the nails.
图 2.5 为模拟,图 2.6 为数字。后者中的尖峰很自然地称为模拟曲线的样本。在二维的钉床情况下,指甲是相应模拟表面的样本。Kotelnikov 的好主意说,我们不需要完全平滑的曲线来表示声音,也不需要完全平滑的表面来表示视觉场景。我们只需要样本。换句话说,第一张图中高亮点之间的点的模拟无穷大可以忽略不计!他似乎在说没有什么可以代表什么。怎么可能?答案当然隐藏在“似乎”中。
Figure 2.5 is analog, and figure 2.6 is digital. The spikes in the latter are called, naturally enough, samples of the analog curve. In the bed-of-nails case for two dimensions, the nails are the samples of the corresponding analog surface. Kotelnikov’s great idea says that we don’t need the full smooth curve to represent a sound or the full smooth surface to represent a visual scene. We need only the samples. In other words, the analog infinity of points between the highlighted points in the first figure can be ignored! He appears to say that nothing can represent something. How could that be? The answer lies hidden, of course, in the “appears to.”
图 2.6
Figure 2.6
您可能会想,如果您只是使用更多样本并将它们“足够接近”放置,它们将成为模拟声音曲线。许多人都有同样的直觉,即像素——无论它们是什么——间隔足够近将成为它们所代表的视觉场景。但这种直觉是错误的。你不能靠得足够近。你不能让数字无限达到模拟无限。你无法计算不可数的东西。然而,Kotelnikov 似乎说你可以。是什么赋予了?
You might imagine that if you simply used more samples and placed them “close enough” they would become the analog sound curve. It’s the same intuition many people have that pixels—whatever they are—spaced closely enough together would become the visual scene they represent. But this intuition is wrong. You can’t get close enough. You can’t make digital infinity ever reach analog infinity. You can’t count what’s uncountable. Yet Kotelnikov appears to say you can. What gives?
此外,他的想法是,在第二张图中,显示的点足够接近——通过采集更接近的样本,你不会获得任何优势,也不会获得额外的信息。你还困惑吗?我希望如此,因为我们正在触及问题的症结——以及它的优雅。
Furthermore, his idea says that in the second figure the dots shown are close enough—that you gain no advantage, no additional information—by taking more closely spaced samples. Are you puzzled yet? I hope so because we’re getting to the crux of the matter—and its elegance.
随着这些问题在空中颤抖,我们几乎已经准备好第一次通过 Kotelnikov 的好主意了。但首先让我们回顾一下傅立叶的想法,因为科捷尔尼科夫的想法依赖于它。傅立叶告诉我们,模拟声音或视野可以用波的总和来表示。图 2.7 显示了我们一直在使用的模拟片段的波总和中的一个波,为方便起见,在顶部重复(用点指定样本位置)。您可以看到片段中没有任何东西比这个波更快地上下摆动,所以这个波是频率最高的那个。片段的傅立叶和中的所有其他波都具有较低的频率,否则您会在片段中的某处看到更快的摆动。
With these questions quivering in the air, we’re almost ready for a first pass at Kotelnikov’s great idea. But first let’s revisit Fourier’s idea, since Kotelnikov’s depends on it. Fourier taught us that an analog sound or visual field can be represented by a sum of waves. Figure 2.7 shows one of the waves in the sum of waves for the analog snippet we’ve been using, repeated at the top (designating the sample locations with dots) for convenience. You can see that nothing in the snippet wiggles up and down any faster than this wave, so this wave is the one with the highest frequency. All the other waves in the Fourier sum for the snippet have lower frequencies, otherwise you would see a faster wiggle somewhere in the snippet.
这是 Kotelnikov 的好主意:如果您以最高傅立叶频率的两倍对平滑的东西进行采样,那么您总是可以仅使用样本准确地恢复平滑的东西。样本是离散的、不连贯的、彼此分离的——绝对不平滑。这是他想法的第一部分——伟大的采样定理——表示可以用数字脱节性代替模拟平滑度的部分。第二部分告诉我们如何从数字样本中实际恢复原始模拟。
Here’s Kotelnikov’s great idea: if you sample something smooth at twice its highest Fourier frequency, then you can always exactly recover the smooth something using only the samples. The samples are discrete, disjointed, separated from one another—definitely not smooth. This is the first part of his idea—the great Sampling Theorem—the part that says it’s possible to substitute digital disjointedness for analog smoothness. The second part tells us how to go about the actual recovery of the original analog from the digital samples.
图 2.7
Figure 2.7
科捷尔尼科夫站在巨人傅立叶的肩膀上。傅里叶频率捕捉模拟图像在视野中的变化速度。然后 Kotelnikov 的伟大想法告诉我们如何数字化表示傅立叶波。令人惊讶的是,对于变化最快的波的每个周期,只有两个样本就足够了。直观地说,它需要两个,因为一个样本代表该波的波峰部分,另一个样本代表波谷部分。
Kotelnikov stands on the shoulders of the giant Fourier. Fourier’s frequencies capture how fast an analog picture changes across a field of view. Then Kotelnikov’s great idea tells us how to digitally represent Fourier’s waves. Astonishingly, only two samples suffice for each cycle of the fastest changing wave. It takes two, intuitively, because one sample represents the cresting part of that wave and the other the troughing part.
Kotelnikov 的视野样本在数字世界中有一个名字。我们称它们为像素。就在那里!这就是像素的定义。它与傅立叶和科捷尔尼科夫密切相关。Kotelnikov 的采样使 Digital Light 成为可能。
There’s a name in the digital world for Kotelnikov’s samples of a visual field. We call them pixels. There it is! That’s the definition of pixel. It’s intimately associated with both Fourier and Kotelnikov. Kotelnikov’s sampling is what makes Digital Light possible.
像素不是小方块!这可能会让您感到惊讶,因为它们经常以这种方式表示——事实上,许多人经常将像素与相邻的小方块等同起来——这可能是对新生数字时代最普遍的误解。像素化这个词甚至使这种误解制度化。
Pixels are not little squares! This may surprise you because very often they’re represented that way—so often, in fact, that many people equate pixels with little abutting squares of color—which is perhaps the most widespread misunderstanding of the nascent digital age. The word pixelation has even institutionalized the misconception.
事实上,像素没有形状。它们只是在规则网格上采集的样本——不均匀的指甲床。它们只存在于一点,因此它们没有范围、没有宽度、零维度。你看不到它们,它们也没有可见的颜色。它们只有一个代表灰色阴影的数字,或三个代表颜色的数字。正如我们将看到的那样,使用 Kotelnikov 的想法,从数字中恢复模拟,似乎给出了像素形状。
In fact, pixels have no shape. They’re just samples taken on a regular grid—the uneven bed of nails. They exist only at a point, so they have no extent, no width, zero dimensions. You can’t see them, and they have no visible color. They just have a number representing a shade of gray, or three numbers representing a color. It’s the recovery of analog from digital, using Kotelnikov’s idea, that appears to give a pixel shape, as we’ll see.
像素这个词本身必须为生存而战。最初,像素被称为许多其他东西——例如点、点阵列、光栅元素、图片点和图片元素。图片元素赢了,但随后发生了一场关于用速记表示该术语的斗争。多年来,IBM 和 AT&T 一直努力将其承包给pel。但是凭借他们的候选像素,1960 年代中期充满活力的年轻图像处理社区战胜了大公司的努力。事实上,在像我这样在动荡的 1960 年代成长起来的计算机图形学家中,禁止 Big Blue 和 Ma Bell 的pel是一种反主流文化的荣誉。理查德·里昂(Richard Lyon)仔细研究了变体词的使用方式和时间,在 1965 年加州理工学院喷气推进实验室的弗雷德·比林斯利(Fred Billingsley)的文件中发现了像素的最早出现,特别是在其图像处理实验室(见图 2.8,并注意KC 表示每秒千次循环)。根据里昂的说法, pel最早的公开使用来自 1967 年麻省理工学院教授威廉·施赖伯 (William Schreiber) 的一篇论文。
The word pixel itself had to fight for existence. Pixels were called many other things at first—spots, point arrays, raster elements, picture points, and picture elements, for example. Picture elements won, but then came a battle over representing the term in shorthand. For many years IBM and AT&T made an effort to contract it to pel. But with their candidate pixel, the vibrant young image-processing community of the mid-1960s triumphed over the efforts of the giant corporations. In fact, it was a point of counterculture honor among computer graphicists like me, who came of age in the tumultuous 1960s, to disallow Big Blue’s and Ma Bell’s pel. Richard Lyon, in a careful history of how and when the variant words were used, found the earliest appearance of pixel in a 1965 document by Fred Billingsley of Caltech’s Jet Propulsion Lab, specifically in its Image Processing Lab (see figure 2.8, and note that KC means thousand cycles per second). The earliest public use of pel, according to Lyon, came from a 1967 paper by the MIT professor William Schreiber.
图 2.8
Figure 2.8
许多专利在 1970 年代发布,包含像素或pel,每年像素专利的数量大大超过 pel 专利的数量。不出所料,这个时代的大多数pel专利都分配给了 IBM 或 AT&T 的贝尔实验室。如果 Nyquist 或 Shannon 为像素使用了一个词——他们没有——那肯定是pel,Ma Bell 的词。13
Many patents were issued in the 1970s containing pixel or pel, with the number of pixel patents greatly exceeding the number of pel patents each year. Most of the pel patents of this era were unsurprisingly assigned to IBM or AT&T’s Bell Labs. If Nyquist or Shannon had used a word for the pixel—they didn’t—it would surely have been pel, Ma Bell’s word.13
像素直接调用采样定理;采样和像素在出生时就被加入了。奇怪的是,声音样本没有像像素这样的词,尽管 Kotelnikov 的采样同样的技巧使数字声音成为可能。不幸的是,采样在音频中具有不同的含义。例如,在嘻哈音乐中,这意味着借用他人的整段音乐,价值几秒钟,然后将它们放在一起,或者将它们混合在一起。在这本书中,一个独特的词非常方便,所以我使用soxel(声音元素的缩写)作为声音样本的名称。
The pixel directly invokes the Sampling Theorem; sampling and pixels were joined at birth. Oddly, there’s no word like pixel for a sound sample, despite the fact that the same trick, Kotelnikov’s sampling, is what makes Digital Sound possible. Unfortunately, sampling has a different meaning in audio. In hip-hop, for example, it means to borrow whole chunks of other people’s music, several seconds worth, and put them together, or mash them up. A distinct word is quite handy in this book, so I use soxel—a contraction of sonic element—as the name of the sound sample.
一个更严重的命名问题出现了,因为在今天的美国,Kotelnikov 的采样定理几乎总是归因于香农。如果你忽略世界其他地方,很容易看出原因。克劳德·香农在美国是一个响亮的名字。在他 1948 年的论文“通信的数学理论”中,他陈述了采样定理。在他 1949 年极具影响力和经典的论文“存在噪声中的通信”中,他陈述并证明了采样定理,其形式现在通篇使用数字世界,尤其是数字光。随着他在美国赢得许多最高奖项——例如,国家科学奖章和广大电气和电子工程师协会 (IEEE) 的荣誉奖章,他的地位不断提高。他是第一位获得 IEEE 信息理论学会同名克劳德 E. 香农奖的人,因为他创立的领域。在国际上,他获得了第一个京都奖,相当于数学科学的诺贝尔奖。14
A more serious naming issue arises because in the United States today, Kotelnikov’s Sampling Theorem is nearly always attributed to Shannon. If you ignore the rest of the world, it’s easy to see why. Claude Shannon is a towering name in America. In his 1948 paper, “A Mathematical Theory of Communication,” he stated the Sampling Theorem. In his massively influential and classic 1949 paper, “Communication in the Presence of Noise,” he stated and proved the Sampling Theorem in the form now used throughout the digital world, particularly in Digital Light. His stature grew as he won many top awards in the United States—for example, the National Medal of Science and the Medal of Honor of the vast Institute of Electrical and Electronic Engineers (IEEE). He was the first recipient of the eponymous Claude E. Shannon Award of the IEEE Information Theory Society, for the field he established. Internationally, he won the first Kyoto Prize, an equivalent of the Nobel for mathematical sciences.14
克劳德·埃尔伍德·香农于 1916 年 4 月 30 日出生于密歇根州的佩托斯基。他在附近的盖洛德长大,据说他在他家和朋友家之间的铁丝网围栏上制作了一条粗糙的电报线。他喜欢杂耍、密码和国际象棋。他是一个顽皮的天才。他骑着独轮车穿过麻省理工学院的大厅,在那里他获得了博士学位,后来又穿过了贝尔实验室的大厅,在那里他发明了信息论。他在一个盒子里制造了一台机器,它只做一件事:当你拨动侧面的开关时,盖子打开,伸出一只手臂,然后拨动开关。
Claude Elwood Shannon was born on April 30, 1916, in Petoskey, Michigan. He grew up in nearby Gaylord where he reputedly crafted a crude telegraph line from the barbed-wire fences between his house and a friend’s. He loved juggling, secret codes, and chess. He was a playful genius. He rode unicycles through the halls at Massachusetts Institute of Technology, where he got his PhD, and later through the halls at Bell Labs, where he invented information theory. He built a machine in a box that did one thing: when you toggled a switch on its side, the lid opened, an arm reached out, and toggled off the switch.
香农是密码学大师,他在 1945 年写了一篇名为“密码学数学理论”的机密论文。在第二次世界大战期间,他分析了用于富兰克林·D·罗斯福和温斯顿·丘吉尔之间安全通信的 X 系统。香农能够在数学上证明其加密方案是牢不可破的。香农也是存在噪音的通信领域的重量级人物,这实际上是他 1949 年论文的标题。他展示了如何在整个太阳系中发送数字信息,从而消除在途中因宇宙噪声而发生的损坏,从而揭示原始信息。香农的想法使得从好奇号一路可靠地发送火星电影成为可能流动站到你的笔记本电脑上——所以很自然地,香农的名字被附在了采样定理上。但这不是香农的主意。他自己也是这么说的。15
Shannon was a master of cryptography and wrote a classified paper in 1945 called “A Mathematical Theory of Cryptography.” During World War II he analyzed the X System that was used for secure communications between Franklin D. Roosevelt and Winston Churchill. Shannon was able to prove mathematically that its encryption scheme was unbreakable. Shannon was also a heavyweight in the field of communication in the presence of noise, the title of his 1949 paper in fact. He showed how to send digital messages across the solar system in such a way that corruption occurring en route from cosmic noise could be removed to reveal the original message. Shannon’s ideas made it possible to reliably send movies of Mars all the way from the Curiosity rover to your laptop—so it was natural that Shannon’s name was attached to the Sampling Theorem. But it wasn’t Shannon’s idea. He said so himself.15
“这是传播艺术中的常识,”他在 1949 年的论文中写道。“它以前曾由数学家以其他形式给出,但尽管它具有明显的重要性,但似乎并没有明确地出现在传播理论的文献中。” 16
“This is a fact which is common knowledge in the communication art,” he wrote in the 1949 paper. “It has been given previously in other forms by mathematicians but in spite of its evident importance seems not to have appeared explicitly in the literature of communication theory.”16
但是通信界的某个人早在香农之前就已经以正确的形式和完整的证明陈述了采样定理。Kotelnikov 早在 1933 年就这样做了,比这早了十多年。为什么香农不提他?也许是因为早期的论文是作为晦涩的俄罗斯会议论文集的一部分发表的,而香农根本不知道。但正如我们将看到的,他保持沉默的原因很难确定。他本可以在二战期间俄罗斯和美国共享的非常秘密的科学背景下了解科捷尔尼科夫的采样定理。但两国之间的冷战分裂会在那些年里,香农要么无法公开他对定理的了解,要么无法了解它。
But somebody from the communications world had stated the Sampling Theorem—in the right form and with the full proof—long before Shannon. Kotelnikov had done so in 1933, well over a decade earlier. Why didn’t Shannon mention him? Perhaps because the earlier paper had been published as part of obscure Russian conference proceedings, and Shannon simply didn’t know about it. But as we’ll see, the reason for his silence is hard to determine. He could have learned about Kotelnikov’s Sampling Theorem in the context of the very secret science Russia and the United States shared during World War II. But the bitter Cold War division between the countries would have prevented Shannon either from making his knowledge of the theorem public or from learning about it during those years.
图 2.9
Figure 2.9
这是两个并排的巨人(图 2.9)。1932 年,24 岁的科捷尔尼科夫在左边——留着更狂野的发型——比他证明采样定理早一年。右边是身材苗条的香农,年龄未定,但可能是 32 岁左右,接近他在 1949 年初证明的时间。两人都是各自国家数字通信的领导者——尤其是在存在噪音或加密的情况下的通信。两人都获得了最高奖项。两者都陈述并证明了今天在数字光中使用的采样定理。
Here are the two giants, side by side (figure 2.9). Kotelnikov is on the left—with the wilder hairdo—in 1932 at age 24, a year before he proved the Sampling Theorem. On the right is the slender Shannon at an undetermined age, but perhaps about 32, near the time of his proof in early 1949. Both men were leaders of digital communications in their respective countries—especially communications in the presence of noise or encryption. Both received the highest awards. And both stated and proved the Sampling Theorem as it’s used today in Digital Light.
我们不禁怀疑是否存在跨文化泄漏。奇怪的是,几年后,年轻的香农经常与科捷尔尼科夫的智力成就相提并论——但我没有发现任何证据表明香农知道科捷尔尼科夫的工作。无论如何,俄罗斯人将这个伟大的想法称为科捷尔尼科夫采样定理也就不足为奇了。我们不应该吗?17
We can’t help but wonder if there was cross-cultural leakage. Curiously, the younger Shannon often paralleled Kotelnikov’s intellectual achievements a few years later—but I’ve found no evidence that Shannon knew Kotelnikov’s work. In any case, it’s no surprise that Russians call the great idea Kotelnikov’s Sampling Theorem. Shouldn’t we?17
Kotelnikov 想法的后半部分——伟大的采样定理——告诉我们如何从非平滑像素重建平滑图像,并准确地做到这一点。这令人惊讶的是,数字图像中似乎几乎不存在任何信息——在每对像素之间简单地省略了模拟的无穷多点。数字音频和每对索素也是如此。采样定理的后半部分告诉我们在哪里可以找到那些缺失的无穷大。
The second half of Kotelnikov’s idea—the great Sampling Theorem—tells us how to reconstruct a smooth picture from non-smooth pixels, and to do it accurately. The surprise about digital is that almost no information seems to exist in a digital image—an analog infinity of points has simply been omitted between each pair of pixels. The same goes for digital audio and each pair of soxels. The second half of the Sampling Theorem tells us where those missing infinities can be found.
图 2.10
Figure 2.10
以下是如何从数字中恢复模拟。用传播器传播每个像素,这是本章的基础形状。将结果相加。而已。采样定理告诉我们,这种扩展和相加过程准确地再现了像素之间缺失的无穷大!与所有伟大的定理一样,这样的推论一点也不明显。我们必须相信数学。
Here’s how to recover the analog from digital. Spread each pixel with the spreader, the shape fundamental to this chapter. Add up the results. That’s it. The Sampling Theorem tells us that this spreading and adding process accurately reproduces the missing infinities between the pixels! As with all great theorems, such deductions aren’t at all obvious. We have to trust the math.
运行示例将再次提供帮助,但为简单起见仅显示了两个 soxel(图 2.10),即两个中心点。(我们将很快将其扩展到像素。)回想一下,soxel 是模拟声音曲线的样本,其中曲线在零线上方的高度代表它的响度。因此,索素的高度代表了索素采样点处曲线的响度。右侧的索克索比左侧的索克索声音更小——更安静。
The running example will help again, but with only two soxels shown for simplicity (figure 2.10), the two central ones. (We’ll extend it to pixels shortly.) Recall that a soxel is a sample of an analog sound curve, where the height of the curve above the zero line represents its loudness. So the height of a soxel represents the loudness of the curve at just that point sampled by the soxel. The soxel at the right is less loud—quieter—than the one on the left.
首先,我们将传播我们在图 2.1 中看到了带有撒布器的左侧索素。回想一下,它以与原始片段的最高频率的傅里叶波相同的频率摆动。它在中央驼峰处的最大振幅(响度)代表音量一直向上。要进行撒播,请将左侧索素替换为撒播器的副本(图 2.11)。我想说的是,这会将 soxel 从无形状(无)传播到显示的形状(有)。它的最高点——中央驼峰的顶峰——与它所取代的索克具有相同的响度。两个索素显示为虚线。特别是,这清楚地表明了扩展器的高度(其最大响度)与左侧索克的高度相匹配。在本例中,响度为全音量的 80%。想象一下,您有一个用于调节响度的旋钮。
First we’ll spread the left soxel with the spreader, which we saw in figure 2.1. Recall that it wiggles at the same frequency as the Fourier wave with the highest frequency of the original snippet. Its maximum amplitude (loudness), at the central hump, represents the volume turned all the way up. To do the spreading replace the left soxel with a copy of the spreader (figure 2.11). I like to say that this spreads the soxel from no shape (nothing) to the shape shown (something). Its highest point—the peak of its central hump—has the same loudness as the soxel it replaces. The two soxels are shown dashed. In particular, this makes clear that the height of the spreader—its maximum loudness—matches that of the left soxel. In this example, that loudness is 80 percent of full volume. Imagine that you have a knob for that loudness adjustment.
现在将扩展器的另一个副本移动到右侧索素上方的位置(图 2.12)并旋转旋钮,直到其最大响度与该索素的响度相匹配,在本例中为全音量的 50%——因此散布第二个索素。
Now move another copy of the spreader into place over the right soxel (figure 2.12) and twiddle the knob until its maximum loudness matches that soxel’s loudness, in this example 50 percent of full volume—hence spreading the second soxel.
这是将这两个“spread soxels”相加的结果(图 2.13)。在每个水平位置,取那里散布的 soxels 的两个高度(浅灰色),从零响度线测量,并将它们加在一起以获得粗曲线上的一个点。
And here’s the result (figure 2.13) of adding these two “spread soxels” together. At each horizontal position take the two heights of the spread soxels there (light gray), measured from the zero-loudness line, and add them together to get a point on the bold curve.
图 2.11
Figure 2.11
图 2.12
Figure 2.12
图 2.13
Figure 2.13
到目前为止,我忽略了现实。吊具——本章的特色形状——在现实世界中并不存在。它无限广阔。它继续永远地左右波动。显然,现实世界的吊具不可能如此广泛,因此现实世界的吊具必须是理想吊具的近似值。
I’ve ignored reality so far. The spreader—this chapter’s featured shape—doesn’t exist in the real world. It’s infinitely broad. It continues to ripple left and right forever. Obviously, no real-world spreader can be that broad, so real-world spreaders by necessity have to be approximations of the ideal spreader.
一种流行、实用且非常精确的吊具称为立方吊具(图 2.14)。请注意它与理想吊具的中间部分有多相似,包括存在两个负向波瓣(低于零响度线)。在中心样本的左侧和右侧两个样本(即由撒布器传播的那个)之外,立方撒布器在任何地方都为零。换句话说,它具有有限的宽度,因此它可以存在于现实世界中。
A popular, practical, and remarkably accurate spreader is called a cubic spreader (figure 2.14). Note how closely it resembles the middle part of the ideal spreader, including the presence of two lobes going negative (below the zero-loudness line). The cubic spreader is zero everywhere beyond two samples left and two right of the central sample—the one spread by the spreader. In other words, it has a finite width, so it can exist in the real world.
图 2.14
Figure 2.14
图 2.15
Figure 2.15
到目前为止,我所描述的是一维传播。声音仅在一维(时间)上变化,因此它是索素的准确图片,但不是像素的准确图片。像素扩展器必须在二维中扩展,因为图像在二维(空间)中扩展,通常称为水平和垂直。像素散布器必须将每个钉子(像素)散布在钉床中,以便每个“散布像素”都有助于我们可以看到的二维表面。您可以认为前面的图准确地显示了像素散布器在水平维度上的横截面,请记住,垂直维度上的横截面是完全相同的。但我们可以做得更好。
What I’ve described so far is one-dimensional spreading. Sound varies in one dimension only (of time) so it’s an accurate picture for soxels, but not for pixels. A pixel spreader must spread in two dimensions since images extend in two dimensions (of space), often called horizontal and vertical. A pixel spreader must spread each nail (pixel) in a bed of nails so that each “spread pixel” contributes to a two-dimensional surface that we can see. You can think of the preceding figures as accurately showing the cross section of a pixel spreader in the horizontal dimension, keeping in mind that the cross section in the vertical dimension is exactly the same. But we can do better.
图 2.15 显示了一个完整的二维像素扩展器。将断头台从其最亮的地方扔下——这样刀片就可以将这座小山切成两半,从山顶到底部,如图所示。然后显示的出血边缘正是上面的立方分布器。如果你把小山切成两半,你会看到同样的边缘。由于这个像素散布器在每个维度上都是一个立方散布器,所以它被称为双三次散布器。它是Adobe Photoshop(最古老和最流行的像素应用程序之一)中内置的那种,用于更改图片的大小。
Figure 2.15 shows a full two-dimensional pixel spreader. Drop a guillotine through its brightest point—so that the blade slices the little mountain in half, from its peak to its base as shown. Then the bleeding edge revealed is exactly the cubic spreader above. You’d see the same edge if you cut the little mountain in half the other way. Since this pixel spreader is a cubic spreader in each dimension, it’s called a bicubic spreader. It’s the kind built into Adobe’s Photoshop (one of the oldest and most popular pixel apps) for changing the size of a picture.
图 2.16
Figure 2.16
图 2.17
Figure 2.17
所以现在让我们展开并添加一行像素,但让我们使用这个双三次展开器而不是理想的展开器来实现。为了简单和一致,我们将在横截面中执行此操作。但是想象一下,每个吊具实际上是一座小山,就像我们刚刚看到的那样——不平坦的钉床在另一个维度上延伸,每个钉子上都有一座小山。首先,我们散布像素(图 2.16)。
So now let’s spread and add a row of pixels, but let’s do it by using this bicubic spreader instead of the ideal one. For simplicity and consistency, we’ll do this in cross section. But imagine that each spreader is actually a little mountain like the one we’ve just seen—and that the uneven bed of nails extends in the other dimension with a little mountain at each of its nails. First, we spread the pixels (figure 2.16).
然后我们将它们全部加起来,以获得无处不在的亮度。图 2.17 显示了沿着通过视觉场景的一条水平线的结果。粗体亮度曲线重建了原始模拟片段,为了便于比较,我在其下方重复了该片段。它并不完美——只是一个近似值——因为我们使用了一个不太理想的吊具,但它很接近。与原始钥匙相比,它就像一把磨损或重复的钥匙。双方的牙齿都打开了锁。
Then we add them all up to get a resulting brightness everywhere. Figure 2.17 shows that result along one horizontal line through a visual scene. The bold brightness curve reconstructs the original analog snippet, which I repeat just below it for ease of comparison. It’s not perfect—just an approximation—since we’ve used a less than ideal spreader, but it’s close. It’s like a worn or duplicate key compared to the original. The teeth of either open the lock.
你可以想象,这些数字——对于十几个像素来说已经很复杂了——对于比如一百万个像素来说会变得非常复杂。重要的一点是每个步骤都很简单:将吊具移动到位,调整其亮度,然后将其添加到其他吊具上。我们有一种野兽,它可以一遍又一遍地重复简单的步骤,而不会感到困惑或无聊——当然是计算机。这就是为什么接下来的两章是关于计算机及其惊人的能力来放大(用大写字母A!)一个微不足道的人类步骤——比如说——将一个像素扩展一百万或十亿倍,而且做得非常快,更不用说将所有这些散布像素加起来。一个加法很简单——即使是人类也能做到——但它需要重复一百万或十亿次。这就是为什么我们需要计算机来真正实现数字光,尽管 Kotelnikov 和傅立叶的数学表明我们原则上可以做到。
You can imagine that these figures—already complex for just a dozen or so pixels—would become hopelessly complex for, say, a million pixels. The important point is that each step is simple: move a spreader into place, adjust its brightness, and add it to the others. We have a beast that can repeat an easy step over and over and not become confused or bored—the computer, of course. That’s why the next two chapters are about the computer and its marvelous ability to Amplify (with a capital A!) a puny human step—spreading one pixel, say—by a millionfold or billionfold, and to do it very fast, not to mention adding up all those spread pixels. One addition is simple—even a human can do that—but it needs to be repeated a million or a billion times. That’s why we need computers to actually realize Digital Light even though Kotelnikov’s and Fourier’s math shows that we can do it in principle.
让我们再次穿越魔法。有人在很远的地方——比如在北京——拍摄了一个事件的视频,也许是一场歌剧,或者是一个声音的录音,也许是一场音乐会,然后把大部分都扔掉了,只保留了一些样本。也许这些像素或索素流是从距离地球数千英里的通信卫星上反弹回来的,或者通过万维网运送给旧金山的你。在您访问它之前,该流可能已经存在于计算机文件或 DVD 中的某处多年。在穿越时空的所有旅程中,原始的模拟无限消失了。它所存在的只是你看不到或听不到的像素或索像素。即使您最终将它们下载到您的计算机或手机上,模拟无穷大仍然丢失,您仍然无法看到或听到它们。然后神奇的事情发生了:你决定看像素或听索素。在那一刻,我刚刚描述的传播和添加——重建——发生了,你会看到北京人在许多英里或几年前所做的完全模拟的无限信息。
Let’s step through the magic again. Someone took a video of an event, an opera perhaps, or an audio recording of a sound, maybe a concert, somewhere far away—in Beijing say—and threw most of it away, preserving only samples of it. Perhaps that stream of pixels or soxels was bounced off a communications satellite thousands of miles above the Earth or shipped across the World Wide Web to you in San Francisco. The stream may have lived in a computer file or on a DVD somewhere for years before you accessed it. During all that journey through space and time, the analog infinity of the original was missing. All that existed of it was pixels or soxels you couldn’t see or hear. Even when you finally downloaded them onto your computer or cellphone, the analog infinity was still missing, and you still couldn’t see or hear them. Then the magic happens: You decide to look at the pixels or listen to the soxels. There, at that moment, the spreading and adding I just described—the reconstruction—happens and you witness the full analog infinity of information that the person in Beijing did, many miles or years ago.
丢失的无穷大只有在屏幕或扬声器上显示时才会重新出现——而不是之前。我们认为我们正在携带图像或声音,但我们不是。我们正在运输一种高度压缩的形式。上个世纪的旧媒体——例如电影和视频——确实保留了从源头到通信通道到显示器的整个路径上的模拟无穷大。新媒体将其缩写为数字样本,并且仅在最后一刻重新发明原始模拟图像或声音。
The missing infinity only reappears when it’s displayed on the screen or the speaker—and not before. We think we’re carrying around the picture or the sound, but we aren’t. We’re transporting a highly compressed form of it. The old media of the last century—film and video, for example—did preserve the analog infinity all along the path from the source through the communication channel to the display. The new medium abbreviates it to digital samples and only reinvents the original analog picture or sound at the last possible moment.
所以这就是采样定理的秘密,以及为什么它不是真的一劳永逸。我们使用的任何吊具,无论它是否理想,都是模拟形状:它具有模拟无限点。通过在每个像素上放置一个扩展器(无穷大的小斑点)并将结果相加,我们有效地在任何地方重新引入了模拟无穷大。像素之间明显的空白被像素扩展器中携带的东西所覆盖。这是一个非常巧妙的技巧。采样定理重新包装了无穷大。数学的力量将我们从直觉的束缚中解放出来,这在科捷尔尼科夫的伟大想法中得到了充分发挥。
So here’s the secret of the Sampling Theorem, and why it’s not really something for nothing. Any spreader that we use, whether it’s the ideal one or not, is an analog shape: it has an analog infinity of points. By putting a spreader at each pixel—little blobs of infinity—and adding up the results, we effectively reintroduce analog infinity everywhere. The apparent nothing between pixels is covered by the something carried in the pixel spreader. It’s a very neat trick. The Sampling Theorem repackages infinity. The power of mathematics to free us from the bounds of our intuition is at full play in Kotelnikov’s great idea.
图 2.18
Figure 2.18
像素在被散布器散布之前是没有形状的。我经常将它们绘制为侧视图或正视图,以方便绘图,作为适当高度的尖峰。图 2.18(左)显示了运行示例的中心两个像素。
Pixels have no shape until they’re spread by a spreader. I’ve often drawn them for pictorial convenience as a side view, or in elevation, as spikes of the appropriate height. Figure 2.18 (left) shows the center two pixels of the running example.
表示像素的另一种方法是从上方查看它们,可以这么说,这样您就可以自然地“看到”它们。但是我们看不到像素。它是我们看到的散布像素。那么,从上方看,散布像素是什么样子的——也就是说,当我们实际查看像素时?图 2.18(中)是使用 Photoshop 的双三次散布器散布的两个像素的图片。这是两座小山,从它们的山峰上往下看。左侧较浅的散布像素几乎看不到,但它就在那里,与较暗的像素重叠。
Another way to represent pixels is by looking at them from above, so to speak, so that you can “see” them in a natural way. But we can’t see pixels. It’s spread pixels that we see. So what does a spread pixel look like from above—that is, as we actually view pixels? Figure 2.18 (middle) is a picture of the two pixels, as spread with Photoshop’s bicubic spreader. It’s two little mountains as seen from above their peaks, looking down. The lighter spread pixel on the left is barely visible, but it’s there, overlapped by the darker one.
两个展开的像素肯定不像图 2.18(右)中的邻接正方形。
The two spread pixels certainly don’t look like the abutting squares in figure 2.18 (right).
如果您必须为像素指定形状,则使用散布像素的斑点图像作为指导,并记住与相邻像素的重叠。但真的,真的,像素没有形状。这是一个直径为零的点。只有散布像素有形状。如果它是一个你可以看到的像素——如果它有一个可见的形状——那么它一定是一个扩展的像素。
If you must give a shape to a pixel, then use the blobby image of spread pixels as your guide and remember the overlap with neighboring pixels. But really, truly, a pixel has no shape. It’s a point with zero diameter. Only spread pixels have shape. If it’s a pixel you can see—if it has a visible shape—then it must be a spread pixel.
很容易理解小正方形概念的来源。常见的应用程序支持这种错觉。我在 Photoshop 中制作了这个小图 2.19(左,仔细看)。它是白色背景上的 14 个灰色像素簇,太小而无法轻易看到。当然,您实际上并没有在这里看到 14 像素。您会看到 14 个散布像素。
It’s easy to understand where the little square notion comes from. Common apps support the illusion. I made this—tiny—figure 2.19 (left, look carefully) in Photoshop. It’s a cluster of 14 gray pixels on a white background, and too small to see easily. Of course, you’re not actually seeing 14 pixels here. You’re seeing 14 spread pixels.
几乎所有像素应用程序都有一个称为缩放的功能,或者一些变体。缩放旨在向您展示图片的近距离外观,就好像它是通过放大镜观看的一样。图 2.19(中)显示了使用 Photoshop 的 Zoom In 将 14 个像素放大 16 倍的结果。
Nearly all pixel apps have a feature called Zoom, or some variant. Zoom purports to show you what a picture looks like up close, as if it were viewed through a magnifying glass. Figure 2.19 (middle) shows the result of using Photoshop’s Zoom In to make the 14 pixels 16 times larger.
图 2.19
Figure 2.19
那么像素肯定是小方块,对吧?一点也不。Zoom 使用了一种快速而肮脏且不准确的技巧,让您认为它在“放大”。缩放只是将每个像素水平重复 16 次,然后将每行 16 个相同的副本垂直重复 16 次。结果是每个原始像素都被替换为 16 x 16 的相同颜色像素的正方形阵列。所以每个数组看起来——真是令人惊讶——就像那个颜色的正方形。但每个正方形绝对不是一张原始像素特写的图片。这是一张200多张的照片每个原始像素的(扩展)像素,排列成一个正方形。Zoom 技巧在过去计算机速度慢的糟糕时代很有用,但在现代世界中,它只是具有误导性。是时候摒弃像素是小方块的概念了。从来都不是真的。
Surely then the pixels must be little squares, right? Not at all. Zoom uses a quick-and-dirty—and inaccurate—trick to make you think it’s “magnifying.” Zoom simply repeats each pixel 16 times horizontally, and then repeats each row of 16 identical copies 16 times vertically. The result is that each original pixel is replaced with a 16 by 16 square array of pixels of the same color. So each array looks—what a surprise—like a square of that color. But each square is definitely not a picture of one of the original pixels close up. It’s a picture of more than 200 (spread) pixels for each original pixel, arranged in a square. The Zoom trick was useful back in the bad old days of slow computers, but in the modern world it is simply misleading. It’s time to scotch the notion that pixels are little squares. It never was true.
图 2.19(右)向您展示了原始图片的真实样子,当 Photoshop 将 Photoshop 适当放大 16 倍时(具有称为图像大小的功能)。采样定理的后半部分解释了为什么你会看到斑点,每个斑点的中心都是原始灰色,但在各个方向都迅速软化为更白的灰色阴影,部分重叠相邻的斑点。
Figure 2.19 (right) shows you what the original picture looks like really, when Photoshop does a proper magnification by 16 (with a feature called Image Size). The second half of the Sampling Theorem explains why you see blobs, each with the original gray in the center but softening rapidly in every direction to whiter shades of gray, partially overlapping neighboring blobs.
斯大林的大清洗——大恐怖——从 1934 年持续到 1939 年。它是由克格勃的前身、臭名昭著的内务人民委员部(NKVD)实施的。许多人在臭名昭著的表演审判中被判处死刑,数十万甚至数百万俄罗斯人被送往古拉格群岛的战俘营——这些岛屿。是索尔仁尼琴向我们讲述了古拉格和正在发生的“在人们记忆中的历史上前所未有”的悲剧。18
Stalin’s Great Purge—the Great Terror—lasted from 1934 to 1939. It was implemented by the notorious NKVD (People’s Commissariat for Internal Affairs), predecessor of the KGB. Many were condemned to death in the infamous show trials, and hundreds of thousands, perhaps millions, of Russians were sent to the prison camps—the islands—of the Gulag Archipelago. It was Solzhenitsyn who taught us about the Gulag and the unfolding tragedy that “was unprecedented in remembered history.”18
Kotelnikov的两个暴君从这种恐怖中出现。大恐怖的权威历史学家罗伯特·康奎斯特(Robert Conquest)将领导清洗的四位强大的年轻斯大林主义者描述为“特别凶残”。其中有科捷利尼科夫的暴君格奥尔基·马林科夫和拉夫伦蒂·贝利亚。19
Two tyrants for Kotelnikov emerged from this horror. Robert Conquest, the definitive historian of the Great Terror, described four powerful young Stalinists who led the purge as “particularly murderous.” Among them were Kotelnikov’s tyrants Georgi Malenkov and Lavrenti Beria.19
马林科夫于 1941 年 2 月在莫斯科向第十八次党代会的报告拉开了又一次清洗的序幕,即斯大林的秘密清洗,仅次于大清洗。马林科夫透露,工业产能锐减,无能横行。因此,就在希特勒于 6 月入侵俄罗斯之前,数十个人民委员会(俄语中的 NK——我们可能称之为联邦局或国家部门)被摧毁,尤其是通讯人民委员会 (NKS)。整个 NKS 都解散了——除了 Kotelnikov 的实验室,因为它在战时的重要性而没有受到影响。20
Malenkov’s report to the Eighteenth Party Conference in Moscow in February 1941 kicked off yet another purge, Stalin’s Secret Purge, second only to the Great Purge. Malenkov revealed that industrial capacity was plummeting, and incompetence was rampant. So just before Hitler invaded Russia in June, dozens of the People’s Commissariats (NKs in Russian—what we might call Federal Bureaus or National Departments) were decimated, including in particular the People’s Commissariat for Communications (NKS). The entire NKS was disbanded—except for Kotelnikov’s lab, which was left untouched because of its wartime importance.20
二战期间,斯大林领导了一个管理国家的五人委员会:马林科夫和贝利亚都是成员。贝利亚还在副手维克托·阿巴库莫夫的协助下管理内务人民委员会,他是科捷利尼科夫的第三位暴君。当斯大林创建 SMERSH(是的,你们伊恩弗莱明的粉丝,这个反情报组织确实存在)时,他让阿巴库莫夫负责。
During World War II, Stalin headed a committee of five that ran the country: Malenkov and Beria were both members. Beria also ran the NKVD with the assistance of a deputy, Viktor Abakumov, a third Kotelnikov tyrant. When Stalin created SMERSH (yes, you Ian Fleming fans, this counterintelligence organization really existed), he put Abakumov in charge.
二战后马林科夫变得强大,起初仅次于斯大林。斯大林控制马林科夫和贝利亚的技巧是将阿巴库莫夫提升到更高的位置。因此,贝利亚和阿巴库莫夫掌管着控制古拉格奴隶劳改营的国家机器。他们在列宁格勒组织了大规模处决他们的对手,并将数千人送往集中营。1953年斯大林去世后,马林科夫成为苏联总理。
After World War II Malenkov became powerful, second only to Stalin at first. Stalin’s technique for keeping Malenkov and Beria under control was to raise Abakumov to a still higher position. So Beria and Abakumov ran the state apparatus that controlled the Gulag slave labor camps. They organized massive executions of their rivals in Leningrad and had thousands more sent to the camps. And when Stalin died in 1953, Malenkov became Premier of the Soviet Union.
但马林科夫对科捷尔尼科夫的重要性主要在于他的妻子瓦莱里娅·戈卢布佐娃。她将成为科捷尔尼科夫职业生涯中的决定性力量——他的保护者。21
But Malenkov’s importance for Kotelnikov lay principally in his wife, Valeriya Golubtsova. She would be the defining force in Kotelnikov’s career—his protectress.21
戈卢布佐娃拥有一流的革命血统。她的母亲奥尔加是涅夫佐罗夫姐妹中的一员——齐奈达、索菲亚、阿夫古斯塔和奥尔加——早在十月革命之前,她们年轻时都是列宁核心圈子的一部分。其中两个姐妹嫁给了有关系的男人:Zinaida 和她的丈夫 Gleb Krzhizhanovsky 在求爱和早婚期间与列宁和他的妻子一起流亡西伯利亚。格列布是列宁的朋友,也是革命运动中最年长的人物之一,自 1893 年以来一直是党员。索菲亚的丈夫谢尔盖·谢斯特宁 (Sergei Shesternin) 是列宁信任的拥有绝密布尔什维克财务的人。22
Golubtsova had a first-rate revolutionary pedigree. Her mother, Olga, was one of the Nevzorov sisters—Zinaida, Sophia, Avgusta, and Olga—who were part of Lenin’s inner circle when they were all young, long before the October Revolution. Two of the sisters married men with connections: Zinaida and her husband Gleb Krzhizhanovsky had spent exile in Siberia with Lenin and his wife during their courtships and early marriage years. Gleb was Lenin’s friend and one of the oldest figures in the revolutionary movement, a Party member since 1893. Sophia’s husband, Sergei Shesternin, was the man Lenin trusted with top-secret Bolshevik finances.22
Golubtsova 非常出色——她自己是莫斯科动力工程学院 (MEI) 的一名学生,当时女性工程师几乎闻所未闻。她也很强大,很难,而且很酷。作为一个坚定的组织者,她成为了 MEI 的长期主管,并将其变成了一个学术强国。当她为她的机构找到一位知识明星——比如科捷尔尼科夫——时,她可以而且会确保他留在那里,而不是在古拉格。如果她自己不完全是一个暴君,她非常有效地利用她的暴君身份得到了她想要的东西。23
Golubtsova was brilliant—a student at Moscow Power Engineering Institute (MEI) herself when women engineers were almost unheard of anywhere. She was also powerful, difficult, and cool. A determined organizer, she became MEI’s longtime director and turned it into an academic powerhouse. When she spotted an intellectual star for her institution—such as Kotelnikov—she could and would make sure he stayed there and not in the Gulag. If not exactly a tyrant herself, she used her tyrant-in-law status very effectively to get what she wanted.23
Kotelnikov 制定了采样理论,并设计了将像素散布到图片中的理想方式。但他当时不知道这些想法将如何实际用于实践。一方面,现代数字世界有一个巨大的实际假设:实际设备,而不仅仅是理论波,将在另一端进行必要的传播和添加,以恢复您眼睛所需的模拟光。
Kotelnikov worked out the theory of sampling, and he designed the ideal way to spread a pixel into a picture. But he had no idea at the time of the way those ideas would actually come to be used in practice. For one thing, there’s a huge practical assumption in the modern digital world: an actual device, and not just a theoretical wave, will be at the other end to do the spreading and adding necessary to restore the analog light your eye requires.
Digital Light 之所以有效,是因为它假设丢失的信息会神奇地出现——以适当的像素散布器的形式——在过程中的某个地方,在显示的那一刻。数字声音的工作方式相同。它假设稍后某处会有一个设备将 soxels 传播到您耳朵所需的原始模拟声音中。声音的显示是一个扬声器系统和为其供电的放大器。实际上,显示是从样本中重建模拟原件(大脑需要的形式)的行为。
Digital Light works because it assumes that the missing information will magically appear—in the form of an appropriate pixel spreader—somewhere in the process, at the moment of display. Digital Sound works the same way. It assumes there’ll be a device somewhere later that will spread the soxels into the original analog sound that your ear requires. The display of sound is a speaker system and the amplifier that feeds it. Display, in fact, is the act of reconstructing the analog original—the form your brain needs—from samples.
显示是现代世界的一个基本假设。伟大的数字融合取决于这样一个事实,即相同的像素——图像的相同抽象表示——可以通过无数种技术以无数种方式显示。
Display is a fundamental assumption of the modern world. The Great Digital Convergence depends on the fact that the same pixels—the same abstract representation of an image—can be displayed in myriad ways by myriad technologies.
如果您用手机拍照,然后在电脑屏幕上查看,您可能会看到两种不同的像素分布。如果您在纸上查看它,毫无疑问您正在目睹不同的传播。唯一不变的是显示器后面的实际像素,由显示器重建的不可见像素,一个带有数字的点 - 如果它是彩色的,则为三个数字。Digital Light 的一项不为人知的成就是将不同显示技术的变幻莫测——毫无疑问还会有更多——减少到称为显示器的薄硬件层及其称为显示驱动程序的软件。每个制造商都有自己的显示器和驱动程序。除了像素本身,我们用户不必担心任何事情。我们的显示器进行传播。
If you take a picture with your cellphone and then look at it on your computer screen, chances are that you’re seeing two different pixel spreads. If you view it on paper, there’s no question that you’re witnessing a different spread. The only thing that’s constant is the actual pixel behind the display, the invisible one that’s reconstructed by the display, a point with a number attached—or three numbers if it’s colored. One of the unsung accomplishments of Digital Light is the reduction of the vagaries of different display technologies—and many more to come, no doubt—to a thin layer of hardware called the display and its software called a display driver. Each manufacturer makes its own displays and drivers. We users never have to worry about anything but the pixels themselves. Our displays do the spreading. This is the Great Digital Convergence at work.
这是一个分裂的融合。它在像素的创建和显示之间形成了一个楔子。在创意空间中,像素是简单、纯粹和通用的。在 Display Space 中,橡胶与道路相遇。现实世界技术的所有肮脏问题都与传播创意空间提供的像素的问题有关。在这里,数千家制造商的工程专业知识专注于在实际物理材料(等离子、液晶、荧光粉、墨水)的现实限制范围内对理想吊具进行高质量近似。我们用户需要担心的只是创意空间的柏拉图像素。这就是为什么我敦促传播可以感知的像素不应与不能感知的实际像素相混淆。让我们不要将稀薄的展示空间与广阔的创意空间混为一谈。
It’s a convergence that divides. It drives a wedge between the creation and display of pixels. In Creative Space, pixels are simple, pure, and universal. In Display Space, the rubber meets the road. All the nastiness of actual real-world technology comes to bear on the problem of spreading the pixels that are supplied from Creative Space. Here’s where the engineering expertise of thousands of manufacturers is focused on high-quality approximations of the ideal spreader within the real-world limitations of actual physical stuff—plasmas, liquid crystals, phosphors, inks. All we users need to worry about are the platonic pixels of Creative Space. That’s why I’ve urged that the spread pixel, which can be perceived, should not be confused with the actual pixel, which cannot. Let’s not conflate thin Display Space with vast Creative Space.
显示器制造商通常将显示器中的小发光元素称为“像素”。但这会将扩展像素与像素混淆。这些应该称为显示元素,而不是像素。这些显示元件之一的辉光——发射的照明,在中心高,从中心逐渐减小到零——是特定显示设备的散光器。一个像素进入显示元素,一个扩展像素出来,这就是你实际看到的。一般来说,发光形状是制造商独有的,甚至在同一家公司的产品之间也会有所不同。
Often display manufacturers call the little glowing elements in their displays “pixels.” But this confuses the spread pixel with the pixel. These should be called display elements, not pixels. The glow—the emitted illumination, high at the center, diminishing to zero away from center—of one of these display elements is the spreader for a particular display device. A pixel goes into the display element, a spread pixel comes out, and that’s what you actually see. Generally, the glowing shape is unique to the manufacturer and can even vary from product to product at the same company.
所以,这就是 Digital Light 的工作原理:它从现实世界中提取像素,甚至从火星或金星——或者从我们将看到的计算机内部的虚幻世界——中提取像素并将它们发送到各处。这些像素只携带离散的位置和强度(或颜色)信息。似乎来自像素的实际光仅在您用眼睛看到它之前的最后一刻由显示设备产生 - 而不是在世界各地或我们姐妹行星之间的任何中间位置。原始画面的流畅度只会重新出现在显示屏中。如果像素的原始创建做得很好,根据采样定理,并且如果将这些像素重建为模拟显示器也做得很好,也根据采样定理,那么您所看到的就是原始的准确表示。我们做从无到有。像素是虚无——它没有维度——而显示器上显示的彩色光斑就是某物。采样定理使这个方案成为可能。没有它,数字世界就不会存在。
So, here’s how Digital Light works: It extracts pixels from the real world, even from Mars or Venus—or from unreal worlds inside computers, as we’ll see—and sends them all over. These pixels carry only discrete position and intensity (or color) information. The actual light that seems to come from a pixel is only produced by a display device at the last possible moment before you see it with your eyes—not at any of those intermediate places around the world or among our sister planets. The smoothness of the original picture only reappears in the display. If the original creation of the pixels is done well, as per the Sampling Theorem, and if the reconstruction of those pixels into an analog display is done well, also per the Sampling Theorem, then what you see is an accurate representation of the original. We do get something from nothing. The pixel is the nothing—it has no dimension—and the displayed colored blob of light of the display is the something. The Sampling Theorem enables this scheme. The digital world wouldn’t exist without it.
“扰频器的想法是通过人工手段再现人声。. . 通过将至少主要谐波加在一起来重现它,每个谐波都由一组单独的脉冲传输。你当然熟悉笛卡尔直角坐标——每个男生都熟悉——但是傅立叶级数呢?”
“The idea of the scrambler is to reproduce the human voice by artificial means . . . to reproduce it by adding together at least the main harmonics, each transmitted by a separate set of impulses. You are familiar, of course, with Cartesian rectangular coordinates—every schoolboy is—but what about Fourier’s Series?”
——亚历山大·索尔仁尼琴,在第一圈24
—Aleksandr Solzhenitsyn, In the First Circle24
1936 年,当 Kotelnikov试图使其更广泛地传播时, Electrichestvo ( Electricity ) 期刊拒绝了 Kotelnikov 的论文——具有采样定理的论文。但那一年还有一件更耐人寻味的事情:科捷利尼科夫访问了美国!我对此有所暗示,并能够找到他下船记录的图像。上面显示他有60天的签证,他的旅行是由苏联政府支付的,他的目的地是纽约市的Amtorg贸易公司。25
Kotelnikov’s paper—the one with the Sampling Theorem—was rejected in 1936 by the Electrichestvo (Electricity) journal when he tried to get it into wider circulation. But there was a far more intriguing event that year: Kotelnikov visited the United States! I picked up a hint of this and was able to find an image of his disembarkation record. It reveals that he had a 60-day visa, his trip was paid for by the Soviet government, and his destination was the Amtorg Trading Corporation in New York City.25
Armand Hammer 于 1924 年成立了 Amtorg,以促进苏联和美国之间的贸易。他是一个迷人的人,是美国共产党创始人的儿子,他以美国社会主义工党的“手臂和锤子”标志命名。Armand 是一位著名的商人(西方石油公司的负责人)、慈善家和艺术品收藏家。
Armand Hammer had formed Amtorg in 1924 to facilitate trade between the USSR and the US. He was a fascinating man, son of a founder of the Communist Party USA, who named him after the “arm and hammer” logo of the Socialist Labor Party of America. Armand was a noted businessman (head of Occidental Petroleum), philanthropist, and art collector.
但 Amtorg 不仅仅是一家贸易公司。它是工业和军事间谍活动的温床。事实上,一份解密的 NSA(国家安全局)报告显示,美国在 1931 年花费了大量精力试图破解在 Amtorg 和莫斯科之间使用的密码。美国的努力失败了,因为“俄罗斯人使用一次性密码本进行加密”。26
But Amtorg was more than a trading company. It was a hotbed of industrial and military espionage. In fact, a declassified NSA (National Security Agency) report reveals that the United States expended major effort in 1931 trying to crack the codes that were used between Amtorg and Moscow. The US effort failed because “the Russians were using a one-time pad for their encipherment.”26
这一点特别有趣,因为依赖一次性预共享密钥的一次性密匙加密系统在接下来的十年里都没有被证明是有效的。Amtorg 间谍显然至少在没有证据的情况下信任它这么长时间。尽管我们并不确切知道 Kotelnikov 在 1936 年在那里做了什么,但创建和破解密码似乎比交易更有可能。
This is particularly interesting because the one-time pad encryption system, which depends on a one-time, pre-shared key, wasn’t proved effective for another decade. Amtorg spies obviously trusted it without proof for that long at least. Although we don’t know exactly what Kotelnikov was doing there in 1936, creating and breaking codes seems a lot more likely than trade.
或者他正在收集一次性垫使用情况的数据——因为证明一次性垫系统可靠性的人是 Kotelnikov。他在 1941 年 6 月 22 日希特勒入侵苏联前三天提交了他的证明。也许并不奇怪,香农也证明了一次性垫系统的可靠性;它于 1945 年出现在机密出版物中,并于 1949 年公开发表。27
Or perhaps he was gathering data on one-time pad usage—because the man who proved the reliability of the one-time pad system was Kotelnikov. He submitted his proof just three days before Hitler’s June 22, 1941, invasion of the Soviet Union. Perhaps not surprisingly, Shannon also proved the reliability of the one-time pad system; it appeared in a classified publication in 1945 and publicly in 1949.27
Kotelnikov 一定是在他的实验室里完成了他的一次性工作——这是斯大林秘密清洗之后唯一的 NKS 通讯委员会残余。该实验室幸存下来是因为军方迫切需要其无线电通信方面的机密工作。但随着德国人在 1941 年末迅速逼近莫斯科,科捷利尼科夫没有抓住他们可能突破的机会。他将他的实验室疏散到乌法,比喀山更东约 300 英里,莫斯科以东 800 英里。28
Kotelnikov must have done his one-pad work in his lab—the only remnant of the NKS communications commissariat after Stalin’s Secret Purge. The lab had survived because its classified work on radio communication was urgently needed by the military. But as the Germans fast approached Moscow in late 1941, Kotelnikov took no chances that they might break through. He evacuated his lab to Ufa, about 300 miles further east even than Kazan, so 800 miles east of Moscow.28
在斯大林格勒战役期间,俄罗斯前线一直依赖有线通信,并且在不可避免地出现电线故障时遭受了严重损失。Kotelnikov 的实验室生产了通过无线电而不是电线进行通信的安全设备,到 1943 年,战场上的军队开始使用这些设备。同年,他因其发展而获得了他的第一个斯大林奖。后来,在 1945 年 5 月,当局使用实验室的设备在德国签署投降协议时将莫斯科与苏联代表团联系起来。次年,科捷尔尼科夫获得了他的第二个斯大林奖。29
During the battle of Stalingrad, the Russian front had depended on wire communications and had suffered gravely when, inevitably, the wires failed. Kotelnikov’s lab produced secure devices that communicated via radio rather than wire, and by 1943 armies in the field were using the equipment. He received his first Stalin Prize that same year for its development. Then later, in May 1945, authorities used the lab’s equipment to connect Moscow to the Soviet delegation at the signing of Germany’s capitulation. Kotelnikov received his second Stalin Prize the following year.29
当实验室从乌法返回莫斯科时,它落入了内务人民委员会的控制之下。在这个危险时刻,莫斯科动力工程学院(MEI)新任院长戈卢布佐娃挺身而出,提出科捷尔尼科夫可能愿意回到她的机构,他的母校。他抓住了这个机会。她的干预将他作为绝密项目的负责人从 NKVD 的监狱系统中解救出来。30
When the lab returned to Moscow from Ufa, it fell under the control of the NKVD. At this dangerous moment Golubtsova, the new director of Moscow Power Engineering Institute (MEI), stepped forward and proposed that Kotelnikov might like to return to her institution, his alma mater. He leapt at this chance. Her intervention saved him, as head of a top-secret project, from the NKVD’s prison system.30
在苏联,成功是危险的。有成就的科学家和工程师是 sharashka 的饲料。sharashka 监狱是内务人民委员会在古拉格经营的臭名昭著的秘密科学研究和开发监狱之一。索尔仁尼琴也向我们介绍了它们。它们是他的天堂岛. 许多科学家和工程师被囚禁在天堂,以确保特定的导弹、飞机或核弹只献给俄罗斯母亲。被送往俄罗斯偏远省份严寒的可怕劳改营的囚犯被饿死、冻死,甚至被活活打死。sharashkas 中的“特权”囚犯吃得饱饱且温暖。但是他们仍然在监狱里,通常是几十年。这些是迄今为止人类设计的最令人惊讶的监狱——为最优秀和最聪明的人而设的监狱,他们离开的希望渺茫。31
Success was dangerous in the Soviet Union. Accomplished scientists and engineers were sharashka fodder. A sharashka was one of the infamous secret scientific research and development prisons run by the NKVD in the Gulag. Solzhenitsyn taught us about them too. They were his paradise islands. Many scientists and engineers were imprisoned in paradise to ensure that a particular missile, plane, or nuclear bomb was devoted only to Mother Russia. Prisoners sent to the horrendous labor camps in the bitter cold of remote Russian provinces were starved, frozen, and worked to death. The “privileged” prisoners in sharashkas were well-fed and warm. But they were in prison nevertheless, often for decades. These are the most surprising prisons yet devised by man—prisons for the best and brightest, with little hope that they could ever leave.31
Marfino sharashka(图 2.20)位于莫斯科北部的前顿悟修道院,专门用于秘密通信设备和安全系统。如果没有戈卢布佐娃,科捷尔尼科夫可能会到那里救了他。他的乌法实验室的其他成员当然做到了,成为其首席科学家和设计师。亚历山大·索尔仁尼琴也这样做了。他的小说《第一圈》讲述了他在 1947 年至 1950 年间生活的这个沙拉什卡的生活。32
The Marfino sharashka (figure 2.20), in the former Monastery of the Epiphany in the northern part of Moscow, was devoted to secret communications equipment and security systems. Kotelnikov would probably have ended up there if Golubtsova hadn’t rescued him. Other members of his Ufa lab certainly did, becoming its principal scientists and designers. And Aleksandr Solzhenitsyn did too. His novel In the First Circle is an account of life in this very sharashka, where he lived from 1947 to 1950.32
图 2.20
Figure 2.20
在第一圈是一个罗马谱号。索尔仁尼琴本人由两个角色代表,而斯大林则以他自己的身份出现。它还有负责 sharashkas 系统的 Beria 和 MGB 的负责人 Abakumov——NKVD 的后裔和克格勃的前身。这部小说包含一个有趣的角色,弗拉基米尔·切尔诺夫,一位数学家、教授和院士,与 MGB 有着特殊的关系——肯定代表弗拉基米尔·科捷尔尼科夫。考虑以下两个来自In the First Circle 的引文:
In the First Circle is a roman à clef. Solzhenitsyn himself is represented by two of the characters, and Stalin appears as himself. It also features Beria, who was responsible for the system of sharashkas, and Abakumov, the head of the MGB—a descendant of the NKVD and forerunner of the KGB. The novel contains an intriguing character, Vladimir Chelnov, a mathematician, professor, and Academician, with a special relationship to the MGB—surely representing Vladimir Kotelnikov. Consider the following two quotations from In the First Circle:
切尔诺夫教授是马菲诺监狱唯一免于穿工作服的囚犯。阿巴库莫夫本人已被要求授权。
Professor Chelnov was the only prisoner at Marfino excused from wearing overalls. Abakumov himself had been asked to authorize it.
切尔诺夫被派到马菲诺研究一个万无一失的扰频器的数学原理——一种自动旋转开关继电器组的装置,从而混淆了电脉冲发出的顺序,从而扭曲了人类的声音即使是配备一百个类似设备的一百个监视器也不会有丝毫的机会解读谈话内容。33
Chelnov had been sent to Marfino to work out the mathematical principles for a foolproof scrambler—a device of which the automatic rotation switched banks of relays on and off, thereby confusing the order in which electrical impulses were sent out and so distorting the sound of human speech over the telephone that not even a hundred monitors equipped with a hundred similar devices would have the slightest chance of unscrambling the conversation.33
Vladimir Kotelnikov 是一位数学家、教授和(未来的)院士,与 MGB 有着特殊的关系——也就是说,受到 Golubtsova 的保护——是语音加扰设备方面的专家。他承认他曾使用贝尔实验室的 Homer Dudley 于 1939 年发表的一篇声码器或语音编码器论文作为俄罗斯扰频器开发的基础。34
Vladimir Kotelnikov, a mathematician, professor, and (future) Academician, with a special relationship to the MGB—meaning, protected from it by Golubtsova—was an expert in voice scrambling devices. He acknowledged that he had used a 1939 vocoder, or voice coder, paper by Homer Dudley of Bell Labs as the basis for scrambler development in Russia.34
小说中的下一段引文将这一切联系在一起:
The next quotation from the novel ties it all together:
“什么?你是什么意思,人工语音设备?” 一名囚犯向阿巴库莫夫报告。“我们这里没有人这么叫。他们在反对向外国科学磕头的运动中更名了。这是一个声码器。语音编码器。或者加扰器。” 35
“What? What d’you mean, artificial speech device?” a prisoner reported to Abakumov. “Nobody at our place calls it that. They changed its name during the campaign against kowtowing to foreign science. It’s a vocoder. Voice coder. Or scrambler.”35
1947 年,真正的阿巴库莫夫把科捷尔尼科夫叫到他的 MGB 办公室,并向他概述了一个专门研究“绝对安全受限”的无线电电话设备的实验室。在第一圈中,这表明特殊设备是偏执狂斯大林的直接要求,而囚犯索尔仁尼琴在马菲诺工作。阿巴库莫夫提议让科捷利尼科夫担任专业实验室的著名负责人,并以津贴和特权使这笔交易更加甜蜜。令人震惊的是,考虑到他正在对付的凶手,科捷尔尼科夫拒绝了这个提议。
In 1947 the real Abakumov called Kotelnikov to his MGB office and outlined to him a Specialized Laboratory for “absolutely security-restricted” radio telephone equipment. In the First Circle suggests that the special equipment was a direct request from a paranoid Stalin, and that prisoner Solzhenitsyn worked on it at Marfino. Abakumov proposed that Kotelnikov be the prestigious head of the Specialized Laboratory, and he sweetened the deal with perks and privileges. Stunningly, considering the murderous man he was dealing with, Kotelnikov declined the offer.
“嗯,很遗憾,”阿巴库莫夫回答,结束了会议。
“Well, that’s a pity,” responded Abakumov, and ended the meeting.
阿巴库莫夫很可怕,连贝利亚都怕他。Kotelnikov 被这句结束语吓得要死,立即去找 Golubtsova,告诉她发生了什么事。
Abakumov was terrifying, even Beria was afraid of him. Deathly frightened by that closing remark, Kotelnikov went immediately to Golubtsova and told her what’d happened.
“嗯,你自己想要什么?”
“Well, what do you yourself want?”
“去MEI工作。”
“To work at MEI.”
“然后继续像以前一样冷静地工作,”她建议道。36
“Then continue to work calmly as before,” she advised.36
她又救了他。
She had saved him again.
科捷尔尼科夫实际上代替斯大林的扰频器或除此之外所做的事情来自于 1947 年在 Golubtsova 的 MEI 办公室举行的一次会议的记录。著名的俄罗斯火箭科学家鲍里斯·切尔托克向她报告了他的导弹开发 sharashka 的需求。
What Kotelnikov actually did instead of—or in addition to—Stalin’s scrambler follows from an account of a 1947 meeting in Golubtsova’s MEI office. Boris Chertok, a famed Russian rocket scientist, reported to her about the needs of his missile development sharashka.
“在很短的时间内,这次会议的结果超出了我们最乐观的预期。39 岁的 Vladimir Kotelnikov 教授负责开发我提出的想法,”他回忆道。“在我与 MEI 科学家会面大约十天后,Golubtsova 的办公室发布了斯大林签署的关于在 MEI 建立一个特别行动部门的政府法令。一年后,团结在科捷利尼科夫周围的集体已经在开发 Indikator-D 系统,我们在 1948 年第一批 R-1 国产导弹的飞行试验中使用了该系统。从这一开发开始,所有后续导弹都配备了 MEI试飞期间的无线电系统。” 37
“Within a short time, the results of this meeting exceeded our most optimistic expectations. Thirty-nine-year-old Professor Vladimir Kotelnikov was in charge of developing the ideas I had posed,” he remembered. “Literally about ten days after my meeting with the MEI scientists, Golubtsova’s office issued a governmental decree signed by Stalin on the creation of a special operations sector at MEI. A year later, the collective that had rallied around Kotelnikov was already developing the Indikator-D system, which we used during the flight tests of the first R-1 domestic missiles in 1948. Beginning with this development, all subsequent missiles were equipped with MEI radio systems during test flights.”37
R-1 是俄罗斯版的 V-2,德国用来轰炸伦敦的沃纳·冯·布劳恩的火箭。
The R-1 was the Russian version of the V-2, Wernher von Braun’s rocket used by Germany to pound London.
“1951 年,MEI 集体参加了一项创建遥测系统的竞赛,第一枚 R-7 洲际导弹配备了现在具有传奇色彩的 Tral 系统。”
“In 1951, the MEI collective entered a competition for the creation of telemetry systems, and the first R-7 intercontinental missile was equipped with its now legendary Tral system.”
R-7是他们的第一个洲际弹道导弹(ICBM)。
The R-7 was their first intercontinental ballistic missile (ICBM).
MEI“团结在 Kotelnikov 周围的集体”是俄罗斯首字母缩略词 OKB MEI 正式已知的 sharashka,大概是在 Chertok 运行他的 sharashka NII-88 时,由他从受保护的位置领导。科捷尔尼科夫对太空竞赛的贡献由此开始。38
The MEI “collective that rallied around Kotelnikov” was the sharashka known formally by the Russian acronym OKB MEI, presumably led by him from his protected position just as Chertok ran his sharashka, NII-88. Thus began Kotelnikov’s contributions to the space race.38
到目前为止,我所说的好像像素可以代表任何亮度级别。但是模拟曲线上的一个点是一个模拟值,这意味着它可以具有任何模拟无穷大的值。严格来说,图片亮度的模拟样本不是像素。它只有在转换为比特时才成为一个像素,然后它才会传播成为您在显示器上看到的光晕。一个数字样本,例如一个像素,只能采用某些离散值,它们的数量是有限的。
So far I’ve talked as if pixels could represent any brightness level whatsoever. But a point on an analog curve is an analog value, meaning it can have any of an analog infinity of values. Strictly speaking, an analog sample of a picture’s brightness isn’t a pixel. It only becomes a pixel when it’s converted to bits and only then will it be spread to become the glow you see on a display. A digital sample, such as a pixel, can take only certain discrete values, a finite number of them.
在我们在接下来的章节中讨论计算机之前,一些“计算机语言”在这里很方便。众所周知,位可以有两个值,通常称为 1 和 0。将位视为电灯开关。它有两个位置,通常称为上下。考虑两个电灯开关。他们可以担任多少职位?嗯,它们可以同时上升,或者都下降,或者以两种不同的方式一个上升另一个下降。所以答案是四个。换句话说,两个位(灯开关)可以有四个值。三可以有八个值。正如我们已经注意到的,第三个开关可以向上或向下,另外两个开关可以处于四个不同的位置。二乘四等于八。一般来说,随着电灯开关的数量增加一,开关可以采取的不同位置的数量增加一倍。为您省去麻烦,
Some “computerspeak” is handy here, before we get to computers in the next chapters. Famously a bit can have two values, usually called 1 and 0. Think of a bit as a light switch. It has two positions, often called up and down. Consider two light switches. How many positions can they be in? Well, they can both be up, or both down, or one up and the other down in two different ways. So the answer is four. In other words, two bits (light switches) can have four values. Three can have eight values. The third switch can be up or down, and the other two switches can be in four different positions, as we’ve already noticed. Two times four is eight. In general, as the number of light switches increases by one, the number of different positions the switches can assume doubles. To save you the trouble, I’ll simply tell you that 8 bits (light switches) can hold 256 values (positions), 10 bits can hold 1,024 values, and 16 bits can hold 65,536 values.
在计算机图形学的前几十年,通常将黑白图像的像素限制为 8 位。这意味着一个像素可以代表仅有的 256 种灰度中的一种。例如,值 0 和 255 可以分别代表黑色和白色,中间分布有 254 种其他灰色。但模拟曲线上的实际值可能是 49.673。要做什么?好吧,最接近的可用灰度值 50 将附加到该点的像素,因此当稍后将其重建到显示器上时,会在图片中引入一个小错误。亮度的微小舍入误差有多严重?50 是否“足够接近” 49.673 无关紧要?什么是像素亮度“足够接近”?
In the first decades of computer graphics it was common to limit a pixel of a black-and-white image to 8 bits. It meant that a pixel could represent one of only 256 shades of gray. For example, values 0 and 255 could represent black and white, respectively, with 254 other grays distributed in between. But the actual value on the analog curve might be 49.673. What’s to be done? Well, the closest available gray value, 50, would be attached to the pixel for that point, hence introducing a small error into the picture when it’s reconstructed later onto a display. How bad is that tiny round-off error in brightness? Is 50 “close enough” to 49.673 to not matter? What is “close enough” for pixel brightnesses?
在这种情况下,我们确实可以选择“足够接近”的值。医生,尤其是放射科医生,会在显示器上阅读 CAT 扫描和 MRI 扫描,并根据他们看到的情况做出诊断。因此,医疗行业的显示器制造商已经精确地测量了人类的灰度感知。他们提供的图表显示,普通人可以在我的特定桌面显示器上区分 630 种灰度。所以有两点很清楚。首先,过去只有 256 个可能值的 8 位像素还不够好。但是,其次,一个 10 位像素,有超过一千个可能的值就足够了。当您在一千多个选择中四舍五入到最接近的值时,人眼无法看到引入的错误。现代数字图像现在使用 16 位灰度像素,具有超过 65000 种灰度。这对于愚弄人脑来说已经绰绰有余了——任何人都可以进行任何展示。声音显示中的 16 位索像素也是如此。39
Here’s a case where we really can choose values that are “close enough.” Doctors, particularly radiologists, read CAT scans and MRI scans on displays and base their diagnoses on what they see. Display manufacturers for the medical profession, therefore, have measured human grayscale perception precisely. A chart they provide shows that normal humans can distinguish 630 shades of gray on my particular desktop display. So two things are clear. First, the 8-bit pixel of yore with only 256 possible values isn’t good enough. But, second, a 10-bit pixel, with over a thousand possible values is more than good enough. The human eye can’t see the error that’s introduced when you round off to the nearest value among a thousand-plus choices. Modern digital images now use 16 bits for a grayscale pixel, with over 65 thousand shades of gray. That’s easily more than enough to fool the human brain—any human for any display. The same goes for 16-bit soxels in the display of sound.39
您是否听过发烧友说 LP(或黑胶唱片)比 CD 更好?在视觉世界中,声称数码摄影永远无法与胶片摄影的微妙之处相提并论。这样的主张往往充满激情。他们有实质内容吗?嗯,当然有。有几种方法可能会导致错误地进行数字采样 - 每个像素或每像素的值不够、散布器糟糕或不够高采样频率。但这些主张的许多拥护者认为,他们批评的是数字化存在本质上的问题,而他们真正批评的是执行不力。如果一位工程师决定制作一张完全复制黑胶长播放 (LP) 专辑内容的 CD,那么理论上说她可以做到。同样,如果另一位工程师下定决心要从复制胶片照片的数字图像中打印出来,那么理论上说他可以做到。这两种情况都不容易。该理论必须尽可能接近理想地实践,但这是可能的。
Have you heard audiophiles say that LPs (or vinyl) are better than CDs? In the visual world the claim is that digital photography will never match the subtlety of film photography. Such claims are often held with great passion. Is there substance to them? Well, of course there is. There are several ways that digital sampling can be done incorrectly—not enough values per pixel or soxel, a lousy spreader, or insufficiently high sampling frequency. But many adherents of these claims believe they are criticizing something intrinsically wrong with digital, when what they’re really criticizing is poor execution. If an engineer set her mind on making a CD that replicated exactly what was on a vinyl long-playing (LP) album, the theory says that she could do it. Similarly, if another engineer set his mind to making a print from a digital image that duplicated a filmed photographic print, the theory says that he could do it. It wouldn’t be easy in either case. The theory would have to be practiced as near ideally as possible, but it would be possible.
一些发烧友声称能够区分以高于每秒 44,100 索像素 CD(光盘)标准的采样率录制的录音,该标准具有每索像素 16 位的特点。回想一下,人耳每秒可以听到高达 20,000 个周期(最高傅立叶频率),因此 Kotelnikov(或 Nyquist)采样率为每秒 40,000 索塞尔。CD 超过了 Kotelnikov 要求的从 soxels 进行完美模拟声音重建的最低要求。因此,如果该理论是可信的,那么没有人应该能够检测到使用更高采样率的系统对 CD 的改进。
Some audiophiles claim to be able to distinguish recordings made at higher sampling rates than the 44.1 thousand soxels-per-second CD (compact disc) standard which features 16 bits per soxel. Recall that the human ear can hear up to 20 thousand cycles per second—the highest Fourier frequency—so the Kotelnikov (or Nyquist) sampling rate is 40 thousand soxels per second. CDs exceed the minimum required by Kotelnikov for perfect analog sound reconstruction from soxels. So, if the theory is to be believed, then nobody should be able to detect an improvement over a CD with a system using a higher sampling rate.
专家可能能够检测到的另一种错误是舍入误差——索克的响度值数量不足。但正如已经提到的,没有人耳能做出比标准 CD 的 16 位索像素提供的更精细的区分——每个索像素大约有 65,000 个可能的响度级别。因此,对于每索像素使用更多位的系统,应该没有人能够检测到对 CD 的改进。
The other kind of error that an expert might be able to detect is round-off error—an insufficient number of values of loudness for a soxel. But as already mentioned, no human ear can make finer distinctions than those provided by the 16-bit soxel of the standard CD—with about 65,000 possible loudness levels per soxel. So nobody should be able to detect an improvement over a CD with a system using more bits per soxel.
两种在采样率和每像素位数方面都超过 CD 的标准数字音频系统是超级音频 CD (SACD) 和 DVD-Audio (DVD-A)。一项精心控制的科学测试得出了这样的结论:
Two standard digital audio systems that exceed the CD in both sampling rate and bits per soxel are Super Audio CD (SACD) and DVD-Audio (DVD-A). A carefully controlled scientific test came to this conclusion:
我们根据音乐类型和具体节目分析了所有的测试数据;高分辨率技术的类型;录音年龄;和听众年龄、性别、经验和听力带宽。这些变量都没有显示出与结果的任何相关性,或者答案和掷硬币结果之间的任何差异。40
We have analyzed all of the test data by type of music and specific program; type of high-resolution technology; age of recording; and listener age, gender, experience, and hearing bandwidth. None of these variables have shown any correlation with the results, or any difference between the answers and coin-flip results.40
换句话说,即使是发烧友也无法区分 CD 与 SACD 或 DVD-As。但是——这很能说明问题——同样的实验者报告说“几乎所有的 SACD 和 DVD-A 录音听起来都比大多数 CD 更好。” 在搜索与录音工程师的对话后,他们发现这是因为他们比制作典型 CD 录音的工程师更正确地使用了采样定理。教训是数字可以是模拟的准确表示,但必须正确完成。或者换一种说法,数字化并没有什么本质上的劣势。
In other words, even audiophiles couldn’t distinguish CDs from SACDs or DVD-As. But—and this is telling—the same experimenters reported that “virtually all of the SACD and DVD-A recordings sounded better than most CDs.” After searching conversations with the recording engineers, they found that this was because they used the Sampling Theorem much more correctly than the engineers who create the typical CD recording. The lesson is that digital can be an accurate representation of analog, but it has to be done correctly. Or stated another way, there is nothing intrinsically inferior about digital.
昨天晚上我们忘了和朋友安排去乡下旅行。我们从床头柜上拿起一个类似烟嘴的小物件。它是我们星球上每个居民都拥有的供私人使用的接收兼传输电视机。我们发出朋友的呼叫信号并按下按钮。. . . 我们肯定会有这些小电视机放在马甲口袋里。
Yesterday evening we forgot to arrange with a friend for a trip into the country. We pick up from the bedside table a small object resembling a cigarette holder. It is a receiving-cum-transmission television set for private use such as every inhabitant of our planet possesses. We give the call signal of our friend and press a button. . . . We shall certainly have these tiny television sets which will go in the waistcoat pocket.
——Kotelnikov,预测手机,1957 41
—Kotelnikov, predicting the mobile phone, 195741
1957 年 8 月 27 日,科捷利尼科夫第二次访问美国,就在人造卫星发射之前——这一事件震惊了美国。这是国际地球物理年,标志着冷战时期科学交流中断的结束。科捷尔尼科夫现在是苏联科学院的正式成员,他正在为美国人携带来自俄罗斯的信息。他在科罗拉多州博尔德举行的一次会议上说,苏联将很快发射一颗卫星,该卫星将以每秒约 20 到 4000 万(兆)周期的频率进行广播。他被忽略了。美国人不会相信苏联科学已经取得了如此大的进步。但在 10 月 4 日,人造卫星以每秒 20.005 和 40.002 兆周期的速度发射和广播。太空竞赛如火如荼地进行着,科捷尔尼科夫也在场。42
Kotelnikov visited the United States a second time, on August 27, 1957, just before the launch of Sputnik—an event that shocked America to the bone. It was the International Geophysical Year, marking the end of the Cold War interruptions in scientific exchange. Kotelnikov was now a full member of the USSR Academy of Sciences, and he was carrying information from Russia for the Americans. He told a conference in Boulder, Colorado, that the Soviets would soon launch a satellite that would broadcast at frequencies of about 20 and 40 million (mega) cycles per second. He was ignored. Americans wouldn’t believe that Soviet science had progressed so far. But on October 4, Sputnik launched and broadcast at 20.005 and 40.002 megacycles per second. The space race was on in earnest, and Kotelnikov was there.42
差不多二十年后,当它结束时,他也在那里。1971 年在莫斯科举行的一次会议上,新任命的苏联科学院代理院长科捷尔尼科夫向美国外交官宣布,由于技术原因,拟议的阿波罗-礼炮试验任务将无法运行,但苏联已准备好继续取而代之的是重命名的阿波罗-联盟号测试项目。始于 1975 年 7 月的阿波罗-联盟号联合航天项目是两国缓和的最有力象征之一。43
He was there too when it ended, almost two decades later. At a 1971 meeting in Moscow, Kotelnikov, the newly appointed acting head of the USSR Academy of Sciences, announced to surprised US diplomats that the proposed Apollo-Salyut Test Mission wouldn’t work for technical reasons, but that the USSR was ready to pursue instead the renamed Apollo-Soyuz Test Project. The Apollo-Soyuz joint spaceflight project, which began in July 1975, was one of the most powerful symbols of the détente between the two countries.43
领导太空竞赛只是科捷尔尼科夫的成就之一。他完成了金星、水星、火星和木星的无线电定位,并因此获得了列宁奖。然后,配备 MEI 的太空任务金星 15 和 16 首次绘制了金星北部的地图——向整个太阳系发送像素。一颗名为 2726 Kotelnikov的小行星表彰了他对俄罗斯太空工作的诸多贡献。44
Spearheading the space race was just one of Kotelnikov’s achievements. He accomplished the radio location of the planets Venus, Mercury, Mars, and Jupiter and got a Lenin Prize for it. Then, MEI-equipped missions to space, Veneras 15 and 16, mapped the northern part of Venus for the first time—sending pixels across the solar system. An asteroid, 2726 Kotelnikov, honors his many contributions to the Russian space effort.44
Kotelnikov 伟大的采样理念告诉我们将像素间隔“足够近”在一起意味着什么。如果违反了这条规则,就会发生坏事。您可能已经看到了结果:阶梯状边缘、马车车轮向后旋转、出现莫尔条纹条纹领带,或电子游戏中令人不快的背景闪光。这些文物是大数字融合早期的祸根。“是”,而不是“曾经”。我最近看了导演米开朗基罗安东尼奥尼的伟大电影l'Avventura和La Notte的 DVD 。在l'Avventura中,令人惊艳的 Monica Vitti 的波点连衣裙因采样错误而受损。她的裙子不规则地闪烁,仿佛波点是随机切换的小灯。几乎每一帧La Notte在被错误采样的窗户和建筑物的边缘闪闪发光。这样的数字伪影不仅是不必要的,而且是不可接受的。它们不是数字世界固有的,但它们是对采样定理的不知情使用的迹象。或者,在电子游戏的情况下,游戏计算机没有足够的能力来正确地进行采样。
Kotelnikov’s great sampling idea tells us what it means to have pixels spaced “closely enough” together. Bad things happen if this rule is violated. You’ve probably seen the results: stair-stepped edges, wagon wheels rotating backward, moiré patterns on striped neckties, or unpleasant background shimmer in videogames. These artifacts are the bane of the early days of the Great Digital Convergence. “Are,” not “were.” I recently watched DVDs of the director Michelangelo Antonioni’s great films l’Avventura and La Notte. In l’Avventura the stunning Monica Vitti’s polka-dot dress was marred because of incorrect sampling. Her dress blinked on and off irregularly as if the polka dots were little lights toggled randomly. And almost every frame of La Notte glittered at the edges of windows and buildings that were incorrectly sampled. Not only are such digital artifacts unnecessary, they’re unacceptable. They’re not intrinsic to the digital world, but they are signs of uninformed use of the Sampling Theorem. Or, in the case of videogames, of game computers without enough power to do sampling correctly.
如果您没有以足够高的速率进行采样,则会出现这些令人不快的伪影。采样定理说你必须以两倍最高傅里叶频率对视觉场景进行采样。因此,要么您必须以更高的速率进行采样以消除丑陋的伪影,要么您必须在采样之前消除场景中过高的频率。实用性通常决定后一种路径。
These unpleasant artifacts occur if you don’t sample at a high enough rate. The Sampling Theorem says you have to sample a visual scene at twice the highest Fourier frequency in it. So, either you have to sample at a higher rate to be rid of the ugly artifacts, or you have to get rid of the too-high frequencies in the scene before you sample. Practicality usually dictates the latter path.
频率峰值的直觉是锐利的边缘意味着高频。非常尖锐的边缘意味着非常高的频率。多高?无限高以获得完美锐利的边缘——也就是说,频率如此之高,你不可能处理它们。当然,您不能经常采样以准确表示它们。所以实用性再次介入。一般来说,要用像素表示一个场景,你首先必须摆脱它太高的频率,它太尖锐的边缘。窗口边缘就是很好的例子。有缺陷的La Notte DVD 的制作人显然没有遵循采样定理。他们在采样之前没有去除过高的频率,结果很丑陋——或者至少让人分心。
The frequencyspeak intuition is that sharp edges mean high frequencies. Very sharp edges mean very high frequencies. How high? Infinitely high for perfectly sharp edges—that is, frequencies so high you can’t possibly deal with them. Certainly you couldn’t sample often enough to accurately represent them. So practicality steps in again. In general, to represent a scene with pixels, you first have to get rid of its too high frequencies, its too sharp edges. Window edges are good examples. The producers of the flawed La Notte DVD clearly hadn’t followed the Sampling Theorem. They didn’t get rid of the too high frequencies before they sampled, and the result is ugly—or at least distracting.
有一种简单的方法可以从视觉场景中去除过高的频率。只需稍微散焦图片 - 但不要让您真正感觉到图片失焦。这种微妙的“涂抹”了所有的边缘。采样定理告诉你散焦多少就足够了。
There’s an easy way to remove too high frequencies from a visual scene. Simply defocus the picture slightly—but not so much that you can actually perceive that the picture is going out of focus. This subtlety “schmudges” out all the edges. The Sampling Theorem tells you just how much defocusing is enough.
科捷尔尼科夫一生中最可耻的一幕——至少在许多西方人眼中——是 1975 年的安德烈·德米特里耶维奇·萨哈罗夫事件。萨哈罗夫是苏联氢弹之父之一,他已经放弃使用核武器,并积极争取不扩散核武器. 他和另一位持不同政见者索尔仁尼琴都受到苏联媒体的诽谤。但是萨哈罗夫获得了 1975 年的诺贝尔和平奖。作为回应,苏联科学院的成员发表了一份声明,谴责他和奖项。作为学院代理院长,科捷尔尼科夫向政治局提交了一份关于该事件的报告:
The most disgraceful episode in Kotelnikov’s life—at least to many Western eyes—was the Andrei Dmitrievich Sakharov affair of 1975. Sakharov, one of the fathers of the Soviet H-bomb, had renounced the use of nuclear weapons and campaigned actively for their nonproliferation. Both he and Solzhenitsyn, another dissident, were vilified in the Soviet media. But Sakharov received the Nobel Peace Prize for 1975. In response members of the USSR Academy of Sciences issued a statement denouncing him and the prize. As acting president of the Academy, Kotelnikov submitted a report about the event to the Politburo:
我们特此报告,该学院的 72 名成员签署了苏联科学家的声明,抗议将诺贝尔和平奖授予 AD Sakharov。45
We hereby report that seventy-two members of the Academy signed the statement of Soviet scientists protesting against the award of the Nobel Peace Prize to A. D. Sakharov.45
该报告还列出了五位拒绝签署声明的院士,其中包括另一位苏联氢弹之父维塔利·拉扎列维奇·金茨堡。作为回应,政治局禁止萨哈罗夫前往奥斯陆接受诺贝尔奖,1975年10月25日,科学家们签署的声明发表在苏联官方报纸《消息报》上。金茨堡写到科捷尔尼科夫在这件事中的角色:
The report also listed the five Academicians who refused to sign the statement, including Vitaly Lazarevich Ginzburg who was another of the fathers of the Soviet H-bomb. In response the Politburo forbade Sakharov to go to Oslo to receive the Nobel, and on October 25, 1975, the statement signed by the scientists was published in Izvestia, the official newspaper of the Soviet Union. Ginzburg wrote about Kotelnikov’s role in the affair:
我们的谈话相当平静。VA [Kotelnikov] 在恳求我,而不是威胁或恐吓我。总的来说,他是在毫无热情地完成任务,但那是他一贯的作风。我拒绝签字。
Our conversation was rather peaceful. V. A. [Kotelnikov] was pleading with me, instead of threatening or intimidating me. On the whole, he was carrying out the assignment without enthusiasm, but that was his usual manner. I refused to sign.
金茨堡继续说道,将当前时代(1991 年)与斯大林统治下的非常严酷的时代进行了对比:
Ginzburg continued, contrasting current times (1991) to the very harsh ones under Stalin:
我想我会在人身胁迫下签署这封信。. . [但是]显然没有被殴打或逮捕的危险,我仍然很困惑为什么这么多人签署了这样的信。46
I think I would have signed the letter under physical coercion . . . [but] there was obviously no danger of being beaten up or arrested, and it is still a mystery to me why so many people signed a letter of that kind.46
事实上,金茨堡和其他四人从未因拒绝而受到惩罚。Kotelnikov 和其他签名者是否还在遭受斯大林时代的恐惧?不管它的动机是什么,这封信只会增加对萨哈罗夫在西方持不同政见的支持,并使他成为英雄。47
Indeed Ginzburg and the other four were never punished for their refusal. Were Kotelnikov and the other signers still suffering from Stalinist-era fears? Whatever the motivations for it, the letter only increased support for Sakharov’s dissent in the West and made him a hero.47
从萨哈罗夫事件的角度来看,值得记住的是,1950 年代美国也发生过类似的事情。学者们转向美国原子弹之父 J. 罗伯特·奥本海默 (J. Robert Oppenheimer),他同意萨哈罗夫对进一步使用核武器的看法。
To put the Sakharov affair in perspective, it’s worth remembering that something similar happened in America in the 1950s. Fellow academics turned on J. Robert Oppenheimer, father of America’s A-bomb, who shared Sakharov’s views on the further use of nuclear weapons.
像傅立叶一样,科捷尔尼科夫不得不巧妙地与他的暴君共舞——而且显然是这样做的。他在这方面非常成功,以至于在萨哈罗夫的信中,他除了领导科学院外,还担任着惊人的高位。因为科捷利尼科夫是俄罗斯最高苏维埃主席,苏联最大共和国的最高立法机构!八年。这怎么可能?
Kotelnikov, like Fourier, had to dance skillfully with his tyrants—and clearly did so. He was so successful at it that he held, at the time of the Sakharov letter, an astonishingly high position in addition to his leadership of the Academy of Sciences. For Kotelnikov was chairman of the Russian Supreme Soviet, the highest legislative body of the largest republic of the Soviet Union! For eight years. How could this be?
“一开始我很好奇,”他在30 年后告诉《消息报》记者。“系统是怎么运作的?然后我明白了。它尽可能简单。发言的人是中央亲自挑选的,发言稿是事先通过的。” 他补充说:“这一定是我一生中最轻松的工作。不过,最引人注目的。命运的讽刺。” 48
“I was curious at the beginning,” he told an Izvestia reporter 30 years later. “How does the system work? Then I got it. It was as simple as can be. Those who took the floor were handpicked by the Central Committee, draft speeches were approved beforehand.” He added, “It must have been the easiest job in my life. The most noticeable, though. An irony of fate.”48
也就是说,这是一个没有实权的职位。这是一个闲暇,本质上是他长期为国家服务的另一个奖项。
In other words, it was a position with no real power. It was a sinecure, essentially another award for his long service to his country.
很明显,为什么今天“街上”的普通人不知道像素是什么。它需要了解采样定理,这需要了解傅里叶频率。公众通常不熟悉这些美丽而优雅的想法。然而,它们是数字媒体的基本理念——实际上,是一种通用的比特媒体。数字媒体主宰当今世界以及可预见的未来。本章和前一章试图传授对这个新世界的外行理解——对这两个伟大思想的直观理解。它们很容易总结:
It’s clear why a typical person “on the street” today doesn’t know what a pixel is. It requires a knowledge of the Sampling Theorem which requires a knowledge of Fourier’s frequencies. The public is generally unacquainted with either of these beautiful and elegant ideas. Yet they are the foundational ideas of digital media—actually, of the one universal medium of bits. Digital media dominate the world of today, and the foreseeable future. This and the preceding chapter attempt to impart a lay level of understanding of this new world—an intuitive understanding of the two great ideas. They are easy to summarize:
现实世界以一种明显连续的方式呈现给我们的感官。傅立叶的想法告诉我们,真实的连续世界可以描述为各种频率和幅度的波的总和——视觉世界可以被认为是我们眼睛的音乐。
The real world presents itself to our senses in an apparently continuous way. Fourier’s idea teaches us that the real continuous world can be described as a sum of waves of various frequencies and amplitudes—that the visual world can be thought of as music for our eyes.
采样定理教我们如何用离散样本来描述那些傅里叶波。因此,值得注意的是,视觉世界的模拟无穷大可以准确地编码为离散的、分离的、不可见的样本。在视觉世界中,这些样本称为像素。采样定理还告诉我们如何从这些离散样本中重建世界的连续表示:只需用散布器传播每个样本并将结果相加。在显示的时刻,每个离散像素在像素附近为重建的视觉场景贡献了一小块模拟无穷大。我们的眼睛理解这种重构的连续性,就像他们理解原始场景一样。
The Sampling Theorem teaches us how to describe those Fourier waves with discrete samples. Thus remarkably, the analog infinity of the visual world can be accurately encoded into discrete, separated, invisible samples. In the visual world those samples are called pixels. The Sampling Theorem also tells us how to reconstruct a continuous representation of the world from those discrete samples: simply spread each sample with a spreader and add up the results. At the moment of display each discrete pixel contributes a small dollop of analog infinity, in the near vicinity of the pixel, to a reconstructed visual scene. Our eyes make sense of this reconstituted continuity just as they would have made sense of the original scene.
这两个基本思想背后的人类戏剧与思想深刻一样引人入胜。傅立叶对拿破仑了解太多,因此几十年来,拿破仑将他从巴黎驱逐到外省。但效果是,傅立叶不受知识资本的喧嚣影响,创造了他的伟大想法,即世界是波浪的总和。Kotelnikov 被凶残的马林科夫的妻子 Valeriya Golubtsova 保护免于被关押在古拉格,在漫长而极其成功的职业生涯中继续发展他的采样定理的结果。傅立叶是在法国大革命中形成的;Kotelnikov 在俄罗斯的扩展革命中——从 1917 年十月革命到第二次世界大战和冷战。罗伯斯庇尔和拿破仑是傅立叶的暴君;斯大林、马林科夫、贝利亚和阿巴库莫夫至少间接属于科捷尔尼科夫。
The human drama behind these two essential ideas is as intriguing as the ideas are profound. Fourier knew too much about Napoleon, who consequently banished him from Paris to the provinces for decades. But the effect was that Fourier, shielded from the hurly-burly of the intellectual capital, created his great idea of the world as a sum of waves. And Kotelnikov, protected from incarceration in the Gulag by Valeriya Golubtsova, wife of the murderous Malenkov, continued throughout a long, immensely successful career to develop consequences of his Sampling Theorem. Fourier was forged in the French Revolution; Kotelnikov in Russia’s extended revolution—from the 1917 October Revolution, through World War II, and the Cold War. Robespierre and Napoleon were Fourier’s tyrants; Stalin, Malenkov, Beria, and Abakumov were Kotelnikov’s, indirectly at least. But Kotelnikov’s generic tyrant was really state security.
在像素的传记中,我们会反复发现收到的故事不一定是正确的。正确的往往比收到的要好——而且是真实的。Vladimir Kotelnikov,而不是美国的巨人克劳德香农,首先将采样定理带到了世界。
In the biography of the pixel we’ll repeatedly find that the received stories aren’t necessarily the right ones. And the right ones are often better than the received ones—in addition to being true. Vladimir Kotelnikov, not America’s giant Claude Shannon, first brought the Sampling Theorem to the world.
这两个人之间的相似之处是不可思议的。Kotelnikov 多年来一直担任苏联(今俄罗斯)科学院无线电工程与电子研究所所长,现在以他的名字命名。美国庞大的电子电气工程师协会 (IEEE) 最初是同名的无线电工程师协会。它将荣誉勋章授予香农,并在 2000 年将亚历山大·格雷厄姆·贝尔奖章授予科特尔尼科夫,标志着千禧年和大数字融合。具有讽刺意味的是,亚历山大·格雷厄姆·贝尔也与贝尔实验室同名——著名的香农的故乡。49
The parallels between the two men are uncanny. Kotelnikov was head of the Institute of Radio Engineering and Electronics of the USSR (today Russian) Academy of Sciences for many years, and it’s now named for him. America’s immense Institute of Electronic and Electrical Engineers (IEEE) was originally the similarly named Institute of Radio Engineers. It gave its Medal of Honor to Shannon, and it marked the millennium and the Great Digital Convergence by giving its Alexander Graham Bell Medal to Kotelnikov in 2000. The irony is that Alexander Graham Bell was also namesake to Bell Labs—famously Shannon’s home.49
尽管科捷尔尼科夫将采样定理带到了世界,但具有讽刺意味的是香农将它传授给了美国。如果不是因为香农从来没有为自己主张过采样定理,我们可能会援引“同时发明”的现象。我们将在下一章再次见到香农,国家安全将再次成为暴君——但这次是西方安全。
Although Kotelnikov brought the Sampling Theorem to the world, it’s a second irony that it was Shannon who taught it to America. We might invoke the phenomenon of “simultaneous invention” if it weren’t for the fact that Shannon never claimed the Sampling Theorem for himself. We’ll meet Shannon again in the next chapter, where state security will again be the tyrant—but Western security this time.
2003 年科捷尔尼科夫 95 岁生日——在他证明采样定理七十周年之际——在克里姆林宫的凯瑟琳大厅,普京总统授予他为服务勋章的全骑士(替代翻译:Chevalier、Knight)祖国,只有第四位持有该命令的人(图2.21)。Kotelnikov 于 2005 年 2 月 11 日去世。他只比香农多活了四年,但他们都看到了他们帮助定义的新千年和新时代。50
On Kotelnikov’s ninety-fifth birthday in 2003—on the seventieth anniversary of his proof of the Sampling Theorem—in the Catherine Hall of the Kremlin, President Putin made him a Full Cavalier (alternative translations: Chevalier, Knight) of the Order for Service to the Motherland, only the fourth person to hold the order (figure 2.21). Kotelnikov died on February 11, 2005. He outlived Shannon by only four years, but they both saw the new millennium and the new era that they helped define.50
图 2.21
Figure 2.21
下一章的主要目的是将数字光从现实世界扩展到虚幻世界。它的重点是数字光的第三个伟大的基础理念——计算。到目前为止,我讨论的像素都是从现实世界中派生出来的。例如,这包括科捷尔尼科夫从金星极地地区拍摄的那些像素,或者就此而言,我们每天用手机摄像头捕捉到的无数像素中的任何一个。另一方面,计算让我们创造了非常丰富但完全虚构的世界。它让我们从头开始生成或制作像素。当这些像素根据采样定理展开和添加并显示到我们的眼睛时,我们看到了一个不存在的世界。这怎么可能?
The main purpose of the next chapter is to extend Digital Light from the real world to unreal worlds. Its focus is the third great foundational idea of Digital Light—computation. The pixels I’ve discussed so far have been derived, taken, from the real world. That includes, for example, those pixels that Kotelnikov took from Venus’s polar regions, or, for that matter, any of the myriad pixels that we capture with our cellphone cameras daily. On the other hand, computation lets us create very rich, but completely fictitious worlds. It lets us generate, or make, pixels from scratch. When those pixels are spread and added per the Sampling Theorem and displayed to our eyes, we see a world that doesn’t exist. How is this possible?
瓦伦丁:之前没有足够的时间。铅笔不够用!这花了她我不知道多少天,她还没有刮伤油漆。现在她只需要按一个按钮,一遍又一遍地按同一个按钮。迭代。几分钟。而我在几个月内所做的事情,只用一支铅笔,计算将花费我余生再做一次——数千页——数万页!而且很无聊!. . .
Valentine: There wasn’t enough time before. There weren’t enough pencils! This took her I don’t know how many days and she hasn’t scratched the paintwork. Now she’d only have to press a button, the same button over and over. Iteration. A few minutes. And what I’ve done in a couple of months, with only a pencil the calculations would take me the rest of my life to do again—thousands of pages—tens of thousands! And so boring! . . .
汉娜:你的意思是那是唯一的问题吗?充足的时间?还有纸?和无聊?瓦尔!这就是你说的吗?. . .
Hannah: Do you mean that was the only problem? Enough time? And paper? And the boredom? Val! Is that what you’re saying? . . .
瓦伦丁:嗯,另一件事是,你必须疯了。
Valentine: Well, the other thing is, you’d have to be insane.
计算机是一个被伪装成设备的存在难题。虽然电器不是超凡的,但计算机更是如此。首先,它是人类发明的最具延展性的工具。它允许我们做比我们想象的更多的事情。其次,它是人类大脑中最强大的放大器。它把我们做这些事情的能力提高到了难以想象的水平。延展性和放大是计算的双重荣耀。
A computer is an existential conundrum masked as an appliance. While appliances aren’t transcendent, a computer is doubly so. First, it’s the most malleable tool ever invented by humankind. It allows us to do many more things than we can possibly envision. Second, it’s the most powerful amplifier that the human mind has ever had. It increases our power to do those things to unimaginable levels. Malleability and Amplification are the twin glories of computation.
最先将全面的计算理念带给我们的人——他的话——是艾伦·马西森·图灵(Alan Mathison Turing),他具有非凡的天赋。
The man who first brought us the full-blown idea of computation—his word for it—was Alan Mathison Turing, in a remarkable burst of genius.
他于 1912 年 6 月 23 日(一个世纪前)出生在伦敦,几乎正好在前一章的英雄科捷尔尼科夫和香农的出生之间。图灵在 22 岁时成为剑桥国王学院的研究员,在 34 岁时获得大英帝国勋章,在 38 岁时成为艾萨克·牛顿皇家学会会员,并在 6 月 7 日时死于 41 岁时的氰化物中毒, 1954. 所以——不像Kotelnikov 和 Shannon——他没有看到新千年和大数字融合。2
He was born in London on June 23, 1912—a century ago—almost exactly halfway between the births of Kotelnikov and Shannon, the heroes of the preceding chapter. Turing was a fellow at King’s College of Cambridge by age 22, received an Order of the British Empire by age 34, became a Fellow of Isaac Newton’s Royal Society by age 38, and was dead of cyanide poisoning by age 41, on June 7, 1954. So—unlike Kotelnikov and Shannon—he didn’t get to see the new millennium and the Great Digital Convergence.2
在 1960 年代,图灵对我们第一代计算机科学专业的学生来说是个谜。我们被教导了他的伟大想法——计算的概念——但他自己仍然是一个密码。从原本笼罩着他的迷雾中升起的是他已经自杀的持续谣言。
Turing was a mystery to us first-generation computer science students in the 1960s. We were taught his great idea—the notion of computation—but he himself remained a cipher. Rising out of the mist that otherwise obscured his person was the persistent rumor that he had committed suicide.
然后突然间,在 1983 年,安德鲁·霍奇斯出版了传记《艾伦·图灵:谜》,这最终使图灵这个人成为了人们关注的焦点。它解释了这个谜团:图灵帮助破解了纳粹德国的 Enigma 密码并赢得了战争。但他在布莱切利公园的工作是绝密的,并被英国的官方保密法扣押了数十年。3
Then suddenly, in 1983, Andrew Hodges published the biography Alan Turing: The Enigma, which finally brought Turing the man into sharp focus. It explained the mystery: Turing had helped crack Nazi Germany’s Enigma code and win the war. But his work at Bletchley Park was top secret and had been impounded for decades by Britain’s Official Secrets Act.3
超越这一启示是另一回事。当同性恋仍然是一种犯罪行为时,图灵就已经是公开的同性恋了,甚至是鲁莽地这样做了。当他在1952年因“不雅行为”被捕时,他无法利用他拯救了英格兰的事实来拯救自己。不雅行为胜过《保密法》。考虑到监狱或化学阉割的选择,他选择了阉割。他的马拉松运动员的身体(图 3.1)从荷尔蒙和发达的乳房。也许,正是这种屈辱驱使他吃了一个(可能)毒苹果——在一个本可以直接从迪斯尼白雪公主中取出的死亡场景中。4
Topping that revelation was another. Turing had been openly gay, even recklessly so, when homosexuality was still a crime. When he was arrested for “indecent acts” in 1952, he couldn’t use the fact that he had saved England to save himself. The indecent acts trumped the Secrets Act. Given the choice of prison or chemical castration, he chose castration. His marathon runner’s body (figure 3.1) grew fatter from the hormones and developed breasts. It was the humiliation, perhaps, that drove him to eat a (possibly) poisoned apple—in a death scene that could have been lifted straight out of Disney’s Snow White.4
图 3.1
Figure 3.1
由剑桥大学国王学院图书馆提供。
Courtesy of King’s College Library, Cambridge.
传记作家霍奇斯本人是国王学院的理论物理学家,也是英国同性恋解放运动的成员,他终于揭开了神秘的面纱。他得到了完整的故事,并仔细、亲密、很好地讲述了它。5
Biographer Hodges, himself a King’s College theoretical physicist and a member of Britain’s gay liberation movement, finally parted the veil of secrecy. He got the full story and told it carefully, intimately, and well.5
在 1950 年代的美国,在参议员约瑟夫麦卡锡的恐怖统治下的“薰衣草恐慌”中,共产党人和“性变态者”被归为国家的敌人。英格兰也遭受了同样的错觉,尤其是在 1951 年以及臭名昭著的受过剑桥教育的间谍和同性恋者盖伊·伯吉斯 (Guy Burgess) 叛逃到莫斯科之后。图灵对共产主义从来没有任何兴趣——他对此嗤之以鼻——而且他是如此公开坦率的同性恋,以至于他不可能被勒索。但麦卡锡和军情五处没有做出这些区分,而图灵有共产主义朋友。6
In 1950s America, Communists and “sexual perverts” were lumped together as enemies of the state in the “lavender scare” of Senator Joseph McCarthy’s reign of terror. England suffered the same delusion, especially after 1951 and the infamous defection to Moscow of Cambridge-educated Guy Burgess, a spy and a homosexual. Turing never had any interest in Communism—he mocked it—and he was so openly and candidly gay that he couldn’t have been blackmailed. But McCarthy and MI5 didn’t make these distinctions, and Turing had Communist friends.6
剑桥大学著名的秘密社团 Apostles 将 Burgess 列为其成员之一。他们中的许多人是马克思主义者或同性恋者或两者兼而有之。图灵的两个最好的朋友和合作者罗宾·甘迪和大卫·尚佩诺恩也是使徒,这对图灵的事业没有帮助。尤其是甘迪,在学生时代是共产党员。
The Apostles, a prestigious secret society at Cambridge, counted Burgess among its members. Many of them were Marxists or gay or both. It can’t have helped Turing’s cause that two of his best friends and collaborators, Robin Gandy and David Champernowne, were also Apostles. Gandy, in particular, was a member of the Communist Party during his student days.
每个人都同意图灵死于氰化物中毒,但他是如何中毒的仍然存在争议。毒苹果自杀是最流行的理论。但实际的苹果从未进行过氰化物测试,为其他解释敞开了大门。他的母亲认为这是一场意外。但另一种说法是政府安全部队暗杀了他。7
Everybody agrees that Turing died of cyanide poisoning, but just how he was poisoned is still controversial. The poison-laced-apple suicide is the most popular theory. But the actual apple was never tested for cyanide, leaving the door open for alternative explanations. His mother believed it was an accident. But another theory is that government security forces assassinated him.7
具有讽刺意味的是,在图灵毒尸被发现后的第二天,麦卡锡的反共恐怖统治终于落下帷幕。1954 年 6 月 9 日那天,美国陆军首席法律顾问约瑟夫·韦尔奇斥责这位参议员,因为他试图暗杀另一个被指控为共产主义的人。
It’s a sad irony that the very day after the discovery of Turing’s poisoned body, McCarthy’s anti-Communist reign of terror was finally brought to heel. On that day, June 9, 1954, Joseph Welch, head counsel for the United States Army, famously rebuked the senator as he attempted to assassinate the character of yet another person with accusations of Communism.
英国政府最终在 1967 年放宽了虚伪的反同性恋法律,并在 2009 年为其骇人听闻的错误公开道歉。但这两个事件都来得太晚了,无法阻止“圣。图灵。” 2012 年全球庆祝他诞辰 100 周年为他辩护——最终在 2013 年圣诞节前夕女王的死后赦免结束。8
The British government eventually relaxed its hypocritical anti-gay laws in 1967 and apologized publicly in 2009 for its appalling mistake. But both events came way too late to forestall the martyrdom of “St. Turing.” The 2012 worldwide celebrations of the centenary of his birth were his vindication—capped off finally by the Queen’s posthumous pardon on Christmas Eve, 2013.8
傅立叶的法国恐怖和科捷尔尼科夫的大恐怖都极其致命。麦卡锡的恐怖,以及相应的英格兰环境,不在同一个联盟中,但它们仍然毁掉了成千上万的生命——并直接导致了图灵的死亡。图灵的暴君不是皇帝也不是党主席,而是国家安全。他没有在肉体上被监禁,但他被《官方保密法》在精神上囚禁——在一个隐喻的布莱切利公园 sharashka 中。
Fourier’s French Terror and Kotelnikov’s Great Terror were vastly and horribly deadly. McCarthy’s terror, and the corresponding milieu in England, weren’t in the same league, but they ruined thousands of lives nevertheless—and led directly to Turing’s death. Turing’s tyrant wasn’t an emperor or a party chairman, but state security. He wasn’t physically imprisoned, but he was held mentally captive by the Official Secrets Act—in a metaphorical Bletchley Park sharashka.
在图灵的故事中,我们再次找到了技术突破的要素:他的伟大计算思想;第二次世界大战的混乱和恐惧推动了计算机的发展,这些机器实现了他的想法;以及国家机密的暴政,将科学家集中在一个地方,并以一种不正当的方式保护他们。
In Turing’s story we again find the ingredients for technological breakthrough: his great idea of computation; the chaos and fear of World War II, which drove the development of computers, the machines that realized his idea; and the tyranny of state secrecy that concentrated the scientists in one place and protected them in a perverse way.
计算机是机器的变形虫。它的本质是它的普遍性,它的模拟能力。因为它可以有千种形式,可以服务千种功能,所以它可以吸引千种口味。
The computer is the Proteus of machines. Its essence is its universality, its power to simulate. Because it can take on a thousand forms and can serve a thousand functions, it can appeal to a thousand tastes.
——Seymour Papert,《头脑风暴》,1980 年9
—Seymour Papert, Mindstorms, 19809
计算机在每个步骤中所做的事情都是微不足道的。一个典型的步骤是这样的:从这里取一些比特,稍微旋转一下,然后把得到的比特放在那里。旋转可能只不过是将每个 0 换成 1,反之亦然,或者每个 0 或 1 向右移动一个位置。
What a computer does at each step is trivial. A typical step has this form: take some bits from here, twiddle them a little, and put the resulting bits there. A twiddle might be nothing more than a swap of each 0 for a 1 and vice versa, or a move of each 0 or 1 a single position to the right.
这些简单可笑的步骤串在一起的长序列使计算机变得强大。这并不明显——无意识的步骤应该导致有意识的结果。那么愚蠢的序列如何变得有意义呢?魔法在哪里?
Long sequences of these laughingly simple steps strung together are what make the computer powerful. It’s not obvious that this should be so—that mindless steps should lead to mindful results. So how does a dumb sequence become meaningful? Where does the magic lie?
随机序列没有什么有趣的。但是一个有意义的序列会导致计算机执行一个有用或有趣的过程。您知道的任何计算机或手机应用程序都是由一系列简单步骤执行的过程。另一个序列产生了皮克斯电影。
A random sequence does nothing interesting. But a meaningful sequence causes a computer to implement a process that’s useful or entertaining. Any computer or phone app you know is such a process performed by a sequence of those simple steps. Another sequence results in a Pixar movie.
计算机硬件所做的很简单——那些微不足道的步骤。但要创建这些步骤的有意义的序列,需要相当大的智力。那就是软件设计。具有这种能力的有创造力的人是程序员。所以,魔法就在他们的脑海里。
What computer hardware does is simple—those trivial steps. But to create meaningful sequences of those steps requires considerable mental prowess. That’s software design. The creative humans who are endowed with such prowess are programmers. So, the magic lies in their minds.
这就像一架音乐会三角钢琴。钢琴可以演奏无数的音调。那是执行简单步骤的硬件。大多数序列只是噪音。但偶尔会出现一些产生美妙音乐的软件。由程序员肖邦诱导的音符序列变成了练习曲、华尔兹或马祖卡。
It’s like a concert grand piano. The piano can play countless sequences of tones. That’s hardware executing simple steps. Most of the sequences are just noise. But occasionally some software appears that produces glorious music. The sequence of notes induced by programmer Chopin becomes an étude, a waltz, or a mazurka.
一台计算机,就像一架钢琴,可以实现无数简单的基本步骤序列。因此,它可以实现无数复杂而有意义的流程它们——可以说是它的音乐——只使用 2 位而不是 88 个钢琴键。正是“无数”这个词捕捉了延展性的超越性,这是一种对计算机至关重要的品质,以至于它应该获得“大写 M”的地位。我们人类的思想被计算机可以实现的广泛的可能过程所淹没。总是有另一个有意义的无意义步骤序列来产生我们想要使用的东西。总有另一个应用程序、游戏或电影要构建。而一个工具,计算机,可以完成所有这些。
A computer, like a piano, can implement countless sequences of its simple basic steps. It can therefore implement countless complex and meaningful processes with them—its music, so to speak—using only 2 bits rather than 88 piano keys. It’s the word “countless” that captures the transcendence of Malleability, a quality so crucial to computers that it deserves its “capital M” status. Our human minds are swamped by the sheer breadth of possible processes that a computer can realize. There’s always another meaningful sequence of meaningless steps to produce something we want to use. There’s always another app, game, or movie to build. And one tool, the computer, does them all.
事实上,延展性本质上是计算的一部分,正如我们将在本章中看到的那样。这是概念的礼物。但延展性的荣耀伴随着一个谜团——不可知性的谜团。尽管计算机采取的每一步都是完全可预测的,但我们并不总是知道这些步骤的顺序将如何展开。在小处确定并不意味着在大处确定。必须确定一个计算——必须有一些关于一系列完全确定的步骤将做什么的答案——但我们并不总是知道那个答案。确定和预定之间的细微差别是潜伏在计算核心的奥秘。因此,计算机简单而深刻。
In fact, Malleability is fundamentally part of what computation means, as we’ll see in this chapter. It’s a gift of the concept. But the glory of Malleability comes with a mystery attached—the mystery of unknowability. Although each step that a computer takes is completely predictable, we can’t always know how a sequence of those steps will unfold. Determined in the small doesn’t mean predetermined in the large. A computation must be determined—there must be some answer about what a sequence of completely deterministic steps will do—but we can’t always know that answer. The subtle difference between determined and predetermined is the mystery that lurks at the heart of computation. So a computer is simple but profound.
另一种非常不同的超越是放大。很明显,计算机可以重复一个动作——它的任何无意识步骤的序列。这很简单。重要的是它可以以我们无法理解的速度重复这个动作无数次。不是无数次。我们可以计算重复次数——或者至少我们的计算机可以。我们只是无法理解与我们人类思维有关的数字。淹没我们的是计算机进程的规模。11-11 skydillion 是一个虚构的愚蠢数字——斯克罗吉叔叔遇到比尔博巴金斯——但它让人想起计算中的数字是多么愚蠢,即使它们是实际数字。我们无法想象它们。正如斯托帕德的瓦尔在题词中所说,“你必须疯了”才能对付它们。精神错乱可能还不够。10
The other, very different kind of transcendence is Amplification. It’s obvious that a computer can repeat an act—any sequence of its mindless steps. That’s simple. What matters is that it can repeat the act an impossible number of times at speeds we can’t understand. Not a countless number of times. We can count the repetitions—or at least our computers can. We just can’t fathom the numbers involved with our human minds. It’s the scale of computer processes that swamps us. Eleventy-eleven skydillion is an invented silly number—Uncle Scrooge meets Bilbo Baggins—but it evokes how silly the numbers in computations are, even when they are actual numbers. We can’t imagine them. As Stoppard’s Val says in the epigraph, “you’d have to be insane” to deal with them. And insanity probably wouldn’t suffice.10
重复您已经对计算机进行编程的任务是微不足道的。只需指示计算机根据需要多次重复该任务。几乎不需要额外的智力努力。但是,与这种简单性相反的是加速计算机以达到难以想象的数字所需的智力。这就是硬件设计。具有这种能力的创造性人类是工程师。
Repeating a task that you’ve already programmed a computer to do is trivial. Simply instruct the computer to repeat the task as many times as you require. There’s almost no additional intellectual effort required. But, countering that simplicity is the mental prowess that’s required to speed up the computer to reach the unimaginable numbers. That’s hardware design. The creative humans with that prowess are engineers.
在电气工程中,放大意味着增加很多。指数是衡量“很多”的方式——例如,不仅仅是两倍或三倍,而是平方或立方。增加不是 2 倍或 3 倍,而是 2 的指数或 3 的指数好几倍——不仅仅是 2 x或 3 x,而是x 2或x 3。如果输入信号是 10 伏,那么放大后的输出不仅仅是 20 或 30 伏,而是 100 或 1,000 伏。放大是技术的礼物。最早的计算机的建造正是因为它们可以超越人类——它们可以增强人类的能力。
In electrical engineering to amplify means to increase—by a lot. Exponentially is how “a lot” is measured—not mere doubling or trebling, for example, but squaring or cubing. The increase is not 2 times or 3 times better but exponent-of-2 or exponent-of-3 times better—not merely 2x or 3x, but x2 or x3. If an input signal is, say, 10 volts, then an amplified output is not just 20 or 30 volts, it’s 100 or 1,000 volts. Amplification is a gift of technology. The earliest computers were built precisely because they could outstrip human beings—they could amplify human capabilities.
第一台计算机将人类能力提高了 10,000 倍。到 1965 年,这一因素已跃升至 1,000,000——至少——是通过制造更大的机器并将基础技术从真空管转换为晶体管而实现的。我们将其称为 Epoch 1 加速。
The very first computer amplified human capability by 10,000. By 1965 that factor had jumped to 1,000,000—at least—accomplished by building ever larger machines and by converting the underlying technology from vacuum tubes to transistors. We’ll call this the Epoch 1 speedup.
但超越放大——放大本身的指数放大——伴随着更现代的技术——集成电路:大量晶体管和它们之间的导线在一个芯片上。1965 年,现在被称为摩尔定律的声明是开启下一个显着加速的绿旗——第二纪元。人类的能力不仅被计算机以指数方式放大,而且,这种放大的速度也以指数方式增加。
But transcendent Amplification—exponential amplification of amplification itself—came with even more modern technology, the integrated circuit: lots of transistors and the wires between them on a single chip. In 1965 the statement now known as Moore’s Law was the green flag that started the next dramatic speedup—Epoch 2. Human capabilities were not only amplified exponentially by computers, but, dramatically, the rate of that amplification increased exponentially too.
简而言之,摩尔定律暗示放大率将每五年上升到 10 的下一个指数——下一个 10 的因子。因此,如果人类的扩增在 1965 年是 10 6(100 万)——事实上——那么它在 1970 年将是 10 7 (1000 万),在 1975 年是 10 8(1 亿),以此类推。它会让早期计算机的创造者感到惊讶,就像今天让我们感到惊讶一样。另一个惊喜是 Epoch 2 中更强大的计算机变得更小,而不是更大。
In a nutshell Moore’s Law implied that Amplification would go up to the next exponent of 10—the next factor of 10—every five years. So if Amplification of humans was by 106 (1 million) in year 1965—as it was—then it would be 107 (10 million) in 1970, and 108 (100 million) in 1975, and so forth. It would have amazed the creators of the early computers as much as it amazes us today. Another surprise was that the more powerful computers of Epoch 2 got smaller, not larger.
就其本质而言,我们无法理解摩尔定律的含义。这是一个数量级的事情。我们人类通常无法看到超过 10 倍的变化。我们在那里碰上了一堵概念墙。所以我们用大的表达数量级来暗示僵局而不是平淡无奇,简单的算术因子10. 宏大的表达意味着一个如此巨大的变化,以至于只有新的思维过程——新的概念化——才能处理它。它不仅仅是更多——它是不同的。我们必须先掌握一个数量级的改进,然后才能开始思考下一个订单可能意味着什么。然而,计算机已经将人类的放大率提高了至少 17 个数量级!前六个订单(一百万倍)出现在摩尔定律之前,之后又有 11 个订单(一千亿倍)。总而言之,有一百亿倍的放大——超出任何人最疯狂的想象,无论是否天才。
By its very nature we can’t understand the implications of Moore’s Law. It’s an order-of-magnitude thing. We humans can’t usually see beyond a factor-of-10 change. We hit a conceptual wall there. So we use the grand expression order of magnitude to connote the impasse rather than the bland, simply arithmetical factor of 10. The grand expression implies a change so great that only new thought processes—new conceptualizations—can handle it. It’s not simply more—it’s different. We have to master one order-of-magnitude improvement before we can even start to contemplate what the next order might mean. Yet computers have improved the Amplification of humans by at least 17 orders of magnitude! The first six orders (a millionfold) came before Moore’s Law, and 11 more have come since (a hundred-billionfold). All told there’s been a hundred-quadrillionfold Amplification—beyond anyone’s wildest imaginings, genius or not.
计算机利用我们人类的智慧超越了我们固有的数量级限制。它将我们微不足道的人类行为放大到我们没有帮助的物种无法达到和无法想象的极端。增幅的荣耀伴随着那些数量级障碍的奥秘。
A computer leverages our human intellect past our inherent order-of-magnitude limitations. It Amplifies our puny human-sized actions to extremes unreachable—and unimaginable—by our unaided species. The glory of Amplification comes with the mystery of those order-of-magnitude barriers.
Kotelnikov 的采样定理告诉我们,相机可以将现实世界变成像素。换句话说,我们可以用相机从真实的视觉世界中获取像素——我们可以拍摄它们。然后我们可以使用它们来重建那个视觉世界的样子——即使是在更晚的时间或很远的地方。
Kotelnikov’s Sampling Theorem taught us that a camera can turn the real world into pixels. In other words, we can take pixels from the real visual world with a camera—we can shoot them. Then we can use them to reconstruct what that visual world looked like—even at a much later time or far distant place.
或者我们可以从头制作像素——我们可以计算它们。如果我们显示的像素按照与现实世界像素相同的规则运行,那么我们也可以看到虚幻世界。新千年的完整数字之光源于这种想法。
Or we can make pixels de novo—we can compute them. If we display pixels that play by the same rules as real-world pixels, then we can see unreal worlds too. The full Digital Light of the new millennium flows from that thought.
我们利用延展性和放大功能为我们提供了成熟的数字光——例如,一部完全数字化的故事片,或者最热门的视频游戏,或者对国际互联网体验的即时视觉访问。计算机创建像素,并从视觉世界中获取它们。
We’ve harnessed Malleability and Amplification to give us full-blown Digital Light—a completely digital feature film, for example, or the hottest videogame, or instantaneous visual access to the international internet experience. Computers create pixels, as well as taking them from the visual world.
本章是关于延展性的超越性,这是艾伦·图灵发明计算的礼物。这是关于想法的。下一章是关于速度的。它是关于硬件计算机的发明,以实现计算的想法。这是关于放大的超越,技术的礼物。这也是关于数字光的黎明——令人惊讶的巧合——与计算机同时发生。通俗地说,本章和下一章是关于摩尔定律到来之前理论和实践——科学和工程——的英雄。在后面的章节中,当摩尔定律出现并在 Epoch 2 加速中驱动放大超新星时,我们重新审视“定律”并更仔细地检查它。
This chapter is about the transcendence that is Malleability, the gift of Alan Turing’s invention of computation. It’s about ideas. The next chapter is about speed. It’s about the invention of hardware computers to realize the idea of computation. It’s about the transcendence that is Amplification, the gift of technology. And it’s also about the dawn of Digital Light which—by a surprising coincidence—occurred simultaneously with that of computers. In mundane terms this chapter and the next are about the heroes of theory and practice—of science and engineering—before the arrival of Moore’s Law. In a later chapter, when Moore’s Law arrives and drives Amplification supernova in the Epoch 2 speedup, we revisit “the Law” and inspect it more closely.
尽管在预兆中的西弗没有自己的象征意义,但他对他人的象征意义却是力量。
Althoughe a sypher in augrym have no might in signifycacion of itselve, yet he yeveth power in signifycacion to other.
——托马斯·乌斯克,《爱的遗嘱》,约。1385 11
—Thomas Usk, The Testament of Love, ca. 138511
图灵的重大突破始于系统过程的想法。这是一个仔细或系统地做某事意味着什么的例子。假设您家中的一位客人,您所在城镇的陌生人,想知道如何去杂货店。你的步行方向可能是这样的:走出前门,在街上右转。步行到第一个十字路口,然后再往前走两个街区。在那里的街道左转,沿着它走三个街区。继续穿过那个十字路口,商店就在右侧,从十字路口进去的第四栋建筑。
Turing’s great breakthrough starts with the idea of a systematic process. Here’s an example of what it means to do something carefully or systematically. Suppose a guest in your home, a stranger to your town, wants to know how to get to a grocery store. Your walking directions might be something like this: Go out the front door and turn right at the street. Walk to the first intersection and then go two blocks beyond. Turn left at the street there and walk along it three blocks. Proceed through that intersection, and the store is on the right side, the fourth building in from the intersection.
因此,直觉上,谨慎或系统意味着进入商店的较大过程被分解为一系列较小的步骤,其中每个步骤或说明对大多数人来说都是简单、明确且显而易见的。一位客人按照给定的顺序准确地执行每一项,一定会到达商店。
Intuitively, then, being careful or systematic means that the larger process of getting to the store is broken down into a sequence of smaller steps, where each step or instruction is simple, unambiguous, and obvious to most people. A guest who accurately performs each, in the order given, will surely arrive at the store.
上面的步行路线是一个简单的说明列表。客人从列表的一端开始,在另一端结束。要遵循的指令数等于列表中的步骤数。然而,一般来说,系统化过程的结构比这更多。考虑一下将钉子钉入木板的方法:(1)取钉子。(2) 如果没有,那么你就完成了,否则继续。(3) 敲钉子。(4) 如果指甲弯曲,则将其拉直并重复步骤 3,否则从步骤 1 重新开始。
The walking directions above are a simple list of instructions. The guest begins at one end of the list and finishes at the other. The number of instructions to be followed equals the number of steps in the list. Generally, however, there’s more structure to a systematic process than that. Consider this one for hammering nails into a board: (1) Fetch a nail. (2) If there isn’t one, then you’re done, otherwise proceed. (3) Hammer in the nail. (4) If the nail bends, then straighten it out and repeat step 3, otherwise start again at step 1.
此列表与步行路线具有相同数量的说明,但在强大的方面有所不同。它有循环。只要有钉子,您就重复外环(步骤 1 到 4),只要钉子在不恰当地敲打时弯曲,就重复内部“嵌套”环(步骤 3 和 4)。你在这个列表的一端进入,你可能永远不会出来——比如说,如果你每次敲钉子时都会弯曲一个钉子。执行的步骤数通常比指令数大得多——有时甚至大得多。
This list has the same number of instructions as the walking directions, but it’s different in a powerful way. It has loops. You repeat the outer loop (steps 1 through 4) so long as there are nails, and the inner “nested” loop (steps 3 and 4) so long as a nail gets bent when it’s inexpertly hammered. You enter at one end of this list and you might never come out—if you bend a nail every time you hammer one, say. The number of steps executed is usually much larger—sometimes vastly larger—than the number of instructions.
钉钉方向有两个分支步骤,形式为“如果 . . . 然后 。. . 否则 。. 。” (步骤 2 和 4)。这些被称为条件分支。如果满足某个条件,则分支到某某步,否则分支到某某步。条件分支(由if表示)允许您更改执行列表中指令的顺序。
There are two branching steps in the nailing directions that take the form “if . . . then . . . otherwise . . .” (steps 2 and 4). These are called conditional branches. If some condition is satisfied, then branch off to step so-and-so otherwise branch off to step such-and-such. A conditional branch—signified by an if—lets you change the order in which you perform the instructions in a list.
它还可以让您逃脱无限循环。例如,考虑这个:(1)说“你好”。(2) 转到第 1 步。没有条件分支可以用来转义循环。因此,一旦这个系统过程开始,它就永远不会停止。
It also lets you escape an infinite loop. Consider this one, for example: (1) Say “Hello.” (2) Go to step 1. There’s no conditional branch with which to escape the loop. So once this systematic process starts, it never halts.
条件分支——系统过程的if ——是计算的关键。可以执行条件分支的机器比不能执行的机器强大得多。它可以简洁地导致一个难以想象的长度的过程小心地展开。它可以实现自我循环的流程——也许是十一十一天——甚至可以修改自己作为流程的一部分。任何声称是计算机的机器都必须具有条件分支指令。一台机器可以有十层楼高,全电子化,速度极快,但如果它没有条件分支指令,那么它就不是计算机。
Conditional branches—the ifs of systematic process—are key to computation. A machine that can execute conditional branches is much more powerful than one that cannot. It can succinctly cause a process of unimaginable length to unfold carefully. It can implement processes that loop on themselves—perhaps eleventy-eleven skydillion times—or even modify themselves as part of the process. Any machine that purports to be a computer must have a conditional branch instruction. A machine can be ten stories tall, fully electronic, and extremely fast, but if it doesn’t have a conditional branch instruction, then it’s not a computer.
如果它只计算数字,那么它就不是计算机。系统过程的概念远大于数字。即使是我们第一个系统过程的例子,步行和锤击指令,也不是关于数字的。毫不奇怪,图灵很早就完全理解了这个概念。
And if it only calculates numbers then it’s not a computer. The notion of systematic process is much larger than numbers. Even our first examples of systematic process, the walking and hammering instructions, weren’t about numbers. Not surprisingly, Turing understood this notion early and completely.
并不是说数字不重要。它们是我们几千年来一直系统化的事情之一。即使在这个计算器无处不在的时代,孩子们仍然学习如何将两个十进制数字相加。众所周知,这样做的方法是将每对数字从右边开始依次相加,然后将它们和的一个数字写入答案。如果(就是这样!)这些数字的总和是 10 或更大,你将“1”带到下一步,向左一个位置,并将其添加到那里。等等。在这个过程中还有另一个隐含的情况:如果你用完了数字或携带 1 来添加,则停止。这是通常称为加法算法的过程的草图. 我敢肯定,我们都很高兴我们的计算器现在为我们“记住”了这个算法的细节,并且对它们足够了解,如果我们坚持的话,它们可以添加两打数字,而不仅仅是两个。
Not that numbers aren’t important. They’re one of the things we’ve been systematic about for millennia. Even in this era of the omnipresent calculator, kids still learn how to add two decimal numbers together. Famously, the way to do it is to add each pair of digits successively, starting at the right, and write one digit of their sum to the answer. If (there it is!) the sum of those digits is 10 or larger, you “carry the 1” to the next step, one position to the left, and add it in there. And so forth. There’s another if implicit in this process: if you run out of digits or carried 1s to add, then halt. This is a sketch of the process that’s often called the addition algorithm. We’re all happy, I’m sure, that our calculators now “remember” the details of this algorithm for us and know them well enough that they can add two dozen numbers, if we insist, rather than just two.
在上个世纪,算法这个词成为我们一直称之为“系统过程”的同义词。这个词是对 9 世纪波斯算术专家花拉子米名字的诬告。他在古代巴格达写了关于涉及十进制数系统的系统过程 - 一个来自印度的新概念,其中包含一个称为 0 的奇怪新事物。后来,在中世纪晚期,印度数字系统本身被称为algorism或augrym,还有两个以他的名字命名的腐败。因此,算法的概念植根于数字和数字操作——但绝不受其约束。
In the last century the word algorithm became synonymous with what we’ve been calling “systematic process.” The word is a corruption of the name of a ninth-century Persian arithmetic expert, al-Khwarizmi. He wrote in ancient Baghdad about systematic processes involving the decimal number system—a new concept just in from India featuring a strange new thing called 0. Later, in the late Middle Ages, that Indian number system itself came to be called algorism or augrym, two more corruptions honoring his name. So the notion of an algorithm is rooted in numbers and number manipulation—but by no means bound by it.
十四世纪的杰弗里乔叟使用奥格利姆中的名词来描述星盘上的标记。但他的朋友 Thomas Usk 以更令人印象深刻的方式使用了这个词。他的题词是关于 0 的力量——在augrym 中的 sypher。它本质上是说,虽然单独的 0 什么都不是,但附加的 0 很多。用我们的话来说,每个附加的 0 都是一个数量级的增加——确实是很多东西。他的预兆远不及我们的算法,但事后看来,他的格言似乎是对放大潜力的早熟观察。12
Geoffrey Chaucer in the fourteenth century used nombres in Augrym to describe markings on an astrolabe. But his friend Thomas Usk used the term in a more impressive way. His epigraph is about the power of the 0—the sypher in augrym. It essentially says that while a 0 alone is nothing, a 0 appended is a lot. In our terms, each appended 0 is an order-of-magnitude increase—a lot of something indeed. His augrym was nowhere near our algorithm, but his aphorism appears in hindsight to be a precocious observation about the potential of Amplification.12
当算法中的步骤数变大、循环数成倍增加、嵌套层次加深、条件分支大量分支时会发生什么?通过在 20 世纪之交询问有关系统过程的问题,数学家开始摸索通往计算世界的道路,但他们还不知道。他们还没有看到延展性和放大的双重荣耀,或与之相关的奥秘。
What happens when the number of steps in an algorithm gets large, the number of loops multiplies, their level of nesting deepens, and the conditional branches ramify vastly? By asking questions about systematic processes at the turn of the twentieth century, mathematicians started to feel their way toward the world of computation, but they didn’t know it yet. They hadn’t yet glimpsed the twin glories of Malleability and Amplification, or the mysteries associated with each.
大卫希尔伯特,一位数学家中的王子,在哥廷根大学,数学世界的中心——直到纳粹对犹太数学家的清洗摧毁了它。从 1900 年开始,希尔伯特利用他的国际声望专注于关注具体的难题,其中一些与数学本身的基础有关。这些著名的问题被命名为希尔伯特第二和希尔伯特第十。解决其中任何一个问题都会立即证明您是世界级的数学家。
David Hilbert, a prince among mathematicians, was at the University of Göttingen, a center of the mathematical universe—until the Nazi purge of Jewish mathematicians destroyed it. Beginning in 1900, Hilbert used his international prestige to focus attention on specific hard problems, some of which concerned the very foundations of mathematics itself. These famous problems took names such as Hilbert’s Second and Hilbert’s Tenth. Solving any one of them would immediately establish that you were a world-class mathematician.
1928 年,希尔伯特提出了另一个难题。这是一个简单的逻辑系统——称为一阶逻辑。数学家使用一阶逻辑来制定措辞准确的陈述,这些陈述可能是对的,也可能是错的。希尔伯特问是否有一种系统的方法,一种算法,来决定这个简单逻辑系统中的一个陈述是否正确。
In 1928 Hilbert posed another hard problem. This one was about a simple logic system—called first-order logic. Mathematicians use first-order logic to formulate precisely worded statements, which may be true or false. Hilbert asked if there was a systematic way, an algorithm, to decide if a statement in this simple logic system is true or not.
这是这样一种说法:所有物体都是松果。这是另一个:所有对象都是 quinces。系统中始终允许的复合语句是通过将任意两个其他语句与单词or组合而成的:所有对象都是 pinecones,或者所有对象都是 quinces。系统有一条规则,允许您用重新排列的与其等效的语句替换此组合语句:所有对象都是 pinecones 或 quinces。这里的词等价意思是如果前者为真,则后者为真,如果前者为假,则后者亦为。因此,单词的重新排列不会改变陈述的真值。简单的重新排列将两个最初的陈述折叠成一个陈述,其中或在松果和木瓜之间。这似乎很明显,但关键是这个逻辑系统中的每一步都使用简单甚至微不足道的操作将一个语句转换为等效的语句。新声明源自旧声明。
Here is such a statement: all objects are pinecones. Here’s another: all objects are quinces. A compound statement that is always allowed in the system is made by combining any two other statements with the word or: all objects are pinecones, or all objects are quinces. The system has a rule that lets you replace this combined statement with a rearranged one that’s equivalent to it: all objects are pinecones or quinces. Here the word equivalent means that if the former statement is true, then so is the latter, and if the former is false, then so is the latter. The rearrangement of words, then, doesn’t change the truth value of the statement. The simple rearrangement collapses the two initial statements that were joined by or into one statement with the or between pinecones and quinces instead. This seems obvious, but the point is that each step in this logic system transforms one statement into an equivalent one using a simple, even trivial, operation. The new statement derives from the old one.
推导是此类步骤的序列,其操作就像在每个步骤中应用的or规则一样简单。到目前为止,我们所描述的是一种系统的方法,它可以在每一步都保持真或假的方式来导出一个又一个陈述。如果你从真实的陈述开始,推导总是会产生真实的陈述。
Derivations are sequences of such steps, with operations as simple as the or rule applied at every step. What we’ve described so far is a systematic way to derive one statement after another in such a way that truth, or falsity, is maintained at each step. If you start with true statements, a derivation will always yield a true statement.
这是数学家感兴趣的真实陈述。它们从非常简单的——显然是正确的——陈述开始,并使用逻辑系统从中得出更多真实的陈述。他们开始的真实陈述被称为公理。例如,一个数等于它自己是一个公理。这显然总是正确的。数学令人敬畏的荣耀在于,即使每一步都很简单明了,这种推导也可能导致完全出乎意料的结果。
It’s the true statements that interest mathematicians. They start with very simple—obviously true—statements and derive more true statements from them using the logic system. The true statements they start with are called axioms. For example, it’s an axiom that a number is equal to itself. That’s obviously always true. The awesome glory of math is that such derivations can lead to totally unexpected results, even though every step is simple and obvious.
但希尔伯特要求的是一种决策算法,而不是推导。他并没有要求系统化过程实际上从公理中生成陈述的推导——只是它准确地确定推导是否可能。区别似乎并不重要。如果您可以确定一个陈述是正确的,为什么说明它实际上是如何从公理推导出来的很重要?事实证明,这非常重要。13
But Hilbert asked for a decision algorithm, not a derivation. He did not ask that the systematic process actually generate a derivation of the statement from the axioms—only that it accurately decide whether a derivation was possible or not. The distinction might seem unimportant. If you can decide that a statement is true, why is it important to show how it was actually derived from the axioms? It turns out to be fundamentally important.13
在学术的家族谱系中,我们可以知道,17 世纪的约瑟夫是今天在世的詹姆斯的直系祖先,但他们之间并没有正式建立父子关系,即世代相传。如果它们在 Y(雄性)染色体上共享相同的 DNA——一个简单的实验室测试证实了这一点——那么它们一定是由一个雄性系相关的。它们之间必须存在一条路径。但知道一条路径的存在与了解将特定 DNA 传递给男性线的实际男性系列完全不同——这通常很难确定。知道这样一条路径的存在可能会鼓励您花费研究精力来寻找实际路径——要知道您没有在徒劳的搜索中浪费时间。
In the scholarly genealogy of families, it’s possible to know that Joseph from the seventeenth century, say, was the direct ancestor of James alive today without formally establishing a father-to-son path, a generation-by-generation descent, between them. If they share the same DNA on the Y (male) chromosome—a straightforward lab test establishes this—then they must be related by a male line. A path between them must exist. But knowing that a path exists is nothing at all like knowing the actual series of males who passed the particular DNA down the male line—something that’s often quite difficult to establish. And knowing that such a path exists might encourage you to expend the research effort to find the actual path—to know you weren’t wasting your time in a futile search.
因此,希尔伯特在 1928 年提出的一个大问题是,简单逻辑是否有一个技巧——就像 DNA 测试一样——可以系统地决定一个陈述是否为真,而无需实际从明显为真的公理中推导出来。这被称为希尔伯特的 Entscheidungsproblem。
So Hilbert’s big question of 1928 asked if simple logic had a trick—like the DNA test—that would decide in a systematic way if a statement was true without actually doing the derivation from the obviously true axioms. This is called Hilbert’s Entscheidungsproblem.
这是一个令人生畏的名字,但它只是德语中的决策问题。是否有系统的方法来确定以简单逻辑表达的陈述的真值?然而,把它放在德语中,肯定会提高它对英语读者的深度。决策问题听起来像是一个商学院的话题,但 Entscheidungsproblem 建议一个 Götterdämmerung 来撼动和更新世界,这实际上就是它所做的。让我们称它为eProblem,因为它导致了电子邮件——并且说 Entscheidungsproblem 很快就会变得令人厌烦。
It’s a forbidding name, but it’s simply German for decision problem. Is there a systematic way to decide the truth value of statements expressed in simple logic? Putting it in German, however, surely heightens its profundity for English readers. Decision problem sounds like a business school topic, but Entscheidungsproblem suggests a Götterdämmerung to shake and renew the world, which is actually what it did. Let’s call it the eProblem since it led to email—and saying Entscheidungsproblem soon becomes tiring.
1934 年在英国,Max Newman 在剑桥大学的一次演讲中提出了 eProblem。他说的是一个系统的过程,但“机械过程”是他实际使用的术语。纽曼的措辞是关键。他也可以说“系统过程”、“有效过程”、“配方”或“算法”等等。这个概念还没有确切的词。这正是问题所在。14
In England in 1934, Max Newman presented the eProblem in a lecture at Cambridge University. He talked about a systematic process, but “mechanical process” was the term he actually used. Newman’s choice of words was key. He could just as well have said “systematic process,” “effective process,” “recipe,” or “algorithm,” among others. There were no precise words for the concept yet. That was exactly the problem.14
学生艾伦·图灵参加了那场讲座。极度字面意思的图灵开始用简单的纸“机器”将纽曼的“机械过程”形式化。纽曼肯定对他自己的学生感到惊讶——这么年轻(只有 22 岁)而且笨拙!结结巴巴!——在那场决定性的演讲后不久,用一台简单的机器解决了深刻的电子问题。事实上,纽曼一开始并不相信。这台机器看起来像一个玩具——不是严肃的数学。当然,如此深刻的数学结果不可能来自如此简单的设备。但他很快就对图灵的结果深信不疑。15
Student Alan Turing attended that lecture. The exceedingly literal-minded Turing proceeded to formalize Newman’s “mechanical process” with a simple paper “machine.” Newman was surely surprised that his own student—so young (only 22) and awkward! and stammering!—solved the profound eProblem with a simple machine not long after that fateful lecture. In fact, Newman didn’t believe it at first. The machine seemed like a toy—not serious math. Surely such a profound mathematical result couldn’t have come from such a simple device. But he quickly became convinced of Turing’s result.15
图灵使用他的机器——当然现在称为图灵机——来解决 eProblem。首先,他发明了计算——这正是图灵机所做的。然后他使用计算——对我们所说的系统或机械过程的精确描述——来解决问题。逻辑推导中的简单步骤序列可能会提醒您计算机采取的琐碎步骤的顺序。这两种情况都会从无意识的单个步骤中产生一些注意事项。图灵是第一个正式将两者联系起来的人,这让他成为了数学界的神。
Turing used his machine—now called a Turing machine, of course—to solve the eProblem. First, he invented computation—it’s exactly what Turing machines do. Then he used computation—a precise description of what we mean by systematic, or mechanical, process—to solve the problem. The sequences of simple steps in logical derivations might remind you of the sequences of trivial steps that computers take. Both cases yield something mindful from mindless individual steps. Turing was the first person to formally connect the two, and it made him a god in mathematics.
他表明,简单的逻辑没有技巧 DNA 测试。如果你能找到一个,你必须做完整的推导。不可能有希尔伯特要求的那种算法。正如数学家所说,图灵发现简单的逻辑是不可判定的。如此出乎意料和令人不安的结果,就连伟大的希尔伯特一开始也不相信。如果图灵没有做任何其他事情——比如拯救英国或发明计算——这将使他进入科学万神殿。他解决了其中一个难题。但正是他的机器——而不是他对 eProblem 的解决方案——让他在数学以外的更大世界中出名。现代计算机是图灵机器的直接概念后代。
He showed that there is no trick DNA test for simple logic. You have to do the full derivation, if you can find one. There can’t be an algorithm of the type that Hilbert had asked for. As mathematicians say, Turing found that simple logic is undecidable. It was such an unexpected and disturbing result that even the great Hilbert didn’t believe it at first. If Turing had done nothing else—like save Britain or invent computation—this would have put him in the scientific pantheon. He had solved one of the hard problems. But it was his machine—not his solution of the eProblem—that made him famous in the larger world outside math. The modern computer is a direct conceptual descendant of Turing’s machine.
在图灵解决 eProblem 的同时,新泽西州普林斯顿大学的 Alonzo Church 也在解决这个问题。大约在希尔伯特宣布 eProblem 的时候,美国数学家 Church 已经在哥廷根大学完成了研究生工作。事实上,Church 比 Turing 早了几个月的时间。按照学术界的规则,教会赢了,荣耀通常都是他的。但是图灵的求解技术与丘奇的截然不同。在数学中,证明方法通常与证明本身的事实一样重要。纽曼认为数学界应该知道图灵的新方法。
While Turing was solving the eProblem, so was Alonzo Church at Princeton University in New Jersey. Church, an American mathematician, had done graduate work at the University of Göttingen about the time that Hilbert announced the eProblem. In fact, Church beat Turing to the solution by several months. By the rules of academia Church had won and the glory would have normally been all his. But Turing’s solution technique was strikingly different from Church’s. In math the method of proof is often as important as the fact of the proof itself. Newman thought that the mathematical world should know about Turing’s new method.
纽曼敦促丘奇承认图灵的贡献,丘奇做到了。他们都在 1936 年通过印刷论文上市。这是一大步,因为启发计算机诞生的是图灵的直观、工业、甚至民俗机器,而不是 Church 的深奥形式化(lambda 可定义性)。它们是等价的概念——图灵在他的论文中证明了这一点——但图灵对词语的选择却产生了截然不同的后果。他们俩解决的难题对 Digital Light 来说并不重要,但图灵的解决技术——他的机器——才是。16
Newman urged Church to acknowledge Turing’s contribution, and Church did. They both went public with printed papers in 1936. This was a big step because it was Turing’s intuitive, industrial, even folksy, machine that inspired the birth of the computer, not Church’s abstruse formalization (lambda definability). They were equivalent concepts—Turing proved it in his paper—but Turing’s choice of words had profoundly different consequences. The hard problem that they both solved isn’t important to Digital Light, but Turing’s solution technique—his machine—is.16
这两种方法预示了一场仍然定义计算机科学的小冲突——象牙塔与臭气熏天的战斗。“带着臭味出去”是剑桥大学的俚语,用于获得自然科学学位——化学首当其冲。图灵在剑桥数学的无味、干净的象牙塔中构想了他的计算的伟大想法,但启发计算机的是他坚韧、真实的工业模型,而不是丘奇的纯数学概念。计算机科学仍然沿着这条线分裂。它与一些大学的数学和其他大学的工程混为一谈。延展性是一种塔现象,而放大是一种臭名昭著的荣耀。疯狂冲向第一台计算机的玩家将不得不跨越高塔-臭气熏天的鸿沟。17
The two approaches presaged a skirmish that still defines computer science—the battle of the ivory tower versus the stinks. “Going out in stinks” was slang at Cambridge for taking a degree in the natural sciences—chemistry bearing the brunt of the insult. Turing conceived his great idea of computation in the scentless, clean ivory tower of Cambridge mathematics, but it was his gritty, real, industrial model that inspired the computer, not Church’s pure mathematical concept. Computer science is still split along that line. It’s lumped with mathematics at some universities and engineering at others. Malleability is a tower phenomenon, and Amplification is a stinks glory. The players in the mad rush to the first computers would have to straddle the tower–stinks divide.17
图灵并不是唯一一个将系统过程的概念正式化的人。正如我们所见,Church 也这样做了,还有其他几个。但是图灵的方法是如此有影响力,以至于其他方法相形见绌。在我们的普通世界中,我们仍然使用他在 1936 年的开创性论文中在剑桥引入的概念。他的词可计算是卡住的词。他还给了我们编程的想法,尽管他没有这么称呼它。这使他成为第一个程序员。而且,唉,他是第一个编写有缺陷的软件的人。18
Turing wasn’t the only person to formalize the notion of systematic process. Church did that too, as we’ve seen, and there were several others. But Turing’s method has been so influential that the other approaches pale in comparison. In our ordinary world we still use the concepts that he introduced at Cambridge in his seminal 1936 paper. His word computable is the one that stuck. He also gave us the idea of programming, although he didn’t call it that. That makes him the first programmer. Also, alas, he was the first to write buggy software.18
他是另一个计算机传统的第一个例子。他古怪的性格——强烈的字面意思、对错误的诚实、社交尴尬和对服装的漠视——使他有资格成为第一个极客。也许我们现在会说他“在光谱上”。19
And he was the first example of another computer tradition. His quirky personality—intense literal-mindedness, honesty to a fault, social awkwardness, and sartorial disregard—qualified him as the first geek. Perhaps we would now say he was “on the spectrum.”19
纽曼担心图灵很快就会成为“被证实的孤独者”,并告诉了丘奇。纽曼认为,与普林斯顿大学的逻辑精英——会说同一种语言的人——交流可能会扭转这种趋势。于是他要求丘奇接受图灵为研究生,丘奇再次答应了。图灵将在美国教堂获得博士学位。
Newman was afraid that Turing was fast becoming a “confirmed solitary” and told Church so. Newman thought that mixing with the logical elite at Princeton University—people who could speak the same language—might reverse this tendency. So he asked Church to accept Turing as a graduate student, and Church obliged again. Turing would earn his PhD under Church in America.
图灵乘坐轮船Berengaria前往美国,于 1936 年 9 月在曼哈顿下船。这只是一个巧合,但 Kotelnikov 最近于 5 月降落在那里,也在Berengaria上。俄罗斯人只逗留了 60 天,可能参与了曼哈顿市中心 Amtorg 贸易公司的密码工作。图灵到达时,他已经启程回家了。两艘船在黑暗中经过,可以这么说——在同一艘船上。
Turing sailed to the States on the steamship Berengaria, disembarking in Manhattan in September 1936. It’s just a coincidence, but Kotelnikov had recently landed there, also on the Berengaria, in May. The Russian stayed only 60 days, probably involved in secret code work at the Amtorg Trading Company in downtown Manhattan. He’d already departed for home by the time Turing arrived. Two ships passing in the dark, so to speak—on the same ship.
在这个巧合之后不久就形成了真正的联系。图灵从曼哈顿前往附近的普林斯顿大学学习。然后,他的导师纽曼来到普林斯顿进行了为期六个月的访问,访问了邻近的高等研究院——有时称普林斯学院以将其与大学区分开来(并将演讲者从 IAS 口中拯救出来)。约翰·冯·诺依曼(John von Neumann)——这个故事中的另一位重要人物——已经在王子学院作为其首批永久学者之一。20
A real nexus formed shortly after this coincidence. Turing proceeded from Manhattan to nearby Princeton for his studies there. Then his mentor, Newman, came for a six-month visit to Princeton, to the neighboring Institute for Advanced Study—sometimes called the Princetitute to distinguish it from the University (and to save the speaker from the IAS mouthful). John von Neumann—another major player in this story—was already at the Princetitute as one of its first permanent scholars.20
要了解图灵的好主意,请考虑图 3.2 中的名片。它有一个角被切除,中间有一个圆孔。正面(有版权)和背面都刻有铭文。您可以欣赏这张卡看似简单的欺骗性,但不要被愚弄——它非常强大。
To get a handle on Turing’s great idea, consider the business card in figure 3.2. It has one corner cut off and a round hole in the center. Both the front (with copyright) and the back are inscribed. You can admire the deceptive simplicity of this card, but don’t be fooled—it’s amazingly powerful.
想象一下卡片后面有一条从左到右的纸带。它被分成方格,通过卡片上的洞你可以看到一个方格。磁带大部分是空白的,但通常有一个或多个带有符号的正方形。在这种情况下,我选择了非空白符号作为数字 1、2、3、4 和 5,但它们也可以是 #、!、$、% 和 &。关键是它们是不同的标记,没有意义。特别是,它们不是数字。我们称它们为符号,但它们没有任何象征意义。只需将 1 替换为 #,将 2 替换为 !,等等,在此名片设备的描述中到处都是,没有任何变化——除了方块上标记的形状。
Imagine that there’s a paper tape running from left to right behind the card. It’s divided into squares, and you can see one square through the hole in the card. The tape is mostly blank, but there are typically one or more squares with symbols on them. I chose the non-blank symbols in this case to be the numerals 1, 2, 3, 4, and 5, but they could just as well be #, !, $, %, and &. The point is that they’re distinct marks, without meaning. In particular, they’re not numbers. We call them symbols, but they symbolize nothing. Simply replace a 1 with #, a 2 with a !, and so on, everywhere in the description of this business card device, and nothing changes—except the shapes of the marks on the squares.
图 3.2
Figure 3.2
图 3.3,第 1 步(顶行)显示了一个磁带,上面只有四个标记:5155。磁带的其余部分是空白的。该卡显示为略微透明,以便您可以通过它看到胶带。卡片右侧的奇怪标记列表——带有圆圈的数字、冒号、箭头等——包含了管理该设备的六个规则。磁带上每个可能的符号都有一个规则。卡片左侧的倒置列表还有六个规则。
Figure 3.3, step 1 (top row), shows a tape with just four marks on it: 5155. The rest of the tape is blank. The card is shown slightly transparent so that you can see the tape through it. The list of strange markings down the right side of the card—with the circled numbers, colons, arrows, and so on—contains six of the rules that govern this device. There is one rule for each possible symbol on the tape. The upside-down list at the left of the card holds six more rules.
名片设备是这样工作的。找到孔中符号的规则。(不要注意颠倒的规则。)对于第 1 步,它是右上角的规则,即空白处的规则。空格后面有一个冒号,后跟一个 5。它说用 5 替换空格——在空格中写一个 5。5 之后是左箭头。它说将卡片向左移动一格。规则右侧的小字形代表名片本身。它说您应该旋转卡片以匹配字形的方向。在这种情况下,这意味着将卡片顺时针旋转半圈,将裁剪的角放在西北位置,从而产生步骤 2 配置。
The business card device works like this. Find the rule for the symbol in the hole. (Pay no attention to rules written upside down.) For step 1, it’s the rule at top right, the one for the blank. There’s a colon after the blank, followed by a 5. It says to replace the blank with a 5—write a 5 in the blank. Following the 5 is a left arrow. It says to move the card left by one square. The little glyph at the right of the rule represents the business card itself. It says that you should rotate the card to match the glyph’s orientation. In this case, it means to rotate the card one half turn clockwise, putting the cropped corner in the northwest position, resulting in the step 2 configuration.
适用于第 2 步的规则位于右下角,用于孔中的符号 5。它说将 5 更改为 2——擦除 5 然后写一个 2——然后向右移动一格。这次没有小卡片字形,所以卡片保持相同的方向。步骤 3 配置就是结果。
The rule that applies in step 2 is at the lower right, for the symbol 5 in the hole. It says to change the 5 to a 2—erase the 5 then write a 2—then move right one square. There’s no little card glyph this time, so the card remains in the same orientation. The step 3 configuration is the result.
图 3.3
Figure 3.3
向前跳过两个步骤给出步骤 5 配置(步骤 4 未显示)。在这些步骤中,卡片保持相同的方向(西北)。在这种情况下应用的规则是从右上角开始的第三个规则:将 2 更改为 3,向左移动一格,然后将卡片旋转到所示方向。这里的意思是把卡片翻过来,把裁剪好的角落放在西南。这揭示了卡片的另一面(如步骤 6 所示)和另外两个不同于我们目前看到的两个列表的规则列表。
Skipping ahead two steps gives the step 5 configuration (step 4 not shown). The card maintains the same orientation (northwest) during these steps. The rule to apply in this case is the third one from the upper right: change the 2 to a 3, move left one square, and rotate the card to the orientation shown. Here it means to turn the card over, putting the cropped corner in the southwest. This reveals the other side of the card (shown in step 6) and two more lists of rules different from the two lists we’ve seen so far.
依此类推。如果你进一步追求这种乏味,你会发现这张牌最终会回到原来的方向,洞里有一个 4。适用的规则没有冒号的权利,这意味着没有其他事情发生。计算停止。
And so on and on. If you pursue this tedium further, you’ll find that the card will eventually end up in its original orientation, with a 4 in the hole. The rule that applies has nothing right of the colon, which means nothing else happens. The computation halts.
这不是一场闲置的游戏。不管你信不信,目标是Digital Light。名片设备是图灵机。这是图灵的玩具之一。这是图灵最著名的发明的硬件实现。
This hasn’t been an idle game. The goal, believe it or not, is Digital Light. The business card device is a Turing machine. This is one of Turing’s toys. It’s a hardware implementation of Turing’s most famous invention.
在 1930 年代,“计算机”是一个人——通常是一个女人——执行例如保险公司的簿记过程,或者后来 Bletchley Park 的密码破译过程。在与他的母亲 Sara 的谈话中,图灵将在那里为他工作的数百台“计算机”称为“奴隶”——这表明了系统(或“机械”)过程的惩罚性质。21
In the 1930s a “computer” was a human—usually a woman—who executed the bookkeeping processes of, say, an insurance company or later the codebreaking processes of Bletchley Park. In conversation with his mother Sara, Turing referred to the hundred or so “computers” working for him there as “slaves”—which indicates the punishing nature of systematic (or “mechanical”) processes.21
图灵捕捉到了“计算机”在仔细执行系统过程(例如添加几十个数字的列表)时用铅笔和纸做的事情,也许会用茶歇来打断工作。图灵机是他设计的模型,它捕捉了他们所做工作的本质简单性。
Turing captured what “computers” did with pencil and paper when they carefully executed a systematic process—such as adding a list of, say, several dozen numbers—perhaps interrupting the effort with a tea break. A Turing machine was the model he devised that captured the essential simplicity of what they did.
但它并没有捕捉到他们的乏味。单调乏味——正如你已经发现,如果你遵循了上面的说明——来自于小步骤的不断重复,不断担心错误,以及努力跟踪——比如说,在茶歇期间。它也没有捕捉到他们的无聊。回想一下斯托帕德的汉娜:“无聊呢?瓦尔!这就是你说的吗?” 机器不会感到乏味或无聊。这些都是人的问题。图灵创建了一个抽象模型,说明“计算机”的作用。他把她的乏味从存在中抽象出来,认为是无关紧要的。他坚持诸如不同的心理状态、多个步骤、书写和擦除符号以及无休止的草稿纸供应等概念。
But it didn’t capture their tedium. The tedium comes—as you’ve discovered if you followed the instructions above—from the unceasing repetition of the tiny steps, the constant worry of error, and the effort of keeping track—during a tea break, say. Nor did it capture their boredom. Recall Stoppard’s Hannah: “And the boredom? Val! Is that what you’re saying?” A machine wouldn’t suffer tedium or get bored. Those are human problems. Turing created an abstract model of what a “computer” does that matters. He abstracted her tedium out of existence as immaterial. He maintained notions such as different states of mind, multiple steps, writing and erasing symbols, and an endless supply of scratch paper.
名片可能采用四种可能的方向或状态,并且有六个符号(计算空白)。因此,卡片的每个方向都有六个规则,每个可能出现在孔中的符号一个。一般规则是,每一步孔中的符号可能会改变,孔向左或向右移动一格,卡片方向可能会改变。或者它可能只是停止。这里的所有都是它的。22
There are four possible orientations—or states—the business card may take, and there are six symbols (counting the blank). So, there are six rules for each orientation of the card, one for each symbol that might appear in the hole. The general rule is that at each step the symbol in the hole may change, the hole moves left or right one square, and the card orientation may change. Or it may simply stop. That’s all there is to it.22
图灵将他的每台机器定义为只有四样东西:一维磁带分成正方形,一组有限的符号,一个带有限元的磁带扫描仪状态数,以及一个“指令表”,告诉您如何处理扫描仪状态和磁带符号的每种组合。在我们运行的示例中,磁带扫描仪是一张有孔的名片,六个符号是数字 1 到 5 和一个空白,四个状态是卡片的四个方向。四组规则构成指令表。还有一件事。磁带在任一方向上都尽可能长。如果您需要,总会有另一个广场。总是有更多的草稿纸。也许你现在可以理解为什么纽曼起初无法相信如此简单的设备——它看起来像是一个玩具——会产生一个深刻的数学结果。但是从这个简单的“机器”概念中产生了所有的计算。
Turing defined each of his machines to have only four things: a one-dimensional tape divided into squares, a finite set of symbols for it, a tape scanner with a finite number of states, and an “instruction table” that tells you what to do with each combination of scanner state and tape symbol. In our running example, the tape scanner is the business card with a hole in it, the six symbols are the digits 1 through 5 and a blank, and the four states are the four orientations of the card. The four sets of rules form the instruction table. And one other thing. The tape is as long as necessary in either direction. There’s always another square if you need it. There’s always more scratch paper. Perhaps you can understand now why Newman couldn’t believe at first that such a simple device—a toy it seems—led to a profound mathematical result. But from this simple “machine” concept came all of computing.
您可能会在名片设备中瞥见现代计算机。磁带扫描仪——卡——是 CPU(中央处理器),磁带是内存。但是现代计算机可以执行任何计算,只需更改其程序,无论这意味着什么。当然,我们简单的名片设备不能执行任何计算,不是吗?这是惊喜。是的,它可以。皮克斯可以用它计算玩具总动员!然而,他们不想这样做,因为它太慢了,可能会占用整个宇宙的生命周期,但速度是一个可分离的问题,将在下一章中讨论。关键是我们的设备不仅仅是任何普通的图灵机。名片机是通用的图灵机。23
You might glimpse the modern computer in the business card device. The tape scanner—the card—is the CPU (central processing unit), and the tape is the memory. But a modern computer can execute any computation, by simply changing its program, whatever that means. Surely our simple business card device can’t execute any computation, can it? Here’s the surprise. Yes, it can. Pixar could compute Toy Story with it! They wouldn’t want to, however, because it’s so tediously slow that it might take the lifetime of the universe, but speed is a separable issue, addressed in the next chapter. The point is that our device isn’t just any ordinary Turing machine. The business card machine is a universal Turing machine.23
图灵的伟大想法不仅在于图灵机可以执行系统化过程——我们所说的“系统化过程”或“机械化过程”正是在图灵机中体现出来的。但这本身就是一个很好的主意。加法算法——如何将两个数字相加得到它们的总和——就是这样一个过程。因此,必须有一台图灵机将其磁带上的两个数字相加,并在其磁带上生成它们的总和。并且什么都不做。
Turing’s great idea wasn’t only that a Turing machine could execute a systematic process—that what we mean by a “systematic process” or “mechanical process” is embodied exactly in a Turing machine. But that was a pretty good idea all by itself. The addition algorithm—how to add two numbers together to get their sum—is such a process. So, there has to be a Turing machine that adds two numbers on its tape together and generates their sum on its tape. And does nothing else.
另一种系统过程是反转任何字母串的过程。例如,给定abcdefg,它交换最外面的一对字母,然后是下一个最外面的一对,依此类推。它继续进行,直到没有更多的对可以交换,或者直到只剩下一个字母,在这种情况下产生gfedcba 。因此,存在一台图灵机,它将对其磁带上的任何字符串进行这种反转,而不是其他任何东西。
Another systematic process is one that reverses any string of letters. For example, given abcdefg, it swaps the outermost pair of letters, then the next most outermost pair, and so on. It proceeds until there are no more pairs to swap, or until only a single letter remains, yielding gfedcba in this case. Therefore, a Turing machine exists that will do this reversal for any string on its tape, and nothing else.
然而,图灵的大师之作是展示了一台图灵机如何能够完成任何其他图灵机所能做的事情。它可以执行所有系统过程——包括两个数字的相加或一串字母的反转。它是一台可以计算任何可计算事物的机器。这就是通用在计算中的含义。当我们说图灵的伟大想法是计算时,我们的意思是它是通用计算。现代计算机是这种特殊的图灵机,通用图灵机的后代。但是图灵机怎么能通用呢?
Turing’s master stroke, however, was to show how a single Turing machine can do what any other Turing machine can do. It can perform all systematic processes—including addition of two numbers or reversal of a string of letters. It’s one machine that can compute anything that’s computable. That’s what universal means in computation. When we say Turing’s great idea was computation, we mean it was universal computation. The modern computer is a descendant of this particular kind of Turing machine, the universal Turing machine. But how can a Turing machine be universal?
不要向外行解释计算机。向处女解释性行为更简单。
——罗伯特 A. 海因莱因,《月亮是个严厉的情妇》24
Don’t explain computers to laymen. Simpler to explain sex to a virgin.
—Robert A. Heinlein, The Moon Is a Harsh Mistress24
海因莱因该死!图灵使他的一台机器通用的技巧很聪明。图灵机是由其规则集定义的简单事物。例如,名片机由其 24 条规则定义,卡片的每个方向有 6 条规则。所以图灵推断,必须有可能设计一个图灵机,它可以描述任何图灵机,加上该机器的输入,并模拟该机器在给定磁带的情况下会做什么。他认为这是可能的原因是这样的模拟是一个系统过程,而图灵机旨在捕捉我们所说的系统过程的意思。模拟任何其他机器的图灵机是通用图灵机,图灵展示了如何构建这样的机器。
Heinlein be damned! Turing’s trick for making one of his machines universal is clever. A Turing machine is a simple thing that’s defined by its set of rules. The business card machine, for example, is defined by its 24 rules, 6 for each orientation of the card. So Turing reasoned that it must be possible to design a Turing machine that could take a description of any Turing machine, plus the input to that machine, and simulate what that machine would do given that tape. The reason he believed it to be possible is that such a simulation is a systematic process, and a Turing machine is meant to capture just what we mean by systematic process. A Turing machine that simulates any other is a universal Turing machine, and Turing showed how you could construct such a machine.
图 3.4 中的 A 代表任何图灵机,被描绘为沿着无限长的磁带左右移动的扫描头。名片机就是一个例子。它的“扫描头”就是卡片上的孔。名片将是我们运行任意图灵机 A 的示例。U 是一个通用图灵机,可以模拟任何图灵机 A,给定 A 的规则的一维描述 - 它的指令集 - 和 A 的磁带数据的描述.
The A in figure 3.4 represents any Turing machine, depicted as a scanning head that moves left and right along an infinite tape. The business card machine is an example. Its “scanning head” is the hole in the card. The business card will be our running example of an arbitrary Turing machine A. U is a universal Turing machine that can simulate any Turing machine A, given a one-dimensional description of A’s rules—its instruction set—and a description of A’s tape data.
在我们的示例中,A 的规则就是指定名片机的 24 条规则。它们被编码成UA 要求的格式。名片上的规则是以两张二维指令表的形式写在名片的两侧,其中一半倒置。U 的磁带上需要这些规则的一维版本,写在 U 在那里使用的符号集中。我们将很快展示 A 规则的示例编码。
In our example, A’s rules are just the 24 rules that specify the business card machine. They are encoded into a form required by U. A’s rules as presented on the business card are in the form of two two-dimensional tables of instructions written on two sides of the card, with half of them upside down. U needs a one-dimensional version of these rules on its tape, written in the set of symbols that U uses there. We will show an example encoding of A’s rules shortly.
图 3.4
Figure 3.4
A 的数据是指最初出现在其磁带上的非空白符号——例如,5155 是前面示例中名片机的初始数据。它也被编码成 U 所需的形式。我们还将展示 A 的数据编码示例。换句话说,通用图灵机磁带上的初始数据 U 由 A 的规则和A 的数据组成,呈一维形式,如图所示。
By A’s data we mean the nonblank symbols that appear initially on its tape—for instance, 5155 was the initial data for the business card machine in the earlier example. It is also encoded into a form required by U. We will show an example of A’s data encoding too. In words, the initial data on the tape of the universal Turing machine, U, consists of both A’s rules and A’s data, in one-dimensional form, as shown.
图灵注意到任何图灵机的规则集都可以写成一行符号。对于名片示例,如果您对名片的四个方向(正面、背面、旋转正面和旋转)使用一个符号缩写 f、b、F 和 B,则可以在一行中列出所有 24 条规则返回——将规则分成这四组,每组有六条规则:
Turing noticed that the set of rules of any Turing machine can be written into one line of symbols. For the business card example, you can list all 24 of its rules in a single line if you use one-symbol abbreviations f, b, F, and B for the four orientations of the card—front, back, rotated front, and rotated back—and divide the rules into those four groups, with six rules per group:
(六f规则) (六b规则) (六F规则) (六B规则)
(six f rules) (six b rules) (six F rules) (six B rules)
请参阅注释以了解此编码的实际外观。
See the annotation for how this encoding might actually look.
图灵的第一个技巧是将单行机器描述写到 U 的磁带上,每个磁带方格一个符号。把它想象成写在磁带的左半边。
Turing’s first trick was to write that one-line machine description onto U’s tape, one symbol per tape square. Think of it as written in the left half of the tape.
图灵的第二个技巧是在 A 的描述右侧写一个 A 的磁带的单行描述,包含它的初始数据。这里的编码很简单。所以我们的名片机的描述和初始数据可能是这样的,使用竖线分隔两者,使用 0 编码空白:
Turing’s second trick was to write a one-line description of A’s tape, containing its initial data, to the right of A’s description. The encoding here is straightforward. So our business card machine’s description and initial data might look like this, using a vertical bar to separate the two and a 0 to encode a blank:
(六f规则) (六b规则) (六f规则) (六B规则) | 000000051550000000
(six f rules) (six b rules) (six F rules) (six B rules) | 000000051550000000
在这一点上,通用图灵机 U“知道”任意图灵机 A 是什么,因为它具有对该机器行为的完整描述,如其规则所表达的那样。通用机器知道任意机器最初查看的是什么磁带。U 知道它的输入数据。
At this point the universal Turing machine U “knows” what the arbitrary Turing machine A is because it has a complete description of that machine’s behavior, as expressed by its rules. And the universal machine knows what tape that arbitrary machine is initially looking at. U knows its input data.
通用机器只需要知道另外两件事来模拟任意机器 A:它当前正在扫描哪个符号以及它当前处于什么状态。图灵的第三个技巧是在磁带的左侧添加一个符号,指示当前状态和另一个符号右半部分表示当前扫描的方块。关于任意机器 A 的这四条信息——它的描述、初始数据、初始状态和初始扫描符号——形成了通用机器的初始数据。下面是 U 的名片机输入磁带在背面方向的表示,在初始数据 5155 上,最初扫描右侧的空白 (0):
The universal machine needs to know only two more things to simulate arbitrary machine A: which symbol it’s currently scanning and what state it’s currently in. Turing’s third trick was to add a symbol on the left part of the tape indicating the current state and another symbol on the right half indicating the currently scanned square. These four pieces of information about arbitrary machine A—its description, initial data, initial state, and initially scanned symbol—form the initial data for the universal machine. Here’s a representation of U’s input tape for the business card machine in back orientation, on initial data 5155, and initially scanning the blank (0) just to the right:
(六f规则) (六b规则) (六f规则) (六B规则) | 00000005155 0 000000
(six f rules) (six b rules) (six F rules) (six B rules) | 000000051550000000
粗体0标记最初扫描的符号,粗体b标记卡片的初始方向,因此使用哪些规则。请参阅注释以了解 U 磁带的实际外观。
The bold 0 marks the initially scanned symbol, and the bold b marks the initial orientation of the card, hence which rules to use. See the annotation for how U’s tape might actually look.
为 U 设计一组规则以便它可以模拟任意机器 A 像这样编码到 U 的磁带上是一个乏味的过程。关键是 U 可以“看到”任意机器的完整描述以及该任意机器的数据的完整描述。它可以查看任意机器的当前状态以及该机器的数据磁带当前扫描的方块。这是对要模拟的机器的完整描述。下一刻可以类似地模拟,因此图灵在他 1936 年的著名论文中设计了一个 U,可以系统地将一个时刻的表示转换为下一个时刻的表示。所以后来在模拟名片机的时候,U的磁带是这样的:
The design of a set of rules for U so that it can simulate an arbitrary machine A encoded like this onto U’s tape is a tedious process. The point is that U can “see” a complete description of the arbitrary machine and a complete description of the data for that arbitrary machine. It can see the current state of the arbitrary machine and the currently scanned square of that machine’s data tape. That’s a complete description—at one moment—of the machine to be simulated. The next moment can be similarly simulated, so Turing designed a U in his famous 1936 paper that could systematically convert the representation for one moment into the representation for the next moment. So at some later time in the simulation of the business card machine, U’s tape looks like this:
(六f规则) (六b规则) (六f规则) (六B规则) | 0000000515 5 5000000
(six f rules) (six b rules) (six F rules) (six B rules) | 000000051555000000
然后它会模拟下一步,然后是下一步,以此类推。实际的构造是痛苦的,但它的要点并不难。如果您愿意失去海因莱因童贞,请阅读注释以了解模拟的更多详细信息。
Then it would simulate the next step, and then the next step, and so on. The actual construction is painful, but the gist of it isn’t hard. If you’re willing to lose your Heinleinian virginity, read the annotation for further details of the simulation.
图灵展示了机器 U 如何模拟任意机器 A 的每个操作步骤。仅模拟 A 的一个步骤需要很多 U 的步骤,但这对论证无关紧要——速度对于计算的概念并不重要。U 是一台通用计算机,因为它可以计算任何其他机器可以计算的任何东西。只需更改 U 磁带的描述部分即可更改计算的内容。
Turing showed how machine U can simulate each step of operation of an arbitrary machine A. It takes lots of U’s steps to simulate only one of A’s steps, but that’s immaterial to the argument—speed doesn’t matter for the concept of computation. U is a universal computer because it can compute anything that any other machine can compute. Just change the description part of U’s tape to change what gets computed.
图灵发明了编程。用现代术语来说,图灵将任意机器的程序存储在通用机器的内存中,他也将数据存储在那里——通用机器磁带的左右两半。要更改通用机器模拟的机器——即它执行的计算——你只需要更改程序,即磁带左半部分的描述部分。
Turing had invented programming. In modern terminology, Turing stored the program of an arbitrary machine in the memory of the universal machine, and he stored the data for it there too—in the left and right halves of the universal machine’s tape. To change which machine the universal machine simulates—that is, which computation it performs—you need only change the program, the description part in the left half of the tape.
通用图灵机本质上就是我们现在所说的存储程序计算机,因为它以相同的方式存储程序和数据——都在机器的内存中。存储程序计算机就是我们今天所说的单字计算机。我们称任何特定的机器 A,如其编码规则所代表的,计算机程序,或只是程序。这也解释了为什么程序员经常称自己为编码员。他们将任意算法(由特定的图灵机实现)编码为计算机 U 所需的一维形式。图 3.5 显示了通用图灵机 U 如何隐喻地对应于现代计算机。
The universal Turing machine is, in essence, what we now call a stored-program computer, since it stores the program and the data in the same way—both in the memory of the machine. And a stored-program computer is what we mean by the single word computer today. We call any particular machine A, as represented by its encoded rules, a computer program, or just program. This also explains why programmers often call themselves coders. They encode an arbitrary algorithm—implemented by a particular Turing machine—into the one-dimensional form the computer U needs. Figure 3.5 shows how a universal Turing machine U corresponds metaphorically to a modern computer.
现代计算机几乎总是将其程序分成至少两个部分。一部分称为操作系统,或OS,例如 Windows、MacOS 或 AndroidOS。该程序部分始终在运行。这是需要无限循环的情况。为满足您的个人需求而进行更改的程序部分称为应用程序 (或app,流行)。类似地,数据存储器将对操作系统重要的数据与应用程序的数据分开保存。操作系统只是“处理事务”,例如将应用程序加载到内存中的正确位置并启动,处理鼠标或手指输入,以及监视电源故障。这是一个代表现代计算机中任意图灵机 A 的应用程序。每个算法或系统过程都有这样一个 A。这就是计算世界的基础。
A modern computer nearly always has its program divided into at least two parts. One part is called the operating system, or OS, such as Windows, MacOS, or AndroidOS. This program part is always running. It’s a case where an infinite loop is desirable. The program part that gets changed to meet your individual needs is called an application (or app, popularly). Similarly, the data memory holds data of importance to the operating system separate from the data for the app. The operating system just “takes care of business,” like getting an app loaded into memory in the right place and started, taking care of mouse or finger input, and watching for power failure. It’s an app that represents an arbitrary Turing machine A in a modern computer. And there’s such an A for every algorithm, or systematic process. That’s the observation that underlies the world of computation.
图 3.5
Figure 3.5
值得再次说明图灵的成就。他表明,有一台机器可以做任何系统化的事情。它不能敲钉子或敲击钢琴键,但它可以做任何可以用符号表示的系统操作(然后符号输出可用于驱动敲钉子或敲击琴键的机器)。要改变机器的功能,你所要做的就是改变它的程序或应用程序。他发明了计算机的概念——我们指的是存储程序计算机。我们在硬件中实现它只是为了让它快速运行。
It’s worth stating again what Turing accomplished. He showed that there’s a single machine that can do anything that’s systematic. It can’t hammer nails or strike piano keys, but it can do anything systematic that can be represented with symbols (and then the symbolic output can be used to drive a machine that hammers nails or strikes keys). To change what the machine does, all you have to do is change its program, or app. He invented the concept of computer—by which we mean stored-program computer. We realize it in hardware only to make it go fast.
一台计算机可以计算多少个程序?它可以运行多少个应用程序?嗯,有这么多,你永远无法数完它们。这就像问一架钢琴可以演奏多少首乐曲。计算机是人类发明的最具延展性的工具。这就是延展性的奇妙之处。Digital Light 只是其无限折叠所拥抱的世界之一。
How many programs can a computer compute? How many apps can it run? Well, there are so many that you can’t ever finish counting them. It’s like asking how many pieces of music a piano can play. The computer is the most malleable tool ever invented by humankind. That’s the wonder of Malleability. Digital Light is just one of the worlds embraced in its infinite folds.
Princetitute——普林斯顿高等研究院的俚语——吸引了天才,尤其是那些逃离纳粹欧洲的天才。它已经收集了一个图灵和纽曼在 1930 年代后期抵达镇上时,这群星团虽小但令人印象深刻,图灵在读研究生,纽曼在休假。最著名的是,阿尔伯特·爱因斯坦已经在那里了。但对于我们的故事来说更重要的是,约翰·冯·诺依曼也是如此。
The Princetitute—slang for the Institute for Advanced Studies in Princeton—was a magnet for geniuses, particularly those fleeing Nazi Europe. It had already collected a small but impressive cluster of stars when Turing and Newman arrived in town in the late 1930s, Turing for his graduate studies and Newman for a sabbatical. Most famously, Albert Einstein was already there. But more importantly for our story, so was John von Neumann.
他于 1903 年 12 月 28 日在布达佩斯出生于 Neumann János Lajos。他的父亲是银行家马克斯·诺伊曼。1913 年,奥匈帝国政府授予马克斯高贵——大概是因为他的经济援助——这使他能够使用冯姓形式。所以马克斯的儿子在美国一直被称为约翰·冯·诺依曼。他于 1933 年永久搬到那里,并成为王子学院最早的成员之一。
He was born Neumann János Lajos on December 28, 1903, in Budapest. His father was Max Neumann, a banker. In 1913 the Austro-Hungarian government ennobled Max—presumably for his financial assistance—which allowed him to use the von surname form. So Max’s son was always known as John von Neumann in America. He moved there permanently in 1933 and became one of the earliest members of the Princetitute.
约翰曾是布达佩斯富裕精英的一员,并在他的新国家继续享受贵族的生活方式。例如,他总是开凯迪拉克,但它们经常被破坏和更换,这是他个性的线索。他回答“约翰尼”,另一个线索。这张约翰尼的著名照片(图 3.6,左上角)显示他身着西装,打着领带——他平时的着装——骑着一头背对着其他人的骡子(你可能会说屁股向后),在开往 Grand 的火车上峡谷。他是一位热情而亲切的主人。他喜欢马提尼酒、可笑的派对帽和一首好色的打油诗。25
John had been a member of the wealthy elite of Budapest and continued to enjoy an aristocratic lifestyle in his new country. He always drove Cadillacs, for example, but they were often wrecked and replaced, a clue to his personality. And he answered to “Johnny,” another clue. This famous photograph of Johnny (figure 3.6, top left) shows him in a business suit and tie—his usual dress—astride a mule that faces away from all the others (ass backward, you might say) in a train headed into the Grand Canyon. He was a bon vivant and gracious host. He loved martinis, ridiculous party hats, and a good salacious limerick.25
冯诺依曼因其对量子物理学和博弈论等多个领域的贡献而闻名,更不用说他在秘密的曼哈顿计划中的成员资格,以发展核武器,并随后成为原子能委员会的成员。但他也因对计算机的贡献而闻名,最著名的是一种被广泛模仿的计算机子系统的通用组织,称为冯诺依曼架构。
Von Neumann became famous for his contributions to fields as diverse as quantum physics and game theory, not to mention his membership in the secretive Manhattan Project for the development of nuclear weapons, and subsequent membership in the Atomic Energy Commission. But he also became famous for his contributions to computers, most notably a widely emulated general organization of computer subsystems called the von Neumann architecture.
他是天才中的天才,是“头脑最快”的“最聪明的人”。他无疑是美国人在计算机竞赛中的常驻天才,他们的对手是英国天才艾伦·图灵。从两者的角度来看,可以很方便地总结一下,Digital Light 的知识遗产来源于存储程序的计算概念,主要归功于 Turing,以及实现该概念的架构,主要归功于 von Neumann。26
He was a genius’s genius, the “cleverest man” with the “fastest mind.” He was certainly the resident genius of the Americans in the race to the computer, their counterpart to the British genius, Alan Turing. To put the two in perspective, it’s convenient to summarize that the intellectual heritage of Digital Light derives from the stored-program conception of computation, principally due to Turing, and from the architecture implementing that conception, principally due to von Neumann.26
冯诺依曼短暂地参与了大卫希尔伯特对数学基础的著名挑战之一。在图灵解决希尔伯特的 Entscheidungsproblem,eProblem 之前几年,他尝试了希尔伯特的第二个问题。
Von Neumann was fleetingly involved with one of David Hilbert’s famous challenges to the foundations of mathematics. He made a stab at Hilbert’s Second Problem several years before Turing tackled Hilbert’s Entscheidungsproblem, the eProblem.
希尔伯特的第二个问题是算术公理——算术的基本,甚至是显而易见的真理——是否一致。重要的是,希尔伯特认为,证明简单的算术——至少——是由一个不会导致矛盾的逻辑系统支持的。这似乎是合理的,但 1931 年库尔特·哥德尔在维也纳证明了这一点一个足够强大以支持算术并且没有矛盾的系统是不完整的。这个令人惊讶的结果,被称为哥德尔不完备定理,意味着在这样一个逻辑系统中必须存在无法在该系统中证明的算术真理。这是另一种说法:一致性的代价要求你满足于不能系统地证明一切。哥德尔的结果表明,不可能有一个通用的数学机器来推导每一个数学真理——这与图灵后来的结果(1936 年)相反,即有一个通用的计算机来处理所有可计算的事情。
Hilbert’s Second asked if the axioms of arithmetic—the fundamental, even obvious, truths of arithmetic—are consistent. It was important, Hilbert thought, to show that simple arithmetic—at the very least—is supported by a logic system that could not lead to contradictions. That seems reasonable, but in 1931 Kurt Gödel in Vienna proved that a system robust enough to support arithmetic and be free of contradictions couldn’t be complete. This astonishing result, known as Gödel’s Incompleteness Theorem, means that there have to be truths about arithmetic in such a logic system that can’t be proved true in that system. Here’s another way to say it: the price of consistency demands that you be content with not being able to prove everything systematically. Gödel’s result said there couldn’t be a universal math machine for deriving every mathematical truth—in contrast to Turing’s later result (1936) that there is a universal computer for everything computable.
图 3.6
Figure 3.6
由玛丽娜·冯·诺依曼·惠特曼提供。
Courtesy of Marina von Neumann Whitman.
哥德尔的结果与数字光的故事密切相关,因为它确立了冯诺依曼的凭据。冯诺依曼实际上是在 1930 年听哥德尔介绍他的革命性成果,在哥德尔发表之前。作为冯诺依曼能力的衡量标准,他几乎立刻就明白了,并直接向哥德尔本人提出了一个更强的结果。我们可以假设,得知哥德尔已经证明了更强的结果,他非常失望。冯·诺依曼性格的另一个一瞥是,从那一刻起,他就停止了对形式逻辑的贡献。如果他不能成为某个领域的佼佼者,那么似乎——如果他不能超越 Gödel Gödel——那么他就会继续统治另一个领域。
Gödel’s result is tangentially germane to the story of Digital Light because it establishes von Neumann’s credentials. Von Neumann actually heard Gödel present his revolutionary result in 1930, before Gödel published it. As a measure of von Neumann’s ability, he almost immediately understood it and proposed a stronger result directly to Gödel himself. He was highly disappointed, we may assume, to learn that Gödel had already proved the stronger result. Another glimpse of von Neumann’s personality is that he ceased contributing to formal logic from that moment on. If he couldn’t be the top dog in a field, it seems—if he couldn’t out-Gödel Gödel—then he moved on to dominate another.
冯诺依曼并没有像图灵那样处理计算,尽管当图灵理论出现时他已经做好充分准备去理解它。相反,他从工程的角度出发,通过考虑实际机器的实现。在开发热核弹或氢弹的过程中,他让自己熟悉了战后 1940 年代美国制造计算机的所有尝试——计算机的直接前身。他正在寻找能够快速进行热核计算的最佳机器。特别是,他在费城找到了一台房间大小的机器,名为 Eniac,建于 1946 年。它类似于我们后来所说的计算机。事实上,他使用 Eniac 进行氢弹计算。这台“几乎是计算机”的缺陷激发了冯诺依曼和他的同事构想出一种计算机的架构——一个带有存储程序的计算机——这将对 Digital Light 的计算机产生重大影响。他们是在恶臭中从必要性中得出的,而图灵在象牙塔中是从理论中得出的。
Von Neumann didn’t approach computation the way that Turing did, although he was fully prepared to understand Turing’s theory when it appeared. Instead he came at it from the engineering angle, by thinking about the realization of actual machines. In his role developing the thermonuclear or H-bomb, he made himself familiar with all the attempts at building calculating machines—immediate predecessors to computing machines—in the United States in the postwar 1940s. He was looking for the best machine to make thermonuclear calculations rapidly. In particular, he found his way to a room-sized machine in Philadelphia, called Eniac, built in 1946. It resembled what we would come to call a computer. Indeed, he used Eniac for H-bomb calculations. The flaws in this “almost-computer” inspired von Neumann and his colleagues to conceive the architecture of a computer—one with a stored program—that would heavily influence the computers of Digital Light. They came at it from necessity in the stinks while Turing did so from theory in the ivory tower.
和图灵一样,冯诺依曼也过着辉煌而短暂的一生。1957 年,53 岁的他被癌症带走,仅仅比图灵晚了三年,因此他也错过了新千年的数字大融合。然而,与图灵不同的是,他的政府在他的有生之年公开庆祝了他。艾森豪威尔总统于 1956 年向他颁发了总统自由勋章。他曾研究过原子弹和氢弹以及美国的洲际弹道导弹战略——他是一个鹰派,没有人怀疑他的忠诚。根据他自己的参议院委员会证词,他是“强烈的反共分子”。但具有讽刺意味的是,他的合作者克劳斯·富克斯将两人开发的秘密信息——一种点燃热核爆炸的方法——传递给了苏联。27
Like Turing, von Neumann led a brilliant but brief life. Cancer took him at age 53 in 1957, just three years after Turing, so he also missed the Great Digital Convergence of the new millennium. Unlike Turing, however, he was openly celebrated by his government in his lifetime. President Eisenhower presented him with the Presidential Medal of Freedom in 1956. He had worked on both the atomic and hydrogen bombs and the ICBM strategy of the United States—and was such a hawk that nobody ever doubted his loyalty. He was “violently anti-communist” by his own Senate committee testimony. But ironically his collaborator Klaus Fuchs passed the secret information that the two developed—a method for igniting thermonuclear explosions—to the Soviets.27
1937 年的某个时刻,冯·诺依曼、马克斯·纽曼和图灵都在普林斯顿——英美计算机事业的未来领袖。1938 年,冯·诺依曼几乎没有错过任何一个节拍,他试图将图灵招募到王子学院。令人惊讶的是,图灵拒绝了这个丰厚的提议。想想看。可能是冯·诺依曼和图灵走出了王子学院的起跑线。第一台计算机可能是美国的。28
There was a moment in 1937 when von Neumann, Max Newman, and Turing were all in Princeton—the future leaders of the British and American computer efforts. Hardly missing a beat, von Neumann attempted to recruit Turing to the Princetitute in 1938. Astonishingly, Turing rejected this plum offer. Think of it. It could have been von Neumann and Turing out of the starting gates at the Princetitute. And the first computer might have been American.28
然而,图灵和冯诺依曼的性格截然相反,以他们两人为主角的团队,极客和快乐生活,可能行不通。冯诺依曼一定已经感觉到他会成为图灵的头号狗。可能图灵也是。然而,这并不能说明问题,因为图灵忠于自己的性格,他自己出击了。他回到英格兰,几乎立即被招募到布莱切利公园。那是 1939 年,英格兰被吓坏了。
Turing’s and von Neumann’s personalities were so diametrically opposed, however, that a team starring the two of them, the geek and the bon vivant, might not have worked. Von Neumann must have sensed he’d be alpha dog to Turing. Probably Turing did too. There’s no telling however because Turing, true to character, struck out on his own. He returned to England, where he was almost immediately recruited into Bletchley Park. It was 1939, and England was frightened for its life.
布莱切利公园是图灵著名的帮助破解德国人用于战争通信的加密方案的地方。他们使用了一种极其复杂的加密机器,名为 Enigma(它的实际商品名),类似于用木头包裹的老式黑色打字机。职员会在 Enigma 中输入一条短信——比如说从德国海军总部的一位海军上将到海上的一艘 U 型潜艇——机器会以一种方式对这些字母进行加密,然后以第二种方式对被加密的字母进行加密,依此类推。乱码有好几层,每一层都可以改变。U-boat 会像发送者一样配置其接收 Enigma。然后,收到的消息将按相反的顺序逐层解扰,直到原始消息被显示出来并为 U 艇船长输入。他们每天使用一次性垫系统重新配置机器的加扰。回想一下,Kotelnikov 和 Shannon 都证明了这样一个系统是牢不可破的——至少如果使用得当的话。但德国人认为该系统是牢不可破的,因为有很多配置是可能的。事实上,他们从来没有想到图灵和他在布莱切利公园的同事已经打破了它。Bletchley 利用了这样一个事实,即操作员并不总是正确使用该系统,但他们大多使用大量计算。这就是计算的用武之地。(Enigma 在 Bletchley 的小屋 8 中被破解,如图 3.7 中的照片 B 和 C 所示。照片 A 是奇怪的庄园。)但德国人认为该系统是牢不可破的,因为有很多配置是可能的。事实上,他们从来没有想到图灵和他在布莱切利公园的同事已经打破了它。Bletchley 利用了这样一个事实,即操作员并不总是正确使用该系统,但他们大多使用大量计算。这就是计算的用武之地。(Enigma 在 Bletchley 的小屋 8 中被破解,如图 3.7 中的照片 B 和 C 所示。照片 A 是奇怪的庄园。)但德国人认为该系统是牢不可破的,因为有很多配置是可能的。事实上,他们从来没有想到图灵和他在布莱切利公园的同事已经打破了它。Bletchley 利用了这样一个事实,即操作员并不总是正确使用该系统,但他们大多使用大量计算。这就是计算的用武之地。(Enigma 在 Bletchley 的小屋 8 中被破解,如图 3.7 中的照片 B 和 C 所示。照片 A 是奇怪的庄园。)
Bletchley Park was where Turing famously helped crack the encryption scheme that the Germans used for war communications. They employed a devilishly complex encryption machine called Enigma—its actual trade name—which resembled an old-fashioned black typewriter encased in wood. A clerk would type a text message into Enigma—say from an admiral at German naval headquarters to a U-boat at sea—and the machine would scramble the letters one way, then scramble the scrambled letters a second way, and so forth. The scramblings were several layers deep, and each could be changed. The U-boat would configure its receiving Enigma just like the sending one. The received message would then be descrambled layer by layer, in reverse order, until the original message was revealed and typed out for the U-boat skipper. They used a one-time pad system to reconfigure the machine’s scramblings each day. Recall that both Kotelnikov and Shannon had proved such a system was unbreakable—at least if used correctly. But the Germans assumed the system was unbreakable because so many configurations were possible. Indeed, they never figured out that Turing and his colleagues at Bletchley Park had broken it. Bletchley exploited the fact that operators didn’t always use the system properly, but mostly they used massive calculations. That’s where computation comes in. (Enigma was cracked in Bletchley’s Hut 8, shown at photos B and C in figure 3.7. Photo A is the odd manor house.)
解扰 Enigma 代码的试错法是一项非常乏味的工作,最初是由人类手动完成的——由美国数百台计算机的手和大脑完成。人类女性变种,图灵的“奴隶”。为了帮助减轻单调乏味并提高解码速度,布莱切利公园的人建造了大型机器,称为 Bombes。它们还不是计算机,正如我们现在所说的那样,但它们肯定正在走向它们。它们不是可编程的,即使使用硬件切换和电缆,在该术语的任何一般含义中也是如此。从某种意义上说,Bombe 是一台图灵机,但不是通用的图灵机。它执行了一项包含许多步骤的系统任务——尝试了一个 Enigma 可能使用过的无数可能的加扰——但这是它唯一能做的计算。硬件炸弹的速度大大超过了有血有肉的计算机。例如,速度是至关重要的,它可以在 U 艇的路径上向美国和英国商船发送信息。所以推动了——进行计算快。
The trial and error approach to descrambling Enigma code was very tedious work, done at first by hand—by the hands and minds of hundreds of computers of the human female variety, Turing’s “slaves.” To help ease the tedium and to increase the speed of decoding, the Bletchley Park people built large machines, called Bombes. They weren’t computers yet, as we mean that word now, but they were certainly on the way to them. They weren’t programmable, even with hardware toggles and cables, in any general meaning of that term. In a sense a Bombe was a Turing machine, but not a universal Turing machine. It performed a systematic task of many steps—trying out the myriad possible scramblings an Enigma might have used—but that was the only computation it could do. The speed of the hardware Bombes greatly exceeded that of the flesh-and-blood computers. Speed was of the essence, to get messages to American and British merchant ships in the path of a U-boat, say. So the push was on—to make computation fast.
图 3.7
Figure 3.7
图灵需要一个合作伙伴,而不是领导者。他太孤独了。这就是马克斯·纽曼(Max Newman)——已经是他的导师和推动者——会再次想到的地方。和图灵一样,纽曼在普林斯顿逗留后回到了英国。与图灵不同的是,他有一个家庭——他的妻子林恩和他们年幼的儿子爱德华和威廉——并且需要保护他们。由于他是犹太人(顺便说一句,冯·诺依曼也是),他担心如果纳粹占领英格兰,他的家人会受到威胁。到 1940 年,他已将林恩和男孩们藏在遥远但熟悉的普林斯顿大学,他们将在那里呆了几年。与此同时,他加入了布莱切利公园。
Turing needed a partner, not a leader. He was too much the loner. That’s where Max Newman—already his mentor and promoter—would figure again. Like Turing, Newman returned to England after his stay in Princeton. Unlike Turing, he had a family—his wife, Lyn, and their young sons, Edward and William—and needed to protect them. Since he was Jewish (as was von Neumann, by the way), he feared for the safety of his family if the Nazis took England. By 1940 he had stashed Lyn and the boys in faraway but familiar Princeton, where they would remain for several years. Meanwhile, he joined Bletchley Park.
图灵用炸弹领导了对 Enigma 加密机的第一波攻击。然后轮到纽曼了。他领导了第二波攻击,针对的是一种较新的德国加密机器——绰号 Tunny(英国的金枪鱼)。这次攻击使用了一台巨大的电子机器 Colossus,它最初是在 1943 年建造的。实际上,使用了十个这样的野兽。所有这些类似于计算机的计算机——它们不是存储程序计算机——在美国几乎计算机的 Eniac 之前都可以运行。29
Turing had led the first-wave attack against the Enigma encryption machine with the Bombes. Then it was Newman’s turn. He led the second-wave attack, against a newer German encryption machine—nicknamed Tunny (British for tuna). This attack employed a giant electronic machine, Colossus, first built in 1943. Actually, ten of these beasts were used. All of these almost-computers—they weren’t stored-program computers—were functional before the almost-computer Eniac in America.29
图灵与 Tunny 及其 Colossi 有很大的间接关系。他提出了一种在布莱切利口中被称为图灵主义的数学见解,这是破解 Tunny 的关键。令人惊讶的是,考虑到他与纽曼的关系以及他自己与 Bombes 的布莱切利公园机器经验,他没有更直接的角色。但他和纽曼当时并没有合作——而且在一段时间内也不会合作——因为解码文本不再让图灵兴奋。他的新兴趣是对声音进行编码。英国政府将他送回美国执行一项特殊任务,从而激发了这种兴趣。30
And Turing indirectly had a lot to do with Tunny and its Colossi. He came up with a mathematical insight known in Bletchley-speak as Turingismus which was key to cracking Tunny. It’s surprising that he didn’t have a more direct part, considering both his relationship with Newman and his own Bletchley Park machine experience with the Bombes. But he and Newman didn’t team up then—and wouldn’t for a while longer—because decoding texts no longer excited Turing. His new interest was encoding voices. The British government ignited that interest by sending him back to America on a special mission.30
图灵和科捷尔尼科夫于 1936 年在曼哈顿擦肩而过,从未见过面,但他们之间仍然存在令人惊讶的联系。它是声码器——“语音编码器”的缩写——而不是你想象的计算、采样或破译代码。声码器不仅将图灵与科捷利尼科夫纠缠在一起,还与香农甚至索尔仁尼琴纠缠在一起。他们都在声码器上工作。回想起来,与计算机相比,声码器似乎是微不足道的干扰。但在当时,它似乎是一项同样重要的技术。回想起来,我们也可以看到它为未来的光和声数字化进步埋下了种子。
Turing and Kotelnikov had slipped past each other in Manhattan in 1936 and never met, but a surprising connection nevertheless existed between them. It was the vocoder—a contraction of “voice coder”—not computing, sampling, or codebreaking as you might imagine. The vocoder entangled Turing not only with Kotelnikov but also with Shannon and even Solzhenitsyn. They all worked on vocoders. In retrospect the vocoder seems like a trivial distraction compared to the computer. But at the time it appeared to be an equally central piece of technology. In retrospect too, we can see that it held the seeds for future digital advances in light and sound.
回想一下第 2 章,Kotelnikov 和随后的 Shannon 证明一次性垫是牢不可破的。使用一次性填充码增强的声码器使口语与书面语一样安全。一个加密的声码器——一个语音加扰器——就像一个用于语音的 Enigma 机器。
Recall from chapter 2 that Kotelnikov, and subsequently Shannon, proved one-time pads to be unbreakable. A vocoder augmented with one-time-pad codes made the spoken word as secure as the written word. An encrypted vocoder—a voice scrambler—was like an Enigma machine for the voice.
斯大林变得越来越偏执,并要求使用语音扰频器来保护他的通信免受潜在间谍的侵害。这种需求将促使科捷利尼科夫和索尔仁尼琴一起在莫斯科北部的 Marfino sharashka。
Stalin became increasingly paranoid and demanded a voice scrambler to keep his communications safe from potential spies. That demand would drive Kotelnikov and Solzhenitsyn together in the Marfino sharashka in northern Moscow.
丘吉尔和罗斯福(以及后来的杜鲁门)虽然不那么不理性,但也需要一个用于战时通信的语音扰频器——X 系统。这促使图灵和香农于 1943 年在贝尔实验室一起工作。英国政府任命图灵为其专家,以验证 X 系统的安全性。这就是为什么他没有在布莱切利公园与纽曼合作。相反,他与美国政府承担相同任务的专家香农短暂会合。出于安全原因,两人不能提及密码学,但他们可以谈论关于计算、计算机国际象棋和计算机作为人类智能模型的一切。31
Churchill and Roosevelt (and later, Truman), though less irrationally, also needed a voice scrambler for wartime communications—the X System. And that drove Turing and Shannon together at Bell Labs in 1943. The British government appointed Turing as its expert to validate the security of the X System. That’s why he wasn’t teaming up with Newman at Bletchley Park. Instead he joined up briefly with Shannon, the expert with the same assignment from the American government. For security reasons the two couldn’t mention cryptography, but they could talk all they wanted about computation, computer chess, and the computer as a model for human intelligence.31
如此多的像素英雄设计了声码器这一事实是了不起的,但该设备与我们的计算故事真正相关的是图灵自己制作了一个。在他的密友罗宾甘迪的建议下,他称它为“大利拉”——意为“男人的骗子”,暗指参孙的圣经情人和背叛者。设计大利拉让他获得了他所缺乏的动手工程经验。Delilah 不是计算机,但经验让图灵设计出了一台真正的通用图灵机。这是从塔楼到臭气熏天的准备工作。32
The fact that so many of the pixel’s heroes designed vocoders is remarkable, but the real relevance of the device to our computation story is that Turing made one of his own. He called it Delilah—for “man deceiver,” an allusion to the biblical lover and betrayer of Samson—at the suggestion of his close friend, Robin Gandy. Designing Delilah gave him the hands-on engineering experience that he had lacked. Delilah wasn’t a computer, but the experience prepared Turing to design one—a real universal Turing machine. It was a preparatory move from the tower to the stinks.32
有充分的理由进一步研究声码器。这是前两章中频率和采样思想的一个很好的例子。
There’s a good reason to delve further into the vocoder. It’s a good example of the frequency and sampling ideas from the previous two chapters.
首先我们使用傅里叶的频率思想。我们将声音使用的频带分成十个更小的频带。假设人声的频率假设为每秒 0 到 3,000 个周期。(语音通信通常不使用人类听觉能力的全部范围,它可以达到每秒 20,000 个周期。)将此频带视为分为十个带宽频带,每个频带每秒 300 个周期。例如,原始语音消息中小于每秒 300 个周期的所有频率都在频段 1 中,每秒 300 到 600 个周期之间的所有频率都在频段 2 中,依此类推。语音加扰器的粗略想法是以一种已知但秘密的方式对这十个频段进行加扰,传输结果,然后在接收端进行解扰。
First we use Fourier’s frequency idea. We break the band of frequencies used by a voice into say ten smaller bands. Suppose the frequencies assumed for the human voice are 0 to 3,000 cycles per second. (Voice communication typically doesn’t use the full range of human hearing capability, which can reach as high as 20,000 cycles per second.) Think of this band of frequencies as divided into ten bands of bandwidth 300 cycles per second each. For example, all frequencies in the original voice message less than 300 cycles per second are in band 1, those between 300 and 600 cycles per second are in band 2, and so forth. The rough idea of the voice scrambler is to scramble these ten bands in a known but secret way, transmit the result, and then unscramble at the receiving end.
现在我们调用采样定理以适当的采样率用十组样本来表示十个波段中的每一个。实际上被加扰然后传输的是这十组样本。如果一次性填充系统用于额外的安全性,那么它的贡献会在加扰步骤之前添加到每个通道中的样本中。在接收端,频段的解扰发生,并且如果使用一次性填充代码,则减去。根据采样定理重构十组频率分量,然后将它们全部加在一起以获得原始语音消息。
Now we invoke the Sampling Theorem to represent each of the ten bands with ten sets of samples at the appropriate sampling rate. What actually gets scrambled, and then transmitted, are these ten sets of samples. If a one-time pad system is used for additional security, then its contribution is added to the samples in each channel before the scrambling step. At the receiving end, the unscrambling of the bands happens, and the one-time pad code is subtracted if used. The ten sets of frequency components are reconstructed per the Sampling Theorem, and these are then all added back together to get the original voice message.
令人惊讶的是,采样定理被完全使用了。回想一下,那是 1943 年,香农直到 1948 年才出版他的版本。显然,在香农出版五年前,西方完全理解了抽样。采样在俄罗斯被用于他们的声码器也就不足为奇了,因为 Kotelnikov 于 1933 年在那里发表了它。此外,图灵在不久之后在他自己的声码器 Delilah 的设计中使用了采样。他报告说,他在 1943 年第二次从美国回国的船上构思了他的声码器版本。
The surprise in all this is the fact that the Sampling Theorem was being used at all. Recall that this was 1943, and Shannon didn’t publish his version until 1948. Clearly sampling was completely understood in the West five years before Shannon published. It’s no surprise that sampling was used in Russia for their vocoders, because Kotelnikov had published it there in 1933. Furthermore, Turing used sampling in the design of Delilah, his own vocoder, shortly thereafter. He reported that he conceived his version of the vocoder on board the ship he took in 1943 returning home from America the second time.
声码器仍在我们身边,但现在内置了一台计算机。在现代主流音乐中,增强声码器的商标名为 Auto-Tune。今天它是关于语音增强,而不是加密。使用它的音乐家——例如雪儿、劳里·安德森和 T-Pain——是图灵、科捷利尼科夫、香农和索尔仁尼琴的遥远概念表亲和奇怪的伙伴。Auto-Tune 是“人声的 Photoshop”,因为它使许多歌手——不如刚才提到的三位歌手——变得完美。Photoshop 参考提醒我们,像素和索素是同一个想法——我们可以用计算机和光从头开始创建声音模式。
The vocoder is still with us—but now has a computer built into it. In modern mainstream music, the augmented vocoder is trade-named Auto-Tune. Today it’s about voice enhancement, not encryption. Musicians—such as Cher, Laurie Anderson, and T-Pain—who use it are distant conceptual cousins and strange bedfellows of Turing, Kotelnikov, Shannon, and Solzhenitsyn. Auto-Tune is “the Photoshop of the human voice” because it enables many singers—not so good as the three just mentioned—to be pitch perfect. And the Photoshop reference reminds us that pixels and soxels are the same idea—that we can create sound patterns from scratch with computers, as well as light.
大多数人认为计算机无法理解,但实际上它们非常简单。您已经体验过名片设备,并使用它进行计算。它只有四个状态和六个符号,而且是纸做的。然而,它可以计算任何可计算的东西。它是一台计算机。
Most people think computers are beyond understanding, but in fact they’re remarkably simple. You’ve already experienced one, the business card device, and computed with it. It has only four states and six symbols, and it’s made of paper. Yet it can compute anything that’s computable. It is a computer.
但是计算机确实必须进行编程。正如您可能怀疑的那样,这是棘手的部分,它可能非常乏味且容易出错。甚至图灵本人也在他的程序中犯了错误。但那是软件,不是硬件。硬件在概念上很简单,并且可以与软件分离。
But computers do have to be programmed. As you might suspect, that’s the tricky part, and it can be quite tedious and error prone. Even Turing himself made mistakes in his programs. But that’s software, not hardware. Hardware is conceptually simple, and it’s separable from software.
了解硬件并不能告诉我们软件。我们可以知道计算机硬件的完整接线图,而无需了解它在计算什么。例如,您现在完全了解名片“硬件”的工作原理。然而,基于这种理解,你不知道它的任何一个软件程序意味着什么。您可以了解施坦威三角钢琴的工作原理,但如果没有乐谱——它的音乐软件,就无法从中演绎出肖邦练习曲。肯定也是确实,您可以在不知道人脑在想什么的情况下知道人脑的完整接线图。
Knowing the hardware doesn’t tell us about the software. We can know the complete wiring diagram of a computer’s hardware without understanding what it’s computing. For example, you now know how the business card “hardware” works—completely. Yet you’ve no clue, based on that understanding, what any one of its software programs means. You can know everything about how a Steinway grand works, but you’ll not deduce a Chopin étude from it without the score—its musical software. Surely it’s also true that you can know the complete wiring diagram of a human brain without knowing what that brain is thinking.
这就是最初激发图灵的难题——eProblem,Hilbert 的 Entscheidungsproblem——发挥作用的地方。需要明确的是,我们在这里主要关心的不是难题——而是计算机,图灵用来解决它的机器。但重要的是要提醒自己,计算的根源有一些深刻的东西。值得提醒的是,很少有人意识到这一点,因此对计算机是什么有错误的直觉。
This is where the hard problem—the eProblem, Hilbert’s Entscheidungsproblem—that originally motivated Turing comes into play. To be clear, our main concern here isn’t the hard problem—it’s the computer, the machine Turing used to solve it. But it’s important to remind ourselves that there’s something profound at the root of computation. It’s worth the reminder because so few people are aware of it and therefore have the wrong intuition about what a computer is.
许多人认为计算机是一台完全确定的机器。这是完全正确的,因为计算机采取的每一步都是完全定义的。例如,名片机的每一步都是由其24条规则的指令表、当前扫描的符号和卡片的当前方向决定的。但是得出的推论——计算机所做的事情因此是完全预先确定的——是错误的。机器的命运是完全确定的,但你不能总是知道那个命运是什么。如果你不能提前知道,那么确定是什么意思?
Many think that a computer is a completely deterministic machine. That’s exactly true because each step that a computer takes is completely defined. For instance, each step of the business card machine is determined by its instruction table of 24 rules, the currently scanned symbol, and the current orientation of the card. But the inference that’s drawn—that what a computer does is therefore completely predetermined—is false. The fate of the machine is completely determined, but you can’t always know what that fate is. And if you can’t know it in advance, then what does determined mean?
要根据机器定义确定,请再次回忆那些多步骤的过程,包括它们的所有循环和分支以及随之而来的自我参考。它们是一种不同的数学动物。毕竟,计算机很困难这种模糊的感觉是有原因的。但这不是因为硬件。这是关于硬件和软件以及一个运行另一个的方式的东西。
To define determined in terms of a machine, recall those many-stepped processes again, with all their loops and branches and attendant self-reference. They’re a different kind of mathematical animal. That vague sense that computers are difficult has something to it, after all. But it’s not because of the hardware. It’s something about hardware and software and the way one runs the other.
请记住,图灵对 eProblem 的解决方案是没有解决方案:简单一阶逻辑中的陈述是真还是假是不可判定的。您当然可以在某些情况下做出决定,但不是全部。没有算法。计算中有一个类似的结果——某种不可知性或不可解性——称为停止问题:一般来说,你甚至无法知道计算是否会停止这样简单的事情!没有系统的测试来决定它是否最终会停止。给定程序及其输入数据,没有任何算法可以发现程序最终会停止还是永远运行。33
Remember that Turing’s solution to the eProblem was that there is no solution: it’s undecidable whether a statement in simple first-order logic is true or false. You can certainly decide in some cases, but not in all. There’s no algorithm for it. There’s a similar consequence in computation—a certain unknowability, or unsolvability—called the halting problem: in general, you cannot even know something as simple as whether a computation will halt! There’s no systematic test to decide if it will eventually stop or not. There’s no algorithm, given a program and its input data, that can discover whether the program will eventually halt or will run forever.33
换句话说,没有用于停止的 DNA 测试。您必须运行该程序才能看到它的作用。也就是说,你必须找到计算机操作从开始到结束的路径——如果有的话。如果它停止了,那么你知道答案,但如果它没有停止,那么你还不知道。如果你让程序运行的时间长一点呢?你可能正在追逐野鹅。它可能处于无限循环中。一般情况下你无法知道。
In other words, there’s no DNA test for halting. You have to run the program to see what it does. That is, you have to find the path of computer operations from the start to the finish—if there is one. If it halts then you know the answer, but if it doesn’t halt, then you don’t yet know. What if you let the program run a little longer? You might be on a wild goose chase. It might be in an infinite loop. You can’t know in general.
所以一台计算机是完全确定在小而在大不可知的。在正常实践中,这种奇怪的行为并不是真正的问题。程序员通常对他们的程序将要做什么有一个很好的想法——只要它正常工作,就是这样。所以在数字光中,不可知主要是理论上的问题。程序员尽量不写不可知的代码。几十年来,许多编程学科已经发展,以帮助他们避免未知的陷阱。
So a computer is completely determined in the small but unknowable in the large. In normal practice this strange behavior isn’t really a problem. Programmers usually have a pretty good idea of what their program is going to do—once it’s working properly, that is. So in Digital Light the unknowable is mostly a theoretical concern. Programmers try their best not to write unknowable code. Many programming disciplines have evolved over the decades to help them avoid the pitfalls of the unknown.
其中一个陷阱是图灵最感兴趣的计算方面的结果:计算在计算时实际改变自身的能力。例如: (1)从输入数y中减去输入数x。(2) 如果结果是否定的,则将步骤 3 中的步骤编号更改为 4,否则将其更改为 5。 (3) 转到步骤 4。 (4) 写入“减号”并停止。(5) 写“加”并停止。
One of the pitfalls is a result of the computing aspect that most interested Turing: the ability for a computation to actually change itself while computing. For example: (1) Subtract input number x from input number y. (2) If the result is negative then change the step number in step 3 to 4 otherwise change it to 5. (3) Go to step 4. (4) Write “minus” and halt. (5) Write “plus” and halt.
让我们尝试将数字 7 分配给x并将 6 分配给y: (1) 7 减去 6 等于 1。 (2) 结果为正,所以: (3) 转到步骤 5。 (5) 写“加号”并停下来。一个程序不仅可以是一个令人讨厌的分支和循环的缠结,而且它可以是一个移动的目标。大多数现代操作系统通过禁止这种自修改代码来“保护”程序员——就像自锁车门一样。它太容易造成破坏。然而,图灵实际上将这个想法带入了真正的计算机世界。当他有机会为实际硬件设计一个条件分支指令时,他的条件分支指令是通过自修改代码实现的。34
Let’s try this with the number 7 assigned to x and 6 assigned to y: (1) 7 minus 6 equals 1. (2) The result is positive, so: (3) Go to step 5. (5) Write “plus” and halt. Not only can a program be a nasty tangle of branches and loops, but it can be a moving target. Most modern operating systems “protect” the programmer—like self-locking car doors—by prohibiting such self-modifying code. It wreaks havoc too easily. Nevertheless, Turing actually pursued the idea into the world of real computers. His conditional branch instruction, when he got a chance to design one for actual hardware, was realized with self-modifying code.34
当您将计算视为人类大脑或思维的模型时,了解这种不可知性是很有用的——就像图灵、冯诺依曼和香农所做的那样。计算结果可能不是一个好的模型,但不能因为声称它是确定性的,因此是预先确定的而立即将其驳回——也就是说,它在某种程度上过于僵化和受限制,不值得我们使用。你只需要让它运行看看它做了什么。
It’s useful to know about that unknowability when you contemplate computation as a model for the human brain or mind—as Turing, von Neumann, and Shannon all did. Computation might not turn out to be a good model, but it can’t be dismissed out of hand by claiming that it’s deterministic and hence predetermined—that is, it’s somehow too rigid and constrained to be worthy of us. You just have to let it run to see what it does.
为数字计算机准备程序的过程特别有吸引力,因为它不仅可以在经济和科学上获得回报,而且还可以是一种审美体验,就像创作诗歌或音乐一样。
The process of preparing programs for a digital computer is especially attractive because it not only can be economically and scientifically rewarding, it can also be an aesthetic experience much like composing poetry or music.
—Donald E. Knuth,计算机编程的艺术35
—Donald E. Knuth, The Art of Computer Programming35
编程是计算的秘密,但科学家们至少花了十年时间才意识到这一点。图灵在他 1936 年的著名论文《论可计算数》中展示了第一个程序。他为引入计算的概念机器(图灵机)编写了它们。所以他发明了编程和存储程序的概念。他给了我们计算这个词,但没有给我们编程这个词。这个词是从哪里来的?图灵使用指令表准备来指代编程。
Programming is the secret to computation, but it took at least a decade for scientists to realize that. Turing exhibited the first programs in his famous 1936 paper, “On Computable Numbers.” He wrote them for the conceptual machines—the Turing machines—that introduced computation. So he invented programming and the stored-program concept. He gave us the word computation but not the word programming. Where did that word come from? Turing used instruction table preparation to refer to programming.
让我们更仔细地看看图灵实际上做了什么。假设他想要一台可以反转输入磁带上任何字符串的机器。他设计了一套规则——指令表——用于实现字母系统反转的特定图灵机。称它为 A。然后他会将 A 的规则交给一台通用计算机。回想一下在其磁带上显示任意机器 A 和在其磁带上显示通用机器 U 的图片。图中的“A 的编码规则”就是我们现在所说的A程序。聪明而有趣的部分是为 A 设计指令表,而不是将其编码为 U 所需的形式。编码很简单,而且,机械的。在我们的名片机示例中,用 0 代替空白,用 f 代替正面方向,等等。很蠢的东西。机器不会觉得无聊,但人类会。
Let’s look more closely at what Turing actually did. Suppose he wanted a machine that reverses any string of letters on its input tape. He designed the set of rules—the instruction table—for a particular Turing machine that implemented a systematic reversal of letters. Call it A. Then he would hand A’s rules to a universal computer. Recall the picture that shows an arbitrary machine A on its tape and the universal machine U on its tape. “A’s encoded rules” in that picture is what we would now call the program for A. The clever, intellectually interesting part is designing the instruction table for A—not encoding it into the form required by U. Encoding is straightforward and, well, mechanical. In our example of the business card machine, substitute a 0 for a blank, an f for front orientation, and so on. Pretty dumb stuff. A machine wouldn’t get bored doing it, but a human would.
将编程分为创意部分和无聊部分仍然存在。在钢琴的隐喻中,乐曲的组成是创造性的部分,而将其编码为音符和乐谱上的休止符是无聊的部分。现代计算机的一个主要用途是为计算执行无聊的编码步骤。它称为汇编或编译。程序员在高符号级别(使用类似英语的语言)工作以创建程序,这是有趣的部分。然后计算机将程序编码成计算机实际理解的冗长乏味的长序列,几乎是微不足道的操作——顺便说一下,这是计算机的常见非数字使用的一个很好的例子。无论如何,这就是它现在的工作方式。
The separation of programming into the creative part and the boring part still holds. In the piano metaphor, the composition of a piece is the creative part, and its encoding as notes and rests on a musical staff is the boring bit. One principal use of modern computers is to do that boring encoding step for computations. It’s called assembly or compiling. A programmer works at a high symbolic level—in an English-like language—to create a program, the fun part. Then a computer encodes the program into those tedious long sequences of almost trivial operations that a computer actually understands—a great example, by the way, of a common nonnumeric use of computers. That’s the way it works now anyway.
然而,在 1940 年代后期,那些准备制造第一台硬件计算机的人使用“设置”一词来描述您如何让机器计算您希望它计算的内容。在几乎是计算机的早期——例如,像 Eniac——这意味着实际插入电缆和切换开关,因为这是可以在硬件上安装程序的唯一方式。后来——正如对存储程序计算机的设想——“设置”似乎不仅意味着创建一个程序,而且确保它被加载到计算机内存中的正确位置。
In the late 1940s, however, those preparing to build the first hardware computers used the term “setting up” to describe how you made a machine compute what you wanted it to compute. In the slightly earlier days of the almost-computers—like Eniac, for example—it meant actually inserting cables and toggling switches, since that was the only way a program could be installed on the hardware. Later—as stored-program computers were contemplated—“setting up” seems to have meant not only creating a program but making sure it was loaded into the memory of the computer in the right place.
起初,它就像是事后的想法——现在我们有了一台机器,让我们开始吧。那时,仅仅制造一台可以工作的计算机就几乎占用了工程师的所有创造性带宽。但他们很快发现“设置”是一项复杂、容易出错且繁重的活动。它变成了摇狗的尾巴。现在这似乎很明显,因为有些程序有数百名程序员编写的数百万个步骤。
At first it was like an afterthought—now that we have a machine, let’s make it go. Back then just building a computer that worked took nearly all the creative bandwidth of engineers. But they soon discovered that “setting up” was a complex, error-prone, and burdensome activity. It became the tail that wagged the dog. This seems obvious now, when some programs have millions of steps written by hundreds of programmers.
但当时,他们需要一套技术来指导和简化“设置”任务,他们也需要一个更好的名称。Princetitute 的冯诺依曼档案中的文件记录了动词to program首次出现的那一刻。它既是编程这个词的诞生,也是编程艺术,一门新学科。36
But back then, they needed a body of techniques to guide and ease the task of “setting up,” and they needed a better name for it, too. Documents in the von Neumann archive at the Princetitute capture the very moment when the verb to program first appeared. It’s both the birth of the word programming and the art of programming, a new discipline.36
在 1945 年 9 月 5 日的一份备忘录中,每个地方编程都是一个有用的术语,冯诺依曼改为使用“设置”,用占位符围绕它引号。他说:“我想再次强调这一点。. . 如此灵活且高度自动化的“设置”机器解决问题的系统对于人们应该考虑的科学用途来说是绝对必要的。” 他说,无论我们怎么称呼它,这都是绝对必要的。37
In a memo dated September 5, 1945, every place programming would have been a useful term, von Neumann instead used “setting up,” surrounding it with placeholding quotation marks. He said, “I wish to reemphasize that . . . such a flexible and highly automated system of ‘setting up’ the machine for a problem [is] absolutely necessary for the scientific uses which one should contemplate.” Whatever we call it, he said, it’s absolutely necessary.37
一封日期为 11 月 1 日的信在保护性引号内暂时建议了“设置”的替代方案:“我们计划的电子精密设备当然会在速度、灵活性(通用字符)和至少会像“设置”或“编程”一样容易。”也就是说,他说,它不能像 Eniac 那样是拨动开关和电缆。38
A letter dated November 1 tentatively suggests, within protective quotation marks, an alternative to “set up”: “The electronic precision device which we are planning would of course surpass it [Eniac] in speed, and flexibility (all-purpose character) and will be at least as easy to ‘set up’ or ‘program.’” That is, he said, it can’t be toggles and cables as it was with Eniac.38
然后它发生了。仅仅几周后的 11 月 19 日,“设置”就再也没有出现过。它现在正在编程,没有带歉意的引号。第三份文件是在项目成员 Vladimir Zworykin 办公室举行的会议记录。“下表列出的代码只是为了证明可以完成这项工作。列出的操作足以完成编程。” 在这几分钟里,不仅编程,而且编码。39
Then it happened. Just a couple of weeks later on November 19, “setting up” never appeared. It was programming now, and without apologetic quotation marks. The third document is the minutes of a meeting held in the office of a project member, Vladimir Zworykin. “The code outlined in the following table is presented simply to prove that it is possible to do the job. The operations listed are sufficient for complete programming.” Not only programming but coding was prefigured in these minutes.39
冯诺依曼团队显然意味着编程是创造性的部分,而编码是无聊的部分,是一项“秘书任务”。今天的程序员称自己为编码员,他们编写代码。它们指的是创造性方面,无论是什么术语。他们明白,无聊的部分现在已归入机器本身。
The von Neumann team apparently meant programming to be the creative part and coding to be the boring part, a “secretarial task.” Programmers today call themselves coders, and they write code. They mean the creative aspect, whatever the term. They understand that the boring part is now relegated to the machine itself.
所以在 1945 年末,冯·诺依曼团队,可能是冯·诺依曼本人,是第一个或多或少地按照我们今天的意思使用编程这个词的人。图灵很快也在 1947 年的一次演讲中使用了这个术语,但他在有限的上下文中只使用了几次。40
So in late 1945 the von Neumann team, probably von Neumann himself, was the first to use the word programming more or less the way we mean it today. Turing soon used the term too, in a lecture in 1947, but he used it only a few times in a constrained context.40
不管是什么术语,很早就清楚地表明,编程,创造性的方面,是计算的困难部分,并且必须发展它的一门学科。世界各地的计算机科学系都从这种认识中脱颖而出。
Whatever the term, it became clear fairly early that programming, the creative aspect, was the difficult part of computing, and that a discipline for it would have to develop. Computer science departments all over the world sprang from that recognition.
编程是制作代表虚构世界的像素的方法。它将 Digital Light 从仅仅拍摄照片扩展到制作它们——从仅仅拍摄它们到计算它们。
Programming is the way to make pixels that represent fictitious worlds. It extends Digital Light from just taking pictures to making them—from just shooting them to computing them.
[它] 变成了一台迷人的织布机,数以百万计的闪烁的梭织出一个消融的图案,永远是一个有意义的图案,但从来没有一个持久的图案;子模式的变化和谐。
[It] becomes an enchanted loom where millions of flashing shuttles weave a dissolving pattern, always a meaningful pattern though never an abiding one; a shifting harmony of subpatterns.
——查尔斯·谢灵顿爵士,《人的本性》41
—Sir Charles Sherrington, Man on His Nature41
下一章是关于将计算概念转化为实际实践——第一台机器的竞赛。在我们到达那里之前,让我们消除关于计算机的三个神话:它们不一定是电子的,它们不一定是由比特组成的,它们不是基于数字的——甚至不是 0 和 1。
The next chapter is about turning the concept of computation into real practice—the race for the first machine. Before we get there, let’s dispel three myths about computers: they don’t have to be electronic, they aren’t necessarily made of bits, and they aren’t based on numbers—not even 0s and 1s.
首先,计算机不必看起来像您通常知道的任何东西:您的手机、笔记本电脑、台式机、大公司的巨型主机或高科技研究机构的超级计算机。名片设备就是一个很好的反例。它是一台计算机,为了满足我在本书中的目的,它被实现为纸上墨水、硬卡片纸和薄金属。这显然不是电子的。
First of all, computers don’t have to look anything at all like those you commonly know: your cellphone, laptop, desktop, the giant mainframe at your large corporation, or the supercomputer at your high-tech research facility. The business card device is a good counterexample. It’s a computer, and to serve my purposes in this book, it’s been realized as ink on paper, stiff card stock, and thin metal. It’s obviously not electronic.
一个流行的教学技巧是让教室里的学生变成一台计算机。让我们把这个想法提升一个档次。假设我们让美国所有 12 岁以上的人排成一排。那条线将成为我们计算机的磁带——它的内存。如果我们需要更多记忆,我们会招募一些加拿大人和墨西哥人。假设每个人有五顶不同颜色的帽子。这五顶彩色帽子将成为我们磁带上的符号。第六个符号将是没有帽子,这将是除了少数人之外的所有人的默认条件。我们将选择一个人作为磁带的扫描仪。当我第一次设计这个例子时,巴拉克奥巴马是总统,所以我们会让他成为我们的磁带扫描仪,让他从磁带正方形的职责中解脱出来。他随身带着名片机的 24 条规则——它的指令集——用五种颜色而不是数字 1 到 5 表示(空白没有帽子)。规矩照常分为四组规矩,每组规矩都在他的一个口袋里,两个在前面,两个在后面。所以他的口袋是四个状态。
A popular pedagogical trick is to have a classroom of students become a computer. Let’s take the idea up a notch. Suppose we get every person in the United States who’s older than 12 to line up in a row. That line is going to be the tape of our computer—its memory. We’ll enlist some Canadians and Mexicans if we need more memory. Suppose each person has five hats of different colors. Those five colored hats will be the symbols on our tape. A sixth symbol will be the absence of a hat, and that’ll be the default condition of all except a few people. We’ll select one person to be the scanner of the tape. Barack Obama was president when I first devised this example, so we’ll make him our tape scanner, relieving him from tape-square duty. He has the 24 rules of the business card machine with him—its instruction set—expressed in the five colors rather than the numerals 1 through 5 (and no hat for the blank). The rules are divided up into four sets of rules as usual, and each set of rules is in one of his pockets, two in the front and two in the back. So his pockets are the four states.
奥巴马从一个戴红帽子的人开始,然后应用一套装在口袋里的规则——比如说他右前口袋里的规则。如果奥巴马右前口袋里的红帽规则规定,被称呼的人会将帽子换成另一种颜色,或者完全摘下帽子。然后奥巴马根据相同的规则向左或向右移动一个人。然后,如果当前规则指示他,他会为下一条规则更换口袋。等等。那是一台由人类组成的计算机,带有用于状态的口袋和用于符号的帽子。它可以计算任何东西,因为它与名片机、通用计算机做同样的事情。这只是同一台机器的不同硬件实现。但它是一台真正的计算机——当然不是电子的(或数字的)。
Obama starts with a person wearing a red hat and applies one of the pocketed sets of rules—say the rules in his right front pocket. The person addressed will swap hats to one of a different color, or remove his hat entirely, if the rule in Obama’s right front pocket for red hats says to. Then Obama moves left or right one person, according to the same rule. He then changes pockets for the next rule if the current rule instructs him to. And so forth. That’s a computer made of humans, with pockets for states and hats for symbols. It can compute anything, because it’s doing the same thing as the business card machine, a universal computer. It’s just a different hardware realization of the same machine. But it’s a real computer—and certainly not electronic (or numeric).
名片计算机,或者它的人类等价物,也是我们第二个被揭穿的关于计算机的信念的反例——它们必须由比特组成。回想一下第 2 章,一个位有两种状态,就像一个可以向上或向下的电灯开关。但是名片机有四种状态,或者说方向。每个磁带方块可以包含六个值或符号。名片机中没有一个只有两个值的部分。它不是由比特组成的。也不是人类的等价物。
The business card computer, or its human equivalent, is also a counterexample to our second debunked belief about computers—that they must be composed of bits. Recall from chapter 2 that a bit has two states, like a light switch that can be either up or down. But the business card machine has four states, or orientations. And each tape square can hold six values, or symbols. Nowhere in the business card machine is there a part with just two values. It’s not made of bits. Neither is the human equivalent.
位不是必需的,但工程师很快发现它们在实践中非常方便。事实上,他们在计算机设计中使用了多年正式将图灵的伟大想法转化为比特。那个人就是克劳德·香农。也许是他 1943 年在曼哈顿与图灵的会面——他们表面上以声码器为导向的会议——引发了这种兴趣。香农表明,具有任意数量符号的图灵机可以被另一个只有两个符号的图灵机替换,并且将计算相同的东西。由于图灵机的磁带是它的内存,香农的等效图灵机中的磁带方块是一个内存位,两个符号作为值。42
Bits aren’t required, but engineers quickly discovered that they are extremely handy in practice. In fact, they used bits in computer design for years before someone got around to formally converting Turing’s great idea to bits. That someone was Claude Shannon. Perhaps it was his 1943 meetings with Turing in Manhattan—their ostensibly vocoder-oriented meetings—that kicked off this interest. Shannon showed that a Turing machine with any number of symbols can be replaced with another that has only two symbols and will compute the same thing. Since the tape of a Turing machine is its memory, a tape square in Shannon’s equivalent Turing machine is one bit of memory, with the two symbols as values.42
第三个神话更有害。相信位的两个值必须是 0 和 1。换句话说,第三个神话是计算机是由 0 和 1 构成的,因此计算机从根本上讲是关于数字的。这个神话将计算器(一种用于数字运算的机器)与计算机混为一谈,这是一个更大的想法。它还将字形(名称)的概念与其可能表示的内容(即,与命名的内容)混为一谈。
The third myth is more pernicious. It’s the belief that the two values of a bit must be 0 and 1. In other words, the third myth is that computers are built of 0s and 1s and that therefore computers are fundamentally about numbers. This myth conflates a calculator, which is a machine for number crunching, with a computer, a much larger idea. It also conflates the notion of a glyph (a name) with what it might represent (that is, with what is named).
这种误解是很自然的,源于我们通常为比特的两种状态选择名称。我们方便地称它们为 0 和 1。但我们可以称它们为昼夜、向下和向上、点和破折号,或者 ooh 和 aah。我想你会同意这些名称不如 0 和 1 方便或简洁。但是,与名片机一样,它们只是名称而不是数字。
The misconception is a natural one, arising from our usual choice of names for the two states of a bit. We conveniently call them 0 and 1. But we could call them night and day, down and up, dot and dash, or ooh and aah. I think you’ll agree that those names aren’t as convenient, or succinct certainly, as 0 and 1. But, as with the business card machine, they’re just names and not numbers.
很容易理解为什么计算会与数字混淆。图灵的原始论文的标题是“关于可计算数”。Eniac 中的“n”代表“数字”。算法一词向早期的算术致敬。当时在非常慢的机器上进行的许多原始计算都是数字化的——例如早期的氢弹计算。数字是新的计算工具最容易攻击的第一个符号。一些早期的实践者自己似乎从来没有理解计算机不仅仅是一个快速的数字运算器——一个计算器——但图灵知道计算机还能做多少。事实上,有趣的是,布莱切利公园的图灵炸弹和纽曼巨像并没有计算或操纵数字,而是使用符号替换来破解密码。43
It’s easy to understand why computation has been confused with numbers. Turing’s original paper was titled “On Computable Numbers.” The “n” in Eniac stands for “numerical.” The word algorithm pays tribute to early arithmetic. Many of the original computations on the very slow machines of the time were numeric—such as the early H-bomb calculations. Numbers were the easiest first symbols to attack with the new tool of computation. Some of the early practitioners themselves seem never to have understood that the computer was much more than a fast number cruncher—a calculator—but Turing knew how much more computers could do. In fact, it’s interesting to note that Turing’s Bombes and Newman’s Colossi at Bletchley Park didn’t calculate or manipulate numbers but instead used symbol substitution to break codes.43
本节题词的作者查尔斯·谢灵顿爵士使用他著名的“魔法织机”比喻来描述人类大脑的清醒皮层,但它也适合现代计算机的工作原理。这是关于改变模式。这与数字无关,除非我们赋予模式的意义是数字。但这只是我们可以对这些模式做出的无数解释之一。对计算机来说,它只是模式。
Sir Charles Sherrington, the author of this section’s epigraph, used his famous “enchanted loom” metaphor to describe the waking cortex of the human brain, but it also fits the workings of a modern computer. It’s about changing patterns. It’s not about numbers unless the meaning we attach to the patterns is number. But that’s only one of myriad interpretations we can make of the patterns. To the computer it’s just pattern.
如果计算机中没有数字,那还有什么?今天世界上几乎所有的计算机都是电子的并且是由比特构成的。它们是由计算机芯片制成的,这也许是我们最伟大的技术成就。如果你能在这样的芯片内部看一下,你会发现高电压和低电压的模式。那些是位。
If there are no numbers in a computer, then what is there? Nearly all the world’s computers today are electronic and built of bits. They’re built from computer chips, perhaps our greatest technological achievement. If you could look inside such a chip in operation, you’d find patterns of high and low electric voltages. Those are the bits.
一个您可以看到且具有相似模式的熟悉的地方——好吧,无论如何都要测量——是你家中的电源插座。我们知道那里的交流电压以傅里叶波的形式从最大电压波峰变化到最小电压波谷每秒 60 个周期(美国)。通过您的插头进入您的计算机实际上是一个不断变化的波,从低电压到高电压再返回。
A familiar place with a similar pattern that you can see—well, measure anyway—is an electrical outlet in your home. We know that the AC voltage there varies in a Fourier wave from a maximum voltage crest to a minimum voltage trough 60 cycles per second (US). What comes through your plug and into your computer is actually a constantly varying wave, going from low to high voltage and back again.
但是在芯片中,电压不会像在交流电源插座上那样平稳且不间断地变化。它保持其值(例如,高),直到计算机规则指示它更改为另一个值(低)。每个芯片位置都可以采用高电压或低电压——并在控制下切换到另一个——实现了位的抽象概念。我们所说的是,在指示更改为 0 之前,位是 1。看看这些名称有多方便!但物理现实是电压——就像交流电源插座上的现实——而不是数字。
But in a chip, voltage doesn’t vary smoothly and incessantly the way it does at an AC outlet. It maintains its value—say, high—until it’s instructed by a computer rule to change to the other value, low. Each chip location that can assume either a high or low voltage—and change to the other under control—realizes the abstract idea of bit. What we say is that a bit is a 1 until instructed to change to a 0. See how convenient those names are! But the physical reality is voltages—like the reality at an AC outlet—not numbers.
如果您考虑一台内置数万亿位的计算机,通常以常规数组的形式,那么您就会明白为什么 Sherrington 的比喻有效。当它以当今计算机的惊人速度运行时,数以万亿计的电压模式在每秒变化数十亿次的电子舞蹈中扭曲和编织。有时他们用整块布编织电影。
If you think about a computer with trillions of bits built into it, often in regular arrays, then you’ll see why Sherrington’s metaphor works. When it’s operating at the tremendous speeds of today’s computers, the patterns of trillions of voltages warp and weave in an electronic dance that changes billions of times per second. Sometimes they weave movies out of whole cloth.
Digital Light 的秘密不在于您可以通过某种方式将图片转化为数字,就像旧的“数字绘画”涂色书一样。就是我们每天看到的视觉模式,明暗和运动的模式,可以用机器中的电压模式来表示。我们用计算机的模式模仿世界的模式。
The secret of Digital Light isn’t that somehow you can turn pictures into numbers, like the old “paint by numbers” coloring books. It’s that the visual patterns we see every day, patterns of light and shade and movement, can be represented by the voltage patterns in a machine. We mimic the patterns of the world with the patterns of our computers.
对于 Bletchley Park 的密码学家和数学家小组来说,文本是加密的德国战争信息。对于伦敦著名的布卢姆斯伯里作家和思想家群体来说,这是高级英国文学。乍一看,布莱切利和布卢姆斯伯里似乎没有什么共同之处。但这两个圈子在 1940 年代和 1950 年代以松散但奇怪的方式相互交织在一起。
To the Bletchley Park group of cryptographers and mathematicians, text was encrypted German war messages. To London’s illustrious Bloomsbury Group of writers and thinkers, it was high English literature. It would appear at first blush that Bletchley and Bloomsbury had little in common. But the two circles intertwined with one another in loose but curious ways in the 1940s and 1950s.
这并不意外,因为英国知识分子,无论是数学还是文学,都倾向于通过剑桥或牛津进行筛选。例如,小说家 EM Forster、出版商伦纳德·伍尔夫和经济学家约翰·梅纳德·凯恩斯都是著名的布卢姆斯伯里成员。他们都属于剑桥的秘密社团使徒,其中包括艾伦·图灵的合作者罗宾·甘迪和大卫·尚佩诺恩。
This is not unexpected since British intellectuals, whether mathematical or literary, tend to filter through either Cambridge or Oxford. For example, the novelist E. M. Forster, the publisher Leonard Woolf, and the economist John Maynard Keynes were all renowned Bloomsbury members. And they all belonged to Cambridge’s secret society, the Apostles, which included Alan Turing’s collaborators, Robin Gandy and David Champernowne.
然而,这是巧合。离它不远的是通过 Stracheys 的家庭联系。Bloomsbury 的 Lytton Strachey 有一个兄弟 Oliver,他是 Bletchley Park 的密码学家,还有一个侄子 Christopher,Oliver 的儿子,他是 Turing 在剑桥的同学。克里斯托弗·斯特拉奇(Christopher Strachey)在下一章中作为第一个有记录的电子游戏的作者而引人注目。
That’s coincidence, however. Not far removed from it is the familial connections via the Stracheys. Bloomsbury’s Lytton Strachey had a brother, Oliver, who was a cryptographer at Bletchley Park, and a nephew, Christopher, Oliver’s son, who was Turing’s classmate at Cambridge. Christopher Strachey is notable in the next chapter as author of the first documented videogame.
但真正有意义的联系将布卢姆斯伯里的福斯特与图灵联系在一起。福斯特的小说莫里斯敢于传达——仅在手稿中——成为“奥斯卡王尔德那种难以言喻的人”的感觉。据他的传记作者说,图灵在这本书中得到了安慰。44
But a truly meaningful connection tied Bloomsbury’s Forster to Turing. Forster’s novel Maurice dared to convey—in manuscript only—what it was like to be “an unmentionable of the Oscar Wilde sort.” Turing took comfort in this book, according to his biographer.44
也许最有趣的领带关系到另一位布鲁姆斯伯里巨人弗吉尼亚·伍尔夫,她的丈夫伦纳德也是她的出版商。弗吉尼亚以保存大量日记而闻名,因此伦纳德的故事编辑之一林恩·欧文的名字出现在其中也就不足为奇了。出人意料的转折是林恩嫁给了图灵的导师和布莱切利公园的贡献者非文学作品马克斯纽曼。45
Perhaps the most interesting tie concerns yet another Bloomsbury giant, Virginia Woolf, whose husband, Leonard, was also her publisher. Virginia famously kept extensive diaries so it’s not surprising that the name of one of Leonard’s story editors, Lyn Irvine, appears in them. The unexpected twist is that Lyn married non-literary Max Newman, Turing’s mentor and fellow Bletchley Park contributor.45
在战争期间担心他们的半犹太人儿子,林恩与新泽西州普林斯顿的男孩们一起流亡。马克斯从战前与图灵一起度过的那段时间就知道该地区。但这一次他留在了英格兰,只留下林恩和孩子们在一起。在一次国事访问中,约翰梅纳德凯恩斯在华盛顿与罗斯福总统呆了几个小时后,在普林斯顿对她进行了搜查。他的举动让她耳目一新,让她想起了伦敦,也让她从智力孤立中解脱出来。
Fearing for their half-Jewish sons during the war, Lyn took exile with the boys in Princeton, New Jersey. Max knew the area from the time he spent there with Turing before the war. But he remained in England this time, leaving Lyn alone with the children. On a state visit, after spending several hours with President Roosevelt in Washington, John Maynard Keynes searched her out in Princeton. His gesture was a refreshing reminder to her of London and a respite from intellectual isolation.
林恩和马克斯的小儿子威廉记得这次访问。凯恩斯陪年轻的威廉去理发店理发,让他坐在冯诺依曼旁边。但有些事情让男孩心烦意乱,他哭着逃走了。凯恩斯在冯诺依曼刮胡子的时候,用银色的舌头追着并哄着他回到椅子上理发。46
Lyn and Max’s younger son, William, remembered the visit. Keynes accompanied young William to a barbershop for a haircut and seated him next to von Neumann. But something upset the boy, who fled in tears. Keynes pursued and coaxed him, with silvery tongue no doubt, back into the chair for his haircut while von Neumann got a shave.46
林恩与图灵的友谊后来开始了,当时两人都回到了英国并住在曼彻斯特。仍然渴望伦敦的文学界,她发现他与马克斯的其他主要谈论数学的来访者不同,令人耳目一新。她认为他是一个“非常简单、谦逊、温和的人”。我们期待她对圣图灵有更深入的了解。
Lyn’s friendship with Turing began later when both were back in England and living in Manchester. Still starved for the London literary scene, she found him a refreshing change from Max’s other visitors who talked mostly of math. She saw him as a “very simple, humble, gentle personality.” We look to her for a deeper understanding of St. Turing.
虽然在她眼中算不上极客,但她确实在印刷品上触及了图灵的极客特征。她在萨拉·图灵关于她儿子的传记的前言中写道:“他的衣服从来都不好看。” 并且,“他有一种奇怪的不让人看到眼睛的方式。”
Although hardly a geek in her eyes, she did touch on Turing’s geeky characteristics in print. She wrote in the foreword to Sara Turing’s biography of her son, “He never looked right in his clothes.” And, “He had a strange way of not meeting the eye.”
林恩在被捕后与图灵变得特别亲近,除了官方机密外,他再也没有什么可隐瞒的了。在最后的日子里,他对她说:“我简直不敢相信和一个女孩上床就像和一个男孩上床一样好。”
Lyn became particularly close to Turing after he was arrested and no longer had anything to hide—other than official secrets. He said to her during those last days, “I just can’t believe it’s as nice to go to bed with a girl as with a boy.”
“我完全同意你的看法,”林回答道。“我也更喜欢男孩。”
“I entirely agree with you,” Lyn replied. “I also much prefer boys.”
他们之间产生了一种与怪胎不相称的亲密关系。现在,他的眼睛不再是“一种不符合眼睛的奇怪方式”,而是“蓝色到彩色玻璃的亮度和丰富性,”她写道。“但一旦他以亲切交谈的自信,直接而认真地看着他的同伴,他的眼睛就再也不能错过了。这样的坦率和理解,从他们身上看,是一种文明到让人几乎不敢呼吸的东西。” 像图灵的母亲一样,林恩从不相信他是自杀的。47
There grew between them an intimacy that belied the geek. Now, instead of “a strange way of not meeting the eye,” his eyes were “blue to the brightness and richness of stained glass,” she wrote. “But once he had looked directly and earnestly at his companion, in the confidence of friendly talk, his eyes could never again be missed. Such candour and comprehension looked from them, something so civilized that one hardly dared to breathe.” Like Turing’s mother, Lyn never believed he committed suicide.47
但林恩对 Digital Light 的持久贡献是她的儿子。威廉纽曼将合着第一本计算机图形学教科书。
But Lyn’s lasting contribution to Digital Light was her son. William Newman would coauthor the first textbook on computer graphics.
当我们准备开始第 4 章关于数字光的诞生以及它如何与计算机的诞生交织在一起时,这里是对第 3 章的快速回顾。我通过在小范围内强调其无意识的简单性,在直观的概念层面上介绍了计算并比较其令人敬畏的延展性和理论上的奥秘——它的不可知性——在大范围内。我建议编程是创造力和困难所在。我将计算确立为操纵符号模式的系统或算法过程。这些过程是通过非常简单的单个步骤来实现的——但其中有很多。我打消了我们认为数字是计算的基础的观念——计算机中没有 0 和 1——并且确定性在某种程度上限制了这个想法。我展示了计算不需要速度、比特和电子设备。
As we get set to start chapter 4 about the birth of Digital Light—and how it’s intertwined with the birth of computers—here’s a quick review of chapter 3. I presented computation at an intuitive, conceptual level by stressing its mindless simplicity in the small and comparing its awesome Malleability and theoretical mystery—its unknowability—in the large. I suggested that programming is where the creativity—and difficulty—lies. I established computation as systematic, or algorithmic, processes that manipulate patterns of symbols. The processes are realized with ever-so-simple individual steps—but lots of them. I disabused us of the notion that number is fundamental to computation—there are no 0s and 1s in a computer—and that determinism somehow limits the idea. I showed that speed, bits, and electronics aren’t required for computation.
然而,下一章是关于速度、比特和电子学的。速度在现实世界中非常重要,而位和电子设备是实现它的关键。意想不到的礼物是令人敬畏的放大及其数量级的奥秘,计算进入超新星并发出数字光。
Nevertheless, the next chapter is about speed, bits, and electronics. Speed matters a great deal in the real world, and bits and electronics are key to achieving it. The unexpected gift is awesome Amplification and its order-of-magnitude mystery, where computation goes supernova and emits Digital Light.
我对计算机不是很感兴趣,我做了一个,我认为一比一是一个很好的分数,所以我没有再做任何事情。
I’m not really interested in computers, I made one and I thought one out of one was a good score so I didn’t make any more.
——弗雷德里克·“弗雷迪”·威廉姆斯爵士1
—Sir Frederic “Freddie” Williams1
我问 Kilburn 教授,为什么每次我打开一本计算机科学教科书我都会看到计算机起源于美国,而英国人却一无所获?于是汤姆 [基尔伯恩] 从嘴里拿出烟斗说:“那些需要知道的人都知道。”
I asked Professor Kilburn, why is it that whenever I open a computer science textbook I get the American origins of computers but the Brits are nowhere? So Tom [Kilburn] took his pipe out of his mouth and said, “Those who need to know do know.”
——Simon Lavington,英国计算机历史学家2
—Simon Lavington, British computer historian2
当我开始写这本书时,我和我的大多数同事一样认为,第一张电脑图片是在 60 年代创作的,尤其是由 Ivan Sutherland 和他在犹他州的团队创作的。但是当我试图确定日期时,我很快意识到没有人确切知道第一张数码照片是什么时候出现的。本章是我寻找它们的结果。在剑桥、牛津、曼彻斯特和波士顿的晦涩档案中呆了很多天后,我终于可以准确而完整地讲述这个故事了。
When I began writing this book, I thought, like most of my colleagues, that the first computer pictures were created in the Sixties, particularly by Ivan Sutherland and his group at Utah. But when I tried to pin down the date, I soon realized that no one knew exactly when the first digital pictures emerged. This chapter is the result of my quest to find them. After many days in obscure archives in Cambridge, Oxford, Manchester, and Boston, I can finally tell the story accurately and fully.
答案是一个巨大的惊喜:第一个像素出现在第一台计算机上。英国工程师 Freddie Williams(图 4.1,左)和 Tom Kilburn(右)创造了它们,加上第一个有效的计算机内存系统,击败了理论重量级人物图灵和冯诺依曼。英国工程师——精明的直言不讳,眼中带着一丝乐趣——肯定会对如此宏大的描述嗤之以鼻,尽管他们私下同意他们的看法。因为这一切都是真的。他们于 1948 年在英国曼彻斯特诞生并养育了那台计算机——令人愉快的名字 Baby。这是图灵 1936 年伟大构想的全电子硬件实现——存储程序通用计算机。这正是我们今天所说的计算机的意思。
And the answer is a massive surprise: the first pixels were on the first computer. British engineers Freddie Williams (figure 4.1, left) and Tom Kilburn (right) created them both, plus the first effective computer memory system, beating out theoretical heavyweights Turing and von Neumann. The Brit engineers—pithy straight-talkers with a touch of in-your-eye fun—would surely have snorted at such grand characterizations, while they agreed with them privately. Because it was all true. They birthed and mothered that computer—delightfully named Baby—in Manchester, England, in 1948. It was a fully electronic hardware realization of Turing’s great idea of 1936—the stored-program universal computer. It was exactly what we mean by a computer today.
争夺第一台计算机的竞争非常激烈。根据上面的描述,英国人赢了,但洋基队紧随其后。新发现的令人兴奋的记录表明这场比赛比以前知道的更接近——几天之内——而且洋基队甚至可能首先到达那里。让我们称之为领带。我们稍后会讨论这种发展。但我们的主要任务是数码光——那些没有争议的第一个像素。
The race to the first computer is closely contested. The Brits won it, by the account above, but the Yanks were hot on their heels. Freshly uncovered and exciting records suggest that the race was closer than previously known—a matter of days—and that the Yanks may even have got there first. Let’s call it a tie. We’ll discuss that development later. But our main mission is Digital Light—those first pixels, about which there is no controversy.
图 4.1
Figure 4.1
Yank von Neumann 和 Turing 本人一样了解英国人图灵的伟大计算理念,两位天才都尝试了它的硬件版本。但是图灵陷入了官僚内讧,这是他最大也是唯一的失败——除非你算上个人的生存。冯诺依曼的团队未能及时获得威廉姆斯和基尔伯恩品种的电子记忆。他们,以及大约十几个其他美国早期的努力,采用了威廉姆斯和基尔本的记忆。
The Yank von Neumann understood the Brit Turing’s great idea of computation as well as Turing himself did, and both geniuses made a try for a hardware version of it. But Turing bogged down in bureaucratic infighting, his biggest and only failure—unless you count personal survival. And von Neumann’s team failed to get an electronic memory of the Williams and Kilburn variety working in time; they, and about a dozen other early American efforts, adopted the Williams and Kilburn memory.
毫无疑问,威廉姆斯和基尔本创造了第一台数码灯。Baby的记忆片段是阴极射线管(CRT)表面的光点。每个点可以有两种尺寸,方便地称为 0 和 1。但由于这些位在 CRT 上是可见的,并且由于它们以整齐的行和列排列在那里,所以它们加倍作为第一个像素。
Without question Williams and Kilburn created the first Digital Light. The bits of Baby’s memory were spots of light on the face of a cathode-ray tube (CRT). Each spot could have two sizes, conveniently called 0 and 1. But since these bits were visible on a CRT, and since they were arrayed there in neat rows and columns, they doubled as the first pixels.
威廉姆斯给了我们第一个显示的像素。然后,Kilburn 在 1947 年从这些散布像素的阵列中创建了第一张数字图片,时间稍早于 Baby 完成——可以说是在子宫内。对我们来说幸运的是,他拍下了这一重大事件的照片(图 4.2)。我称之为显示First Light。这张不起眼的照片是数码光的开端,是黎明的曙光。这是整个现代图像世界的开始——一个没有像素无法想象的世界。重要的是,这是一个有意的二维图片,而不是任意不连贯的点阵列。
Williams gave us the first displayed pixel. Then Kilburn created the first digital picture from an array of those spread pixels in 1947, slightly before Baby’s completion—in utero, so to speak. Luckily for us he took a photograph of the big event (figure 4.2). I call that display First Light. This humble picture was the very beginning, the dawn of Digital Light. It was the beginning of the whole modern world of images—a world unimaginable without pixels. Importantly, it was an intentional two-dimensional picture, not an arbitrary incoherent array of dots.
图 4.2
Figure 4.2
汤姆·基尔本,《第一道曙光》,1947 年。
Tom Kilburn, First Light, 1947.
因为在计算机的早期,制作图片被认为是轻浮的,所以历史学家几乎没有提到它们。Digital Light 是早期计算机故事中被忽视的一部分,因此 First Light 一直是不可见的和无法识别的。
Because making pictures was considered frivolous in those early days of computers, historians have barely mentioned them. Digital Light is a neglected part of the story of early computers, and so First Light has been invisible and unrecognized.
故事从图灵的伟大想法开始。他为我们带来了延展性,这是计算的第一个奇迹——一种控制和执行无限复杂过程的方法。但他没有给我们速度。起初计算速度非常缓慢——回想一下名片计算机。图灵和冯诺依曼意识到,要让软件快速运行,他们必须将其转换为硬件。将图灵的软思想实现为硬件,即计算机,是加快计算速度的关键。放大——计算的第二个奇迹——需要它。计算机以两个容易标记的步骤到达。
The story begins with Turing’s great idea. He brought us Malleability, that first miracle of computation—a way to control and execute an infinity of complex processes. But he didn’t give us speed. Computation was tediously slow at first—recall the business-card computer. Turing and von Neumann were aware that to make software go fast, they must convert it to hardware. Realizing Turing’s soft idea as hardware, the computer, was the key to making computation fast. Amplification—the second miracle of computation—required it. Computers arrived in two easily marked steps.
我将第一步,即 1948 年至 1965 年称为 Epoch 1。这是一个巨大的恐龙机器时代——以房间甚至英亩来衡量——但并不是那么聪明。他们是沉重的,受到小记忆的限制。房间大小的 Baby 起初只有 1000 位——在今天的测量中是 128 字节。但 Baby 标志着硬件辅助计算时代的开始,第一次加速和 Amplification 的开始。
I call the first step, the years 1948 to 1965, Epoch 1. This was the era of dinosaur machines of immense size—measured in rooms and even acres—but not all that smart. They were ponderous and limited by small memories. Room-sized Baby at first had only a thousand bits—128 bytes in today’s measure. But Baby signified the launch of the age of hardware-assisted computation, the first quickening and the beginnings of Amplification.
本章标题中的Quickening指的是婴儿和一般计算机的概念。但更重要的是,它也意味着加速。Baby 的计算机使计算速度更快。那是,现在也是,他们的目的。
Quickening in this chapter’s title refers to the conception of Baby and of computers in general. But more importantly it also means speedup. Computers from Baby on made computation fast. That was, and is, their purpose.
Epoch 2 始于 1965 年,目前正在进行中。尽管计算机在 Epoch 1 期间速度有所提高,但直到 1965 年才出现了一种特别有效的加速,即第二次加速。当前的超新星时代由此而来,随着物理尺寸的急剧缩小,计算机能力呈指数级增长。摩尔定律抓住了它的本质:计算机的所有优点每五年就会提高一个数量级. 这个惊人的声明是如此具有革命性,以至于我们很难理解。它告诉我们,计算机在短短五年内提高了 10 倍——此后每五年这样做一次。例如,一辆 1965 年时速为 60 英里/小时的汽车,按照摩尔定律衡量,在 1970 年和 1975 年时速为 600 英里/小时,而价格不会上涨。对于汽车来说是不可想象的,但对于计算机来说却是这样。名副其实的奇迹。摩尔定律的硬件奇迹直接催生了Amplification的生产力奇迹。放大实现了大数字融合并创造了现代世界。
Epoch 2 began in 1965 and is ongoing. Although computers increased in speed during Epoch 1, it wasn’t until 1965 that a particularly potent kind of quickening, the second quickening, took hold. From it comes the current supernova era, when computer power explodes exponentially as physical size shrinks dramatically. Its nature is captured by Moore’s Law: everything good about computers gets better by an order of magnitude every five years. This astonishing statement is so revolutionary that it’s difficult for us to grasp. It tells us that computers improve by a factor of ten in just five years—and do so every five years thereafter. An automobile in 1965, say, capable of 60 mph, would by Moore’s Law measure go 600 mph in 1970 and 6,000 mph in 1975—at no increase in price. Unthinkable for cars, but true of computers. A veritable miracle. The hardware miracle of Moore’s Law led directly to the productivity miracle of Amplification. And Amplification enabled the Great Digital Convergence and created the modern world.
这是一场古老的比赛——至少自美国独立战争以来。刻板印象维持它:美国佬夸大其词,而英国人则轻描淡写。或者更糟糕的是:美国佬使用美元,而英国人使用大脑。英国间谍小说家约翰·勒卡雷 (John le Carré) 曾将美国人称为表兄弟,而他并不是指接吻类。表兄弟是反对希特勒和冷战的盟友,但合作往往不情愿。两支队伍在争夺第一台计算机的过程中既竞争又合作。这是一场势均力敌的比赛——如此之近,以至于一些历史学家仍在争论。
It’s an old competition—since the American Revolution at least. Stereotypes maintain it: Yanks overclaim while Brits understate. Or worse: Yanks use bucks where Brits use brains. The British spy novelist John le Carré famously called Americans the Cousins, and he didn’t mean the kissing variety. The Cousins were allies in the war against Hitler and then the Cold War, but cooperation was often reluctant. The two teams both competed and cooperated in the race to the first computer. And it was a close race—so close that some historians are still debating it.
在 1960 年代,我这一代人被教导说,1945 年出生在费城的 Eniac——一台由 Yanks(我们)制造的机器——是第一台电子计算机。但它不是——不是按照今天计算机作为电子存储程序机器的含义。它甚至不是第一台几乎计算机。英国人(他们)已经赢得了那轮比赛,但我们洋基队却不知道。有那个官方保密法——图灵的暴君——又上场了。英国人在洋基队甚至没有意识到的情况下赢得了第一次小规模冲突。
In the 1960s my American generation was taught that Eniac, born in Philadelphia in 1945—a machine made by Yanks (us)—was the first electronic computer. But it wasn’t—not by today’s meaning of computer as an electronic stored-program machine. It wasn’t even the first of the almost-computers. The Brits (them) had already won that round, but we Yanks couldn’t have known it. There’s that Official Secrets Act—Turing’s tyrant—in play again. The Brits had won the first skirmish without the Yanks even being aware of it.
在发表不知情或不准确的声明时,英国人也不是无可指责的。他们声称 1944 年初在布莱切利公园的机器 Colossus 是第一台电子计算机。那也是错误的。Colossus 和 Eniac 一样,使用的是硬件程序,而不是软件。两者都很大,都是电子的,但它们不是存储程序的计算机。重新编程这两种野兽都需要切换开关和重新插入电缆——以人类的速度手动重新布线机器硬件。图灵存储程序计算机思想的美妙之处在于程序本身可以存储在保存其数据的同一内存中。更改程序及其操作的数据是相同的过程。如果计算机是电子的,那么改变程序的速度就会以电子速度发生,这会让人类望而却步。3
The Brits aren’t blameless either, when it comes to making uninformed or inaccurate pronouncements. They’ve claimed that their machine Colossus at Bletchley Park in early 1944 was the first electronic computer. That’s wrong too. Colossus, like Eniac, used hardware programs, not software. Both were big and both were electronic, but they weren’t stored-program computers. Reprogramming either beast required toggling switches and replugging cables—a manual rewiring of the machine hardware at pokey human speeds. The beauty of Turing’s stored-program computer idea is that a program itself can be stored in the very same memory that holds its data. To change a program and the data it manipulates are the same process. If the computer is electronic, then changing programs happens at electronic speeds that leave humans in the dust. You don’t need an external guy—or, more often in fact, gal—to slowly swap out cables and throw switches.3
但那些房间大小的庞然大物为表兄弟们服务得很好。几乎是计算机在军事上增强了洋基人和英国人。Eniac 进行了氢弹计算。Colossus 帮助破解了德国的加密方案,并确保诺曼底登陆成功。对于将着手设计和制造真正的计算机的工程师来说,这些机器是非凡的电子训练场——或至少是灵感。那些真正的计算机将由存储在计算机中的软件程序驱动,就像数据一样,而不是由电缆从外部强加。4
But those room-sized behemoths served the Cousins well. The almost-computers boosted both the Yanks and the Brits militarily. Eniac made H-bomb calculations. Colossus helped to crack a German encryption scheme and ensured a successful D-Day landing in Normandy. The machines were extraordinary electronic training grounds—or inspirations, at least—for the engineers who would proceed to design and build true computers. Those true computers would be driven by software programs stored in the computer just like data, not imposed from the outside by a cable gal.4
弗雷迪·威廉姆斯于 1946 年 12 月搬到曼彻斯特大学。他的第一个目标不是制造一台计算机,而是一台快速的内存。他在战时雷达方面的经验——在屏幕上显示光点——激发了他的想法,即最好的解决方案可能在于阴极射线管。1946 年,他在纽约贝尔实验室看到了一种很有前途的雷达技术。5
Freddie Williams moved to the University of Manchester in December 1946. His first goal wasn’t to build a computer but rather a fast memory for one. His experience with wartime radar—featuring blips on a screen—inspired his idea that the best solution probably lay with the cathode-ray tube. He had seen a promising radar technique at Bell Labs in New York when he visited in 1946.5
就在他搬到曼彻斯特之前,威廉姆斯成功地在 CRT 上存储了一个位。换句话说,他设计了一种方法,可以在管子扁平端的屏幕上的某个位置显示一个小斑点(一个点)或一个大斑点(一个破折号)。他可以写一点。此外,他(嗯,他的电子电路)可以查看已经存储在管表面上的斑点,并确定它是大还是小——他可以读取存储在那里的一点。他也可以将一个大斑点变成一个小斑点,反之亦然。用方便的现代术语来说,他可以将 0 或 1 任意写入一个位置,并且他可以读取那里存储的内容。最重要的是,他写到一个位置的值一直存在,直到他或计算机明确更改它。换句话说,它被记住了。瞧!1946 年,威廉姆斯创造了第一个可见的计算机位。6
Just before his move to Manchester, Williams had succeeded in storing one bit on a CRT. He had devised, in other words, a way to display a small blob (a dot) or a big blob (a dash) at a location on the screen at the flattened end of the tube. He could write a bit. Furthermore, he (well, his electronic circuits) could look at a blob that was already stored on the face of the tube and determine whether it was big or small—he could read a bit stored there. He could also change a large blob to a small one, or vice versa. In convenient modern terminology, he could arbitrarily write a 0 or 1 to a location, and he could read what was stored there. Most importantly, a value he wrote to a location persisted there until he, or a computer, explicitly changed it. In other words, it was remembered. Voila! In 1946 Williams had created the first visible computer bit.6
他正在着手创造所谓的威廉姆斯管。它应该被称为 Williams-Kilburn 管——但几乎从来没有——因为 Tom Kilburn 很快就在曼彻斯特加入了威廉姆斯,并且到 1947 年 3 月已经积极参与管设计。到年底,Kilburn 能够以矩形阵列的形式在管表面存储 1,024 位,并创建并拍摄了 First Light 的照片,这是第一个数字光显示器(图 4.2)。然后他很快就提高到 2,048 位,创建了另一张照片,并拍摄了照片(图 4.3)。但是这个词还不存在,正如我们从第 3 章中知道的那样,所以他使用了digit反而。他写了一篇报告,他的博士论文,“用于二进制数字计算机的存储系统”,发表于 1947 年 12 月 1 日。他 26 岁。那是那个时刻。
He was on his way to creating what would be called a Williams tube. It should be called a Williams-Kilburn tube—but hardly ever is—because Tom Kilburn soon joined Williams at Manchester and by March 1947 was already actively involved in the tube design. By the end of the year Kilburn was able to store 1,024 bits on the face of the tube in a rectangular array—and to create and take the photograph of First Light, that first Digital Light display (figure 4.2). Then quickly he advanced to 2,048 bits, created another picture, and took its photograph (figure 4.3). But the word bit didn’t exist yet, as we know from chapter 3, so he used digit instead. He wrote a report, his doctoral thesis, “A Storage System for Use with Binary Digital Computing Machines,” issued December 1, 1947. He was 26. That was the moment.
基尔本 1947 年的报告用两张照片公开宣布了数码光的曙光。它们不仅仅是任何一系列景点的照片。它们是两张以数字方式渲染并存储在电子数字存储器中的图片。Kilburn打算将它们做成二维图片。
Kilburn’s 1947 report publicly announced the dawn of Digital Light with the two photographs. They weren’t photos of just any array of spots. They were two pictures rendered digitally and stored in an electronic digital memory. Kilburn intended them to be two-dimensional pictures.
Kilburn 通过手工为 1,024 个光点中的每一个进行照明的“过于费力”的方法,创作了第一张数码照片 First Light。显示器是一个由 32 x 32 扩展像素组成的阵列。他使用“以打字机的形式排列”的 32 个键来切换位。Kilburn 将显示器描述为一组“图片元素”。正如我们所见,短格式像素还不存在——直到 1965 年。他将显示元素(可见)与图片元素(不可见)混淆了。我们在 Kotelnikov 章节中讨论了这种区别,但对于 Kilburn 来说还没有这种区别。7
Kilburn created First Light, the first digital picture, by the “far too laborious” method of lighting each of 1,024 spots by hand. The display was an array of 32 by 32 spread pixels. He used 32 keys “arranged in the form of a typewriter” to toggle in the bits. Kilburn described the display as an array of “picture elements.” The short form pixel didn’t yet exist—not until 1965, as we’ve seen. And he confused display elements (visible) with picture elements (invisible). We discussed this distinction in the Kotelnikov chapter, but there was no such distinction yet for Kilburn.7
Kilburn 使用同样繁琐的类似打字机的方法在 2,048 位内存中创建了第二张数字图片。这些图片中的每个散布像素都有两种状态,破折号(大斑点)和点(小斑点),方便地称为 1 和 0。这里的散布像素是圆形飞溅或斑点,具有两种不同大小的光。即使在最早的日子里,也没有小广场。
Kilburn created the second digital picture in the 2,048-bit memory using the same tedious typewriter-like method. Each spread pixel in these pictures had two states, dash (big blob) and dot (little blob), known conveniently as 1 and 0. A spread pixel here is a rounded splash, or blob, of light of two different sizes. There were no little squares—even in the earliest days.
Kilburn 的目的——在他的报告和标题中明确说明——是为计算机设计内存。他在报告中描述了这样一台假设的计算机。然后他和威廉姆斯立即着手建造一台真正的计算机,并在半年内交付了著名的婴儿。8
Kilburn’s purpose—clearly stated in his report and in its title—was to design a memory for a computer. He described just such a hypothetical computer in the report. Then he and Williams promptly proceeded to build an actual computer, and within half a year delivered the famous Baby.8
在图 4.4 中,清醒的、适当奖励的 Kilburn 是皇家学会会员,他拿着他的名声标志,一个 Williams 管——一个 Williams-Kilburn 管,确切地说是笨拙的——而 Baby 则在背景中徘徊。威廉姆斯和基尔本在他们的一生中都获得了巨大的荣誉。到 1977 年弗雷迪·威廉姆斯去世时,他已经是弗雷德里克爵士,也是皇家学会会员。基尔本于 2001 年去世一年后加利福尼亚的计算机历史博物馆让他成为研究员,这是新千年的合适开始。
The sober, suitably rewarded Kilburn in figure 4.4, a Fellow of the Royal Society, holds an icon of his fame, a Williams tube—a Williams-Kilburn tube to be clumsily exact—while Baby hovers in the background. Williams and Kilburn both received great honors during their lifetime. By the time Freddie Williams died in 1977, he was Sir Frederic and also a Fellow of the Royal Society. Kilburn died in 2001 one year after the Computer History Museum in California made him a Fellow, a fitting beginning of the new millennium.
图 4.3
Figure 4.3
图 4.4
Figure 4.4
但没有证据表明 Kilburn 曾经了解计算机上的第一张照片 First Light 的重要性。据我们所知,他在 1947 年创作了前两张照片后,就再也没有创作过另一张照片。事实上,也没有其他人在 Baby 上拍过照片。人们似乎觉得,拍照并不是对计算机的认真使用。这是亵渎神明的。那是禁果——虽然不完全是雕刻的图像。战争刚刚结束,计算资源稀缺,对它们的需求非常强烈。与 Williams 和 Kilburn 合作开发 Baby 的 David “Dai” Edwards 表示,当时用户对这款机器“绝望”。团队的另一名成员 Geoff Tootill 表示,当时团队仍然在战时精神下运作,没有时间放松。9
But there’s no evidence that Kilburn ever understood the momentousness of First Light, the first picture on a computer. After he created the first two pictures in 1947, he never made another one, so far as we know. In fact, nobody else made pictures on Baby either. People seem to have felt that picture making just wasn’t a serious use of the computer. It was profane. It was forbidden fruit—although not exactly a graven image. The war was just over, computation resources were scarce, and the need for them was intense. David “Dai” Edwards, who worked with Williams and Kilburn on Baby, said that users were “desperate” for the machine then. Another member of the team, Geoff Tootill, said that the team still operated under a wartime ethos then and had no time for relaxing.9
拍照对他们来说是一种轻松、愉快的活动。一张图片作为记忆测试模式是一回事,否则为了这种轻浮和世俗的追求而浪费宝贝稀有的计算资源就完全是另一回事了。相反,机器应该计算一些“严肃”的东西。
Making pictures was a relaxing, good-time activity to them. A picture as a memory test pattern was one thing, but otherwise wasting Baby’s rare computing resource for such a frivolous and profane pursuit was something else altogether. Instead, the machine should be computing something “serious.”
从角度来看,考虑几十年后完全不同的环境,即 1998 年,婴儿的精确复制品是为 50 周年而建造的。庆祝活动的编程竞赛引发了几个 Baby 程序,这些程序在 Baby 的显示器上创建了图片,甚至是动画图片。一生成词BABY。
For perspective, consider the totally different environment decades later, in 1998, when an exact replica of Baby was built for its fiftieth anniversary. A programming contest for the celebration elicited several Baby programs that created pictures, even animated ones, on Baby’s monitor. One generated the word BABY.
婴儿重建由克里斯·伯顿在曼彻斯特带头。2013 年 7 月 4 日,他安排我去曼彻斯特科学与工业博物馆看 Baby。BabyPIXAR滚动显示器(图 4.5)——一个电脑动画来欢迎我!我的主持人 Brian Mulholland 前一天为它编写了 Baby 程序。但它本可以在 1948 年在 Baby 身上运行。10
The Baby rebuild had been spearheaded in Manchester by Chris Burton. He arranged a visit for me to see Baby at Manchester’s Museum of Science & Industry on July 4, 2013. Baby welcomed me with PIXAR scrolling across its monitor (figure 4.5)—a computer animation! My host, Brian Mulholland, had written the Baby program for it the previous day. But it could have run on Baby in 1948.10
对于那些安于和平时期、充斥着计算资源并且更熟悉计算机作为图片制作者而不是数字处理器的现代程序员来说,图片创作是显而易见的——甚至是不可抗拒的。没有视觉显示、动画和交互的计算机现在几乎闻所未闻。我们称它们为服务器。
Picture creation is obvious—irresistible even—for modern programmers who are comfortable in peacetime, flush with computational resources, and more familiar with computers as picture producers than as number crunchers. Computers without a visual display, animation, and interaction are almost unheard of now. We call them servers instead.
梳理计算机的早期历史仍然不容易。即使是曼彻斯特婴儿的单一故事也很复杂。完整的历史将有太多人、机器和国家——以及太多的细微差别——不能舒适地放在一本书中,更不用说一章了。我仔细定义了我们所说的计算机的含义,并只关注那些导致数字光的途径,从而修剪掉了大部分的灌木丛。这使得早期计算机历史的一个非常强大的部分完好无损。
It’s still not easy to sort out the early history of computers. Even the single story of Baby at Manchester is complicated. A complete history would have too many people, machines, and countries—and too much nuance—to fit comfortably in a book, much less a chapter. I prune away much of this thicket with a careful definition of what we mean by a computer and by focusing only on those pathways that led to Digital Light. This leaves intact a remarkably robust part of early computer history.
图 4.5
Figure 4.5
然而,那个较小的部分仍然有数十名玩家。为了提供结构,我继续将他们分成两支球队——英国队和洋基队——并假设他们之间有一场戏剧性的比赛。这是一部奥林匹克小说。参赛者不再是国家队,也不是奥运代表队——只受他们挥舞的旗帜和奖牌数量的约束。然而,该设备组织和跟踪复杂的奥运会,它也适用于计算机历史。竞争背后也有一些真相。
Yet that smaller part still has dozens of players. To give structure I continue to divide them into two teams—the Brits and the Yanks—and posit a dramatic race between them. It’s an Olympian fiction. The competitors were no more national teams than Olympic teams are—bound only by the flag they wave and the medal count. Nevertheless, the device organizes and tracks the complex Olympic games, and it works for computer history too. And there’s a bit of truth behind the competition too.
计算机早期历史的“流程图”(图 4.6)给予硬件和软件贡献者同等的赞誉。计算机几乎从未出现过这种情况——这反映了永无止境的高塔与臭气熏天的战斗。这里的软件被概括为包括所有仅是精神上的工作。
A “flow chart” (figure 4.6) of the early history of computers gives hardware and software contributors equal credit. This has hardly ever been the case for computers—a reflection of the never-ending tower versus stinks battle. Software here is generalized to include all work that is only mental.
同时也是著名理论家的软件贡献者——特别是图灵和冯诺依曼——经常被授予荣誉,但事实并非如此。Baby 的硬件“母亲”Williams 和 Kilburn(实线)对 Baby 本身来说比其早期的程序员 Turing 和 Newman(虚线)更重要。
Software contributors who were also famous theoreticians—Turing and von Neumann, notably—often got assigned the glory when it just didn’t happen that way. Baby’s hardware “mothers,” Williams and Kilburn (solid lines), were more important to Baby itself than its early programmers, Turing and Newman (dashed lines).
流程图也让各个参与者之间的相互联系更加明显。人用圆圈表示,计算机用矩形表示,概念用平行四边形表示。图表中没有可行的直线叙述路径。但它是有根的。最重要和最中心的是图灵 1936 年的“论可计算数”,该概念文件以计算的定义和对存储程序计算机的详细描述开始了这一切。从中流出了冯诺依曼 1945 年的Edvac 报告和图灵 1946 年的Ace 报告,其中描述了实际计算机的两种不同架构。
The flow chart also makes the interconnectedness of the various players obvious. People are represented by circles, computers by rectangles, and concepts by parallelograms. There’s no viable straight-line narrative path through the chart. But it is rooted. Topmost and center is Turing’s 1936 “On Computable Numbers,” the concept paper that started it all with its definition of computation and its careful description of a stored-program computer. From it flowed von Neumann’s 1945 Edvac report and Turing’s 1946 Ace report, which described two different architectures for actual computers.
编程是最著名的软件形式。计算的数学是另一回事,如“论可计算数”。第三种脑力劳动以 Edvac 和 Ace 报告为代表。因此,完全意义上的软件贡献包括存储程序计算机的概念、一个架构或它的程序。图表中 Edvac 报告的虚线显示了它对图表中几乎所有计算机的概念(软)贡献,除了图灵的直线。
Programming is the best-known form of software. The mathematics of computation is another, as in “On Computable Numbers.” The third type of mental work is represented by the Edvac and Ace reports. A software contribution in its full sense therefore includes the idea of the stored-program computer, an architecture for one, or programs for it. The dotted lines flowing from the Edvac report in the chart show its conceptual (soft) contribution to almost every computer in the chart aside from Turing’s direct line.
同样,但在硬件方面,Williams 和 Kilburn 影响了两个团队的几台早期机器的设计。它们的设计(硬)贡献由流程图中每个的实线表示。他们不是任何其他非曼彻斯特计算机的工程师,但 Williams-Kilburn 管直接影响了这些计算机的设计。
Similarly, but in hardware, Williams and Kilburn influenced the design of several early machines on both teams. Their design (hard) contribution is indicated by solid lines from each in the flow chart. They weren’t engineers on any of the other non-Manchester computers, but the Williams-Kilburn tube directly influenced the design of those machines.
想法之间
Between the idea
而现实
And the reality
动作之间
Between the motion
和行为
And the act
落下阴影
Falls the Shadow
——TS艾略特,“空心人” 11
—T. S. Eliot, “The Hollow Men”11
听起来,计算机架构是一个计划。它与计算机设计明显不同。我将保留这个熟悉的词,以使架构存在于现实世界中,使用实际的电子设备。建筑是理念;设计就是现实。设计是一个硬件问题,至少需要与建筑一样多的创造力——有些人会说得更多。但这是一种不同的创造力。那是因为架构并不规定或指导设计。一所房子的建筑可以体现在许多设计中。一个标有厨房的盒子激发了——但绝不是指导——花岗岩、瓷砖、木材、把手、灯、水龙头、油漆、窗扇等的无数组合。
A computer architecture is—as it sounds—a plan. It differs markedly from a computer design. I’ll reserve that otherwise familiar word for the act of making an architecture exist in the real world, with actual electronic devices. Architecture is idea; design is reality. Design is a hardware issue, requiring at least as much creativity as architecture—some would say more. But it’s a different kind of creativity. That’s because architecture does not dictate or instruct design. One house architecture can be manifested in many designs. A box labeled Kitchen inspires—but in no way directs—a myriad combinations of granites, tiles, woods, handles, lights, faucets, paints, casements, and so forth.
图 4.6
Figure 4.6
图 4.7
Figure 4.7
Edvac 报告中指定的著名架构——称为冯诺依曼架构——至少影响了流程图中显示的六种不同的计算机设计,甚至更多。图 4.7 显示了它的典型平面图。考虑标记为Memory的简单框。没有指定实际的内存技术——这是硬件设计问题。
The famous architecture specified in the Edvac report—called the von Neumann architecture—influenced at least the six different computer designs shown in the flow chart, and many more. Figure 4.7 shows it in typical plan view. Consider the simple box labeled Memory. There’s no actual memory technology specified—that’s a hardware design concern.
设计人员必须拿出那个空盒子,并弄清楚如何在现实世界中制造一个能够正确地将那个盒子连接到计划中的其他空盒子的设备。然后他们必须掌握他们选择的物理特性,并使所有设备与一个真正的内存一起工作,该内存保存实际的比特,与自身外部的世界通信,并在给定的电网上工作。从建筑中的空盒子到设计的步骤是一个重要的创造性步骤。它没有算法。
The designers have to take that empty box and figure out how to make a device in the real world that will correctly connect that box to the other empty boxes in the plan. Then they must master the physics of their choices and make the devices all work together with a real memory that holds actual bits, communicates to the world outside itself, and works off the given power grid. The step from an empty box in an architecture to a design is a major creative step. There is no algorithm for it.
尽管洋基队开发了获胜的建筑,但英国人创造了获胜的设计并因此赢得了比赛。那个盒子的设计,内存,是第一台计算机和数码照片竞争的关键因素。
Although the Yanks developed the winning architecture, the Brits created the winning design and hence won the race. The design of that one box, Memory, was the crucial factor in the race to the first computer—and digital pictures.
冯诺依曼和图灵架构是等效的想法。两者都是实施图灵存储程序通用计算机概念的计划。图灵的架构也有一个存储盒,以及控制、算术、逻辑和输入输出盒。在这两种架构中,内存和输入输出都相当于通用图灵机的磁带,其余的盒子构成了它的扫描头。图灵在 1947 年的一次关于 Ace 的演讲中明确说明了这种联系。同样,尽管 Edvac 的报告并不明确,但冯诺依曼在 1943 年和 1944 年告诉人们图灵的根本重要性。12
The von Neumann and Turing architectures were equivalent ideas. Both were plans for implementing Turing’s stored-program universal computer concept. Turing’s architecture had a box for memory too, and control, arithmetic, logic, and input-output boxes. In both architectures the memory and input-output are equivalent to the tape of the universal Turing machine, and the remaining boxes form its scanning head. Turing made the connection explicit in a lecture on Ace in 1947. Similarly, although the Edvac report wasn’t explicit, von Neumann told people about Turing’s fundamental importance in 1943 and 1944.12
一般的经验法则是,任何软件过程都可以通过在硬件中实现来加快速度。事实上,计算机本身就是图灵的软硬件实现,但速度非常慢,存储程序通用计算机的想法。算术和逻辑可以是软件,但冯诺依曼和图灵走得更远。他们都指定这些非常流行的操作应该在硬件中实现——尽可能快地进行。这是导致人们普遍误解计算机只是算术机的规范。
A general rule of thumb is that any software process can be made to go faster by implementing it in hardware. In fact, a computer itself is a fast hardware realization of Turing’s soft, but painfully slow, idea of a stored-program universal computer. Arithmetic and logic can be software, but von Neumann and Turing went further. They both specified that these very popular operations should be realized in hardware—to go as fast as possible. This is the specification that led to the common misperception that a computer is only an arithmetic machine.
图灵的架构与冯诺依曼团队的架构有着深刻的不同。图灵指定了一个新的硬件支持概念:软件层次结构。程序员(阅读图灵)很快了解到分层创建程序是一种很好的软件实践。层次结构为那些极长的无意义指令的线性列表之一赋予了意义和结构。
Turing’s architecture differed from the von Neumann team’s in a profound way. Turing specified hardware support for a new concept: the software hierarchy. Programmers (read Turing) quickly learned that it’s good software practice to create a program hierarchically. Hierarchy gives meaning and structure to one of those extremely long linear lists of meaningless instructions.
创建软件层次结构就像作者将一本书分成章节列表。假设一个程序有数十万条指令——这在当今世界并不罕见,而且令人难以置信。但是你可以把它分解成一百个部分,每个部分平均有几千条指令,并给每个部分起一个有意义的名字。对程序员来说,程序然后简化为这数百个命名的、有意义的部分——每个都称为一个子程序(不是图灵的话)。在层次结构的最高级别,程序在概念上只有一百条“指令”长,其中每条指令都是一个子程序。它就像一个目录及其章节。
Creating a software hierarchy is like an author breaking a book into a list of chapters. Suppose a program is hundreds of thousands of instructions long—not that unusual in today’s world, and mind-boggling. But you could break it up into, say, a hundred parts averaging a few thousand instructions each, and give each part a meaningful name. To the programmer, the program then reduces to only these hundred named, meaningful parts—each called a subroutine (not Turing’s word). At the highest level of the hierarchy, the program is conceptually only a hundred “instructions” long, where each instruction is a subroutine. It’s like a table of contents and its chapters.
程序员仍然必须创建所有已命名的部分、子程序,以及所有繁琐的细节,而作者仍然必须编写每一章。但是编写每个部分的任务不那么令人难以置信,而且更紧凑。此外,这是一个分层的想法。程序员可以进一步将每个子程序细分为它自己的子子程序,并将它们细分为它们的子程序,依此类推。咬变成小点心,甚至更容易编程。子程序概念将极其复杂的任务驯服为可理解性——例如进一步将章节分解为标题,将标题分解为段落,最后分解为单词本身。图灵的架构指定了一个硬件提升,使子程序的分层使用变得快速和容易。
The programmer still has to create all the named parts, the subroutines, in all their tedious detail, and the author still has to write each chapter. But the task of writing each part is less mind boggling and more bite-sized. Furthermore, it’s a hierarchical idea. A programmer can further subdivide each subroutine into its own sub-subroutines, and they into theirs, and so forth. Bites become nibbles, even easier to program. The subroutine concept tames an overwhelmingly complex task into comprehensibility—like further breaking chapters into headings, headings into paragraphs, and finally into the words themselves. And Turing’s architecture specified a hardware boost that makes the hierarchical use of subroutines quick and easy.
当然,图灵的架构——具有复杂的子程序支持——应该是被采用的架构,但事实并非如此。Yanks 在 1940 年代广泛传播冯诺依曼的 Edvac 报告,但英国人直到 1986 年才公开发表 Turing 的 Ace 报告。13
Surely Turing’s architecture—with its sophisticated subroutine support—should’ve been the one that got adopted, but it wasn’t. The Yanks disseminated von Neumann’s Edvac report far and wide in the 1940s, but the Brits didn’t publish Turing’s Ace report publicly until 1986.13
伟大的进化生物学家的孙子查尔斯·达尔文爵士在战后试图建立一个英国国家计算资源。他开始得很好。他聘请了图灵并将他带到伦敦附近的国家物理实验室。1945 年底,图灵开始了 NPL 计算机的架构——被称为 Ace——并在不久之后交付了该计划。他在 1946 年的 Ace 报告提到了冯诺依曼稍早一些的 Edvac 报告,该报告展示了 Yanks 的竞争架构。但 Ace 的报告走得更远。它包含一个设计和一个架构——可能是第一个电子计算机设计。图灵投入到构建 Pilot Ace 的项目中,这是基于 Ace 架构的原型计算机。当然,图灵的计算机——来自发明计算的人——应该是长子,但事实并非如此。14
Sir Charles Darwin, a grandson of the great evolutionary biologist, sought to establish a British national computing resource just after the war. He started well. He hired Turing and brought him to the National Physical Laboratory near London. In late 1945 Turing began the architecture for the NPL computer—to be called Ace—and delivered the plan soon afterwards. His 1946 Ace report referred to von Neumann’s slightly earlier Edvac report, which presented the Yanks’ competing architecture. But the Ace report went further. It contained a design as well as an architecture—probably the first electronic computer design. Turing dived into the project of building Pilot Ace, the prototype computer that was based on the Ace architecture. Surely Turing’s computer—from the man who invented computation—should’ve been the firstborn, but it wasn’t. Pilot Ace had delivery problems.14
一个问题是图灵本人。首先,他不断地改变架构,因为他想到了绝妙的新想法。其次,他不能很好地发挥团队合作的作用。或者,从积极的角度来说,他具有异常强烈的个性。但其他问题并不是他造成的,例如官僚机构的无能以及概念和工程的不幸物理分离——塔和臭气。将硬件和软件分开并不适合生产计算机。可悲的是,对于达尔文的爱好者来说,孙子达尔文是负责那个烂摊子的官僚。15
One problem was Turing himself. First, he kept changing the architecture as brilliant new ideas occurred to him. Second, he was unable to function well as a team player. Or, to spin it positively, he had an unusually strong individuality. But other problems weren’t of his making, such as bureaucratic incompetence and an unfortunate physical separation of concept and engineering—of tower and stinks. Keeping hardware and software apart doesn’t work for producing computers. Sadly, for Darwin enthusiasts, grandson Darwin was the bureaucrat in charge of that bungle.15
飞行员王牌变得如此混乱,以至于图灵在项目完成之前就离开了这个项目,幻想破灭和灰心丧气。达尔文写道:“我们一致认为,最好让图灵暂时停止使用它。” 飞行员艾斯迟到的第一次哭声终于发生在 1950 年 5 月 10 日——几乎是在宝贝之后两年。Pilot Ace 勉强进入前十台计算机的名单。而完整的王牌本身,飞行员王牌和图灵主要目标的孩子,直到他离开十年后才会完成。
Pilot Ace became such a mess that Turing left the project, disillusioned and disheartened, long before it was completed. Darwin wrote, “We are agreed that it would be best that Turing should go off it for a spell.” Pilot Ace’s exasperatingly overdue first cry finally occurred on May 10, 1950—almost two years after Baby. Pilot Ace barely made it onto the list of the first ten computers. And the full Ace itself, the child of Pilot Ace and Turing’s principal goal, wouldn’t be complete until a decade after he left.
然而,在他离开这个项目之前,1947 年,图灵就 Ace 做了他著名的演讲——他使用了新词编程。观众中有工程师汤姆·基尔伯恩,他在前往曼彻斯特的途中短暂停留,他将在那里与弗雷迪·威廉姆斯会合。16
Before he left the project though, in 1947, Turing gave his notable lecture on Ace—and he used the new word programming. In the audience was the engineer Tom Kilburn, who had stopped by briefly on his way to Manchester where he was to join Freddie Williams.16
图灵也将在大约一年后到达那里。他不愉快地离开 Ace 项目的幸福结果是他可以使用其他计算机项目。马克斯纽曼需要他。纽曼是剑桥大学的教授,他最初启发了图灵实现他的计算理念的飞跃。然后纽曼敦促图灵去普林斯顿学习。所以现在图灵的老老师和导师中标了他在曼彻斯特的服务,为威廉姆斯和基尔本的婴儿开发软件。
Turing would be on his way there too, in about a year. The happy consequence of his unhappy departure from the Ace project was that he was available for other computer projects. And Max Newman needed him. Newman was the professor at Cambridge who had originally inspired Turing to make the leap to his idea of computation. And then Newman had urged Turing to study at Princeton. So now Turing’s old teacher and mentor made the winning bid for his services in Manchester, to develop software for Williams and Kilburn’s Baby.
婴儿于 1948 年 6 月 21 日在曼彻斯特大学出生。威廉姆斯和基尔本在一个臭气熏天的实验室——电气工程部门——从零开始设计和建造了它。他们直接负责设计和建造它。Kilburn 编写了它的第一个程序。他们在著名的科学杂志《自然》的九月刊上宣布了婴儿的诞生——我们很自豪地假设。17
Baby was born on June 21, 1948, at the University of Manchester. Williams and Kilburn designed and built it from scratch in a lab in the stinks—the electrical engineering department. They were directly responsible for designing and building it. And Kilburn wrote its first program. They announced Baby’s birth—proudly we assume—in the September issue of the prestigious science journal Nature.17
纽曼将把图灵带入这个项目,当时他在曼彻斯特数学系的塔楼里。在 Bletchley Park 对几乎是计算机的 Colossus 进行了积极体验之后,他打算在曼彻斯特拥有一台功能齐全的计算机。他认真考虑了洋基队的做法,就像冯诺依曼一样,直到他发现威廉姆斯和基尔本的曼彻斯特主队实际上领先。他立即改变了忠诚度并开始与他们协商关于塔对面的宝贝——臭味分歧。
Newman, who would bring Turing into the project, was in the tower at Manchester—the mathematics department. After his positive experience with the almost-computer Colossus at Bletchley Park, he was intent on having a full-blown computer at Manchester. He seriously considered the Yanks’ approach, à la von Neumann, until he discovered that the Manchester home team of Williams and Kilburn was actually ahead. He promptly switched loyalties and began to consult with them about Baby across the tower–stinks divide.
Baby 的第一个程序是 Kilburn 的,而不是 Turing 的。图灵为搬到曼彻斯特做准备的第一件事就是获得Baby的指令集。他在 1948 年 7 月编写了他的第一个(越野车)婴儿程序,大约在它诞生一个月后,仍然缺席。大约三个月后,也就是 10 月,他抵达曼彻斯特。18
Baby’s first program was Kilburn’s, not Turing’s. The first thing Turing did in preparation for his move to Manchester was to obtain Baby’s instruction set. He wrote his first (buggy) Baby program in July 1948, about a month after its birth and still in absentia. He arrived in Manchester about three months later, in October.18
曼彻斯特的工程人员受到了攻击,这是理所当然的,因为太多的功劳归功于图灵和纽曼的宝贝,特别是因为图灵直到后来才出现。其中一些只是塔和臭之间的常用砂纸,但它说明了为一项具有改变世界重要性的复杂技术发明分配功劳的难题。
Manchester engineering people have taken offense, rightfully, because too much credit goes to Turing and Newman for Baby, especially since Turing wasn’t even there until later. Some of this is just the usual sandpaper between tower and stinks, but it speaks to the difficult problem of assigning credit for a complex technical invention of world-changing importance.
但是威廉姆斯和基尔本自己告诉我们,图灵和纽曼是宝贝创造的亲密部分。1975 年,威廉姆斯回忆说:“汤姆·基尔本和我对计算机一无所知,但对电路却知之甚少。Newman 教授和 AM Turing 先生对计算机了解很多,而对电子学几乎一无所知。他们牵着我们的手,解释了数字如何住在有地址的房子里,以及如何在计算过程中跟踪他们。” 这可能是威廉姆斯表现出来的讽刺幽默感,而不是准确的历史叙述,但他多次重复这个故事。19
But Williams and Kilburn themselves told us that Turing and Newman were intimately part of Baby’s creation. In 1975 Williams recalled, “Tom Kilburn and I knew nothing about computers, but a lot about circuits. Professor Newman and Mr. A. M. Turing knew a lot about computers and substantially nothing about electronics. They took us by the hand and explained how numbers could live in houses with addresses and how, if they did, they could be kept track of during a calculation.” This might have been Williams’s wry sense of humor on display rather than an accurate historical recounting, but he repeated the story several times.19
基尔本 1947 年的博士论文使巴比的历史更加复杂,因为它在参考书目中列出了图灵和冯诺依曼的“未发表的作品”。Kilburn 肯定指的是图灵 1947 年的 Ace 演讲和冯·诺依曼 1945 年的 Edvac 报告。尽管威廉姆斯后来只给了图灵和纽曼的荣誉——“数字可以住在有地址的房子里”的俏皮话——但他和 Kilburn 并没有选择图灵的架构. 基尔本在听完图灵的演讲后明确表示,他永远不会那样设计机器。相反,他们为 Baby 使用了冯诺依曼架构。他们口头上称赞了主队,但显然是从另一边的洋基队那里借鉴了想法。20
Kilburn’s PhD dissertation of 1947 further complicates Baby’s history because it listed in its bibliography “unpublished work” by Turing and by von Neumann. Surely Kilburn was referring to Turing’s Ace lecture of 1947 and von Neumann’s Edvac report of 1945. Although Williams later gave only Turing and Newman credit—the “numbers could live in houses with addresses” quip—he and Kilburn didn’t opt for Turing’s architecture. Kilburn explicitly said, after he heard Turing’s lecture, that he would never design a machine that way. Instead they used a von Neumann architecture for Baby. They gave the home team verbal credit but clearly borrowed ideas from the other side, the Yanks.20
婴儿茁壮成长,可以说是第二代机器。Mark I(曼彻斯特 Mark I 的缩写)在 1949 年 6 月 18 日运行了一个无错误的程序。Mark I 的记录日期是软的,但保守的出生日期使它成为世界上第四台计算机。图灵为 Mark I 设计了早期的软件规范。21
Baby thrived and begat, so to speak, a second-generation machine. Mark I—short for Manchester Mark I—ran an error-free program on June 18, 1949. Recorded dates are soft for Mark I, but that conservative birth date establishes it as the fourth computer in the world. Turing devised the early software specifications for Mark I.21
Mark I 很快就诞生了 Ferranti Mark I,它于 1951 年 2 月 12 日首次亮相,是世界上第一台商用计算机。Ferranti——尽管它的名字是一家英国公司——起初称这台电脑为女士,《卫报》将这个称号美化为“一位具有不可预测倾向的‘女士’”。一张宣传照片显示图灵在夫人的控制台上盘旋。他为 Ace 编写了计算机的编程手册。22
Mark I soon begat Ferranti Mark I, which debuted on February 12, 1951, as the world’s first commercial computer. Ferranti—a British firm despite its name—called the computer Madam at first, a title that The Guardian embellished to “a ‘madam’ with unpredictable tendencies.” A publicity photo featured Turing hovering over Madam’s console. He wrote the computer’s programming manual as he had for Ace.22
与此同时,在剑桥,莫里斯(发音为“莫里斯”)威尔克斯正在建造 Edsac,这注定是世界上第三台计算机。他为什么不邀请图灵加入那个项目?毕竟,剑桥是图灵的天然家园。他是其国王学院的研究员。图灵一定考虑到了这一点,因为他在 1948 年 5 月访问了威尔克斯,然后于 10 月在曼彻斯特加入纽曼。
Meanwhile in Cambridge, Maurice (pronounced “Morris”) Wilkes was building Edsac, destined to be the third computer in the world. Why didn’t he invite Turing to join that project? Cambridge was Turing’s natural home, after all. He was a fellow of its King’s College. Turing must have considered it because he visited Wilkes in May 1948 before he joined Newman in Manchester in October.
相互仇恨很可能压制了这种选择。图灵谈到他与威尔克斯的访问时说,“我一个字都听不进去。” 他早些时候曾批评威尔克斯的一项提议“更符合美国通过大量设备而不是思想解决困难的传统”。(同样来自图灵的那种陈旧的刻板印象。)23
Mutual enmity very likely squelched the option. Turing said about his visit with Wilkes, “I couldn’t listen to a word he said.” He’d earlier criticized a Wilkes proposal as being “much more in the American tradition of solving one’s difficulties by means of much equipment rather than by thought.” (There’s that old stereotype, from Turing no less.)23
威尔克斯写道:“我发现图灵非常固执己见,并认为他的想法与计算机开发的主流方向大相径庭。” 24
And Wilkes wrote, “I found Turing very opinionated and considered that his ideas were wildly at variance with what the main stream of computer development was going to be.”24
两者在某种程度上都是对的。威尔克斯此时直接从洋基队的冯诺依曼那里获得灵感。像往常一样,图灵正在向他自己的鼓手进军——创造了一个很少有人采用的架构(为 Ace)。
Both were right in a way. Wilkes was taking his inspiration directly from the Yanks’ von Neumann by this time. And Turing, as usual, was marching to his own drummer—having created an architecture (for Ace) that few others adopted.
Edsac 的第一次哭泣是在 1949 年 5 月 6 日,比 Baby 晚了将近一年,就在 Mark I. Wilkes 故意选择双胞胎名字来命名冯诺依曼的 Edvac 之前,所以 Edsac 毫不掩饰地挥舞着星条旗上场。25
Edsac’s first cry was on May 6, 1949, almost a year after Baby and just before Mark I. Wilkes chose the twin name to von Neumann’s Edvac on purpose, so Edsac came onto the field unabashedly waving the Stars and Stripes.25
1999 年,我参加了在剑桥举行的“计算机 50 周年”活动,庆祝 Edsac 成为第一台计算机。听众中有一位来自施乐帕洛阿尔托研究中心的老熟人,威廉纽曼,马克斯纽曼的儿子。Baby 创建时,他们俩都住在曼彻斯特。不久之后,当数学家来到曼彻斯特时,年轻的威廉甚至和艾伦·图灵一起玩过棋盘游戏。威廉在威尔克斯声称 Edsac 优先权时转向我,并以他平静的方式说:“这与我们记忆中的不太一样。” 26
I attended the “50th anniversary of the computer” at Cambridge in 1999, which celebrated Edsac as the first computer. In the audience was an old acquaintance from Xerox Palo Alto Research Center, William Newman, son of Max Newman. Both of them had lived in Manchester when Baby was created. Young William had even played board games with Alan Turing when the mathematician came to Manchester soon afterwards. William turned to me during a Wilkes claim of Edsac priority and said in his quiet way, “That’s not quite the way we remember it.”26
在美国,冯诺依曼(和团队)创建了 Edvac 报告,并在此基础上设计了一台计算机。Edvac 计算机直到很久以后才真正运行,但这并不重要。它所基于的架构——冯诺依曼的——影响深远。有影响力的 1945 年 Edvac 报告广泛传播。即使在今天,这种架构也被广泛使用。令人惊讶的是,甚至连英国人的 Baby 和 Edsac 也使用了它。因此,可以公平地说,存储程序计算机和计算的想法来自图灵,但实际上的计算机——世界上一台有效的机器——起源于冯诺依曼。. . 需要注意的是,图灵和冯诺依曼彼此了解并理解对方的工作,并明确地给予了对方的信任。27
In America, von Neumann (and team) created the Edvac report, and designed a computer based on it. The Edvac computer didn’t actually run until much later, but it doesn’t matter. The architecture it was based on—von Neumann’s—was far-reaching. The influential 1945 Edvac report proliferated it widely. Even today that architecture is widely used. Surprisingly, even the Brits’ Baby and Edsac used it. So, it’s fair to say that the idea of the stored-program computer and computation comes from Turing but the computer as it actually is—an effective machine in the world—descends from von Neumann . . . with the caveat that Turing and von Neumann knew and understood each other’s work and explicitly gave each other credit.27
Edvac 至少有 16 个孩子的庞大后代(流程图中显示了 6 个)在许多地方发育。重要的是,它在 Princetitute 开始了 Maniac,von Neumann 担任软件负责人,Julian Bigelow 担任硬件负责人。Maniac 创立了 IBM 701,这是蓝色巨人的第一台商用计算机,它开启了这家巨头公司对计算机的统治。
Edvac’s large progeny of at least 16 children (6 shown in the flow chart) developed in many places. Importantly it begat Maniac at the Princetitute, with von Neumann as software lead and Julian Bigelow as hardware lead. Maniac begat IBM 701, Big Blue’s first commercial computer, which launched that giant corporation’s domination of computers.
好像疯子还不够开玩笑,埃德瓦克还生了约翰尼亚克——当然是以约翰尼·冯·诺依曼的名字命名的。这种乐趣让我们在电影Desk Set (1957)中获得了 Emerac,这台计算机与凯瑟琳赫本争夺斯宾塞·特蕾西的注意力和赫本的工作。甚至还有 DC Comics 的超人超级反派 Brainiac。尽管ac在早期的首字母缩略词中通常代表自动计算机,但它在 Maniac 中表示和计算机,在 Edsac 中表示自动计算器(以及在 Emerac 中表示算术计算器,没有抓住重点)。
As if Maniac weren’t joke enough, Edvac also begat Johnniac—named for Johnny von Neumann, of course. Such fun gave us Emerac in the film Desk Set (1957), the computer that vied with Katherine Hepburn for Spencer Tracy’s attention and Hepburn’s job. And even Brainiac, the Superman super-villain of DC Comics. Although ac usually stood for automatic computer in the early acronyms, it meant and computer in Maniac and automatic calculator in Edsac (and arithmetic calculator in Emerac, missing the point).
但命名的乐趣也让普林斯顿大学的塔楼与臭臭之战成为焦点,该学院已经获得了一个有点不体面的绰号来区分其官方自我,普林斯顿大学的普林斯顿高等研究院,也在普林斯顿。在 IAS 的塔楼纯粹主义者的听力范围内,没有人会听说过Maniac这个名字。那里的纯粹主义者称 Maniac为 IAS 机器,它仍然是它的正式名称,并且可以忘记。他们只会容忍工程师和他们的焊枪的存在,而不是他们幼稚的命名欢乐。(毫无疑问,王子学院会让他们不寒而栗。)只要他们留下,冯·诺依曼就是让王子学院臭气熏天的人。就在他 1957 年去世后——就在图灵离奇死亡三年后——这些恶臭被消除了,王子学院也有可能成为计算机科学研究的中心。28
But the naming fun also brought the tower versus stinks battle into focus at the Princetitute, already the recipient of a slightly undignified moniker to distinguish its official self, the Institute for Advanced Study in Princeton, from Princeton University, also in Princeton. No one within earshot of the tower purists at the IAS would have heard the name Maniac. The purists there called Maniac the IAS machine, which remains its formal, and forgettable, name. They would no sooner tolerate the presence of the engineers and their soldering guns than their puerile naming glee. (No doubt Princetitute would have made them shudder.) Von Neumann was all that kept the stinks at the Princetitute for as long as they stayed. Immediately after his death in 1957—just three years after Turing’s strange death—the stinks were banished and with them the possibility that the Princetitute would become the center of computer science research.28
冯诺依曼注意到,作为 Edvac 工作的结果,几乎是计算机的 Eniac 可以通过一些硬件修改变成真正的计算机。进行了修改,冯·诺依曼负责该项目的同事赫尔曼·戈德斯汀(Herman Goldstine)记录了 Eniac 的可编程版本(本书中称为 Eniac+)于 1948 年 9 月 16 日在马里兰州的阿伯丁试验场开始全面运行。Goldstine 的妻子 Adele 帮助对其进行了编程。它的小内存只能存储几十条指令,所以它像Baby一样小,但它是一台计算机。29
Von Neumann noticed, as a consequence of the Edvac work, that the almost-computer Eniac could be turned into a true computer with some hardware modifications. The modifications were made, and Herman Goldstine, von Neumann’s colleague in charge of the project, recorded that the programmable version of Eniac—dubbed Eniac+ in this book—began full operation on September 16, 1948, at the Aberdeen Proving Ground in Maryland. Goldstine’s wife, Adele, helped program it. It could only store a few dozen instructions in its tiny memory, so it was small like Baby, but it was a computer.29
Goldstine 的约会将使 Eniac+ 成为世界上第二台计算机。但新的证据有力地表明,与巴比的比赛更接近了。Eniac+ 诞生于 1948 年 4 月 6 日至 7 月 12 日之间的某个时间,具体取决于在任何给定时间执行了多少指令:换句话说,这是一个移动的目标——尽管在该间隔结束时日期会变硬,因为进一步的改进停止了。将最后一个日期作为保守估计,并扣除 Goldstine 的 9 月日期,得出 Eniac+ 的替代生日是 1948 年 7 月 12 日,距离 Baby 于 6 月 21 日出生不到一个月。30
Goldstine’s date would make Eniac+ the second computer in the world. But new evidence strongly suggests that the race with Baby was much closer. Eniac+ was born sometime between April 6 and July 12, 1948, depending on how many instructions were implemented at any given time: a moving target, in other words—although the date hardens at the end of that interval, when further improvements ceased. Taking the last date as a conservative estimate, and discounting Goldstine’s September date, yields an alternative birthdate for Eniac+ of July 12, 1948, less than a month after Baby’s birth on June 21.30
但在 1948 年 5 月 12 日写给约翰·冯·诺依曼的信中,斯坦尼斯劳·乌兰说:“我从尼克 [Metropolis] 的电话中得知,Eniac 的奇迹真的发生了,并且生产了 25,000 张卡片。(到现在还有更多?)这真的很棒,尤其是尼克说他们(卡片)似乎有道理。” 这是令人印象深刻的证据。1948 年 5 月 12 日,也就是 6 月 21 日婴儿出生前一个多月,氢弹的一位创造者对另一位说,Eniac+ 成功地计算了一个困难的氢弹模拟程序。无论您如何称呼这场比赛,Eniac+ 都是一项以前未被普遍认可的重大成就。31
But in a letter to John von Neumann dated May 12, 1948, Stanislau Ulam said, “I heard from Nick [Metropolis] on the telephone that the miracle of the Eniac really took place and that 25,000 cards were produced. (By now many more?) this is really wonderful, especially as Nick says that they (the cards) seem to make sense.” This is impressive evidence. It has one of the creators of the H-bomb stating to another that Eniac+ was successfully computing a difficult H-bomb simulation program on May 12, 1948, more than a month before the June 21 birth of Baby. Whichever way you call the race, Eniac+ was a significant achievement that hasn’t been generally recognized before.31
以奥运会的方式来看待英国人与洋基队的比赛——按奖牌数量计算——1948 年底的比分是 1 比 1(Baby,Eniac+)。到 1949 年中期,伯爵以 3 比 1 的比分青睐英国人(Edsac,Mark I)。但随后洋基队开始以这些引人注目的(但完全不包括在内)命中得分:哈里·赫斯基(Harry Huskey)——一名在双方都打球的自由球员工程师——在洛杉矶的国家标准局 (NBS) 建造了 Zephyr。它是 Edvac 的另一个孩子,它于 1950 年 8 月投入使用(并重新命名为 Swac)。1951 年 4 月,Jay Forrester 的旋风(Edvac 的另一个孩子)在麻省理工学院 (MIT) 上线。可以说,它的测试版本更早出现在 1949 年 8 月,Whirlwind–(“Whirlwind minus”)的名称是根据 Eniac+(“Eniac plus”)的精神创造的。1952 年,在王子学院的冯诺依曼团队凭借 Maniac 的奉献精神,洋基队再次得分,并在 1953 年凭借 IBM 701 再次得分。洋基队向前冲锋,从未回头。世界其他地方也加入了这场游戏。到 1953 年,大约十几个国家有 150 个计算机项目。32
To look at the Brits versus Yanks competition the Olympian way—by medal count—the score at the end of 1948 was 1 to 1 (Baby, Eniac+). By the middle of 1949, the count favored the Brits at 3 to 1 (Edsac, Mark I). But then the Yanks began to score with these notable (but not at all inclusive) hits: Harry Huskey—a free-agent engineer who played on both sides—built Zephyr at the National Bureau of Standards (NBS) in Los Angeles. Yet another child of Edvac, it was operational in August 1950 (and rechristened Swac). Then Jay Forrester’s Whirlwind, another child of Edvac, went online in April 1951 at the Massachusetts Institute of Technology (MIT). Arguably, a test version of it came earlier, in August 1949, with Whirlwind– (“Whirlwind minus”) its name coined in the spirit of Eniac+ (“Eniac plus”). The Yanks scored again in 1952 with the dedication of Maniac by the von Neumann team at the Princetitute, and in 1953 with IBM 701. The Yanks blasted ahead and never looked back. The rest of the world had joined in the game too. By 1953 there were 150 computer projects in about a dozen countries.32
电脑到了。在宏伟的计划中,它还不是很快。在 Epoch 2 中,这需要摩尔定律的指数级“速度”来处理。但对完整数字光的所有要求最终并有效地到位——傅里叶波、Kotelnikov 的样本和图灵的计算。
The computer had arrived. It wasn’t very speedy yet in the grand scheme of things. It would require the exponential “pace” of Moore’s Law to take care of that in Epoch 2. But all the requirements for full Digital Light were finally and effectively in place—Fourier’s waves, Kotelnikov’s samples, and Turing’s computations.
英国人也在与洋基队争夺快速存储设备。对于 Digital Light 来说幸运的是,两个团队都在寻找可见的真空管记忆。两者都将位存储为显示在二维网格上的不同大小的点。因此,每个位置自然既是一位扩展像素又是一位存储器。英国人通过改编普通阴极射线管——威廉姆斯管赢得了这场小规模冲突,然后是这场战斗。洋基队也立即采用了该解决方案。
The Brits vied with the Yanks in the race for a fast memory device too. Luckily for Digital Light, both teams looked for visible vacuum tube memories. Both would store bits as spots of different sizes displayed on a two-dimensional grid. Hence each location was naturally both a one-bit spread pixel and a one-bit memory. The Brits won this skirmish, and then the battle, with an adaptation of an ordinary cathode-ray tube—the Williams tube. The Yanks immediately adopted that solution too.
名片计算机,或任何通用的图灵机,都有无限的内存条。它可以存储无限数量的模式——可数或数字的无限类型。这对于理想的机器来说很好,但是物理计算机必须具有有限的内存。但是不要让有限这个词误导你。即使是第一台计算机也能记住大量的模式。
The business card computer, or any universal Turing machine, has an infinite tape for its memory. It can store an infinite number of patterns—of the countable, or digital, type of infinity. That’s fine for an ideal machine, but a physical computer has to have a finite memory. But don’t let that word finite mislead you. Even the first computer could remember an immense number of patterns.
实际数字如此之大,毫无意义。有趣的数字googol(一个 1 后面跟着一百个 0)是对即使是小婴儿所拥有的状态数量的粗略估计。(谷歌公司就是以这个数字命名的,但创始人拼错了。)更有趣的数字googolplex——一个 1 后跟一个 googol 0——是对即使是最大的现代计算机中的模式数量的严重高估。但是,介于 googol 和 googolplex 之间的那个范围可能会让您了解计算机中的可能模式。然后另一方面,经过更深入的思考,您可能会发现它只是介于两个非常大的数字之间的一个可笑的大数字。真正重要的一点是,计算机让我们这些微不足道的人类处理如此庞大的数量而无需考虑甚至不知道它们——而且从一开始就是这样。33
The actual number is so large that it’s meaningless. The funny number googol—a 1 followed by a hundred 0s—is a gross underestimate of the number of states that even little Baby had. (Google, the company, was named for the number, but the founders misspelled it.) The even funnier number googolplex—a 1 followed by a googol 0s—is a gross overestimate of the number of patterns in even the largest modern computer. But that range, between a googol and a googolplex, might give you a sense of the number of possible patterns in a computer. Then on the other hand, upon keener reflection, you might see that it’s just a ridiculously large number somewhere between two insanely large numbers. The truly important point is that the computer lets us puny humans deal with quantities of such vast size without thinking or even knowing about them—and it has from the very beginning.33
两个团队的创始工程师都必须选择一种可以存储所有这些状态的实用存储设备。在这两种情况下,他们都选择了电子管的某种变体——因为它的绝对速度。赢得这场比赛的英国人选择使用阴极射线管 CRT。在大数字融合之前,CRT 是一种熟悉的设备。我们用这本书庆祝伟大的数字融合,但它的一个后果是模拟电视的消亡。在那之前,CRT 是每个家庭每台电视机中的巨大玻璃瓶。瓶子扁平的一端是电视屏幕。在过去,电视被亲切地称为“电子管”。
The founding engineers on both teams had to choose a practical memory device that could store all those many states. In both cases they settled on some variation of an electronic tube—for the sheer speed of it. The Brits, who won this game, chose to work with a cathode-ray tube, a CRT. Before the Great Digital Convergence, the CRT was a familiar device. We celebrate the Great Digital Convergence with this book, but one consequence of it was the death of analog television. Until then, a CRT was the giant glass bottle in every TV set in every home. The flattened end of the bottle was the television screen. In those olden days, TV was affectionately called “the tube.”
然后工程师们不得不设计一种方法来通过管子移动比特,这是一种模拟设备的数字用途。众所周知,电流是电子的流动,而铜线为其提供了良好的通路。编织在我们每个家庭中的是一个铜线网络,将电流引导到所有这些墙上的插座。但是,电流也可以流过真空——不通过任何东西,这一点并不为人所知。
Then the engineers had to devise a way to move bits through the tube, a digital use of an analog device. It’s common knowledge that electric current is a flow of electrons, and that copper wire forms a good pathway for it. Woven through each of our homes is a network of copper wires guiding electric current to all those wall outlets. But it’s not so well known that electric current can also flow through a vacuum—through nothing.
这正是阴极射线管中发生的事情。电子“枪”是一块加热的金属,它发射电子并将电子从管子的薄端“射”到远、肥、平的一端。如果管中有空气,电子会与其分子碰撞,改变方向并失去能量。为了确保不会发生这样的交通堵塞,所有的空气都被抽出管子,使之成为现实。. . 一个真空管。高压推动电子从一端到另一端。我们将加热的金属片称为阴极,从枪中射出的电子电流称为阴极射线,整个封装称为阴极射线管。
That’s exactly what happens in a cathode-ray tube. The electron “gun” is a heated piece of metal that emits electrons and “shoots” them from the thin end of the tube to the far, fat, and flat end. If there was air in the tube, the electrons would collide with its molecules, change direction, and lose energy. To ensure no such traffic jam takes place, all the air is pumped out of the tube, making it . . . a vacuum tube. The high voltage propels the electrons from one end to the other. We call the heated piece of metal a cathode, the current of electrons shot from the gun a cathode ray, and the whole package a cathode-ray tube.
但是我们看不到电子。CRT 必须有其他东西可以将电子转化为光子——转化为可见光。那个东西是管子扁平端的涂层,当它被电子撞击时会发出磷光 - 发光。所谓的磷光体涂层从电子中吸收能量并发射光子。荧光粉在被电子枪射击时会发光。阴极射线的能量越高,发射的光子越多,辉光越亮。光芒在光线的中心最亮,并且随着远离中心的距离平滑地下降。它具有必要的形状,即是一个像样的像素散布器。
But we can’t see electrons. A CRT has to have something else that converts electrons to photons—to visible light. That something is a coating on the flat end of the tube that phosphoresces—emits light—when it’s struck by electrons. The coating of so-called phosphors absorbs energy from the electrons and emits photons. A phosphor glows when it’s shot by an electron gun. The higher the energy of the cathode ray, the more photons are emitted and the brighter the glow. The glow is brightest at the center of the ray and drops down smoothly with distance from the center. It has the necessary shape, that is, to be a decent pixel spreader.
它作为存储设备起作用的原因是,在阴极射线停止发送电子后,辉光会持续很短的时间。在那个时间间隔内(比如说五分之一秒),由辉光表示的位被“记住”。它可以使用直到它衰变。通过有条不紊地重绘或刷新,在它衰减之前(每秒五次),我们可以自动让记忆持续多久,只要我们愿意。我们人类用户只看到一个点显示在屏幕上并停留在那里。我有时会说一个点被写入屏幕或在屏幕上绘制,但两者的含义与显示在屏幕上的含义相同。
The reason this works as a memory device is that the glow persists for a short time after the cathode ray ceases to send electrons. During that interval (one-fifth of a second, say) the bit represented by the glow is “remembered.” It can be used until it decays. And by methodically repainting, or refreshing, the spot before it decays (five times per second, say), we can automatically make the memory last as long as we wish. We human users see only that a spot gets displayed on the screen and stays there. I will sometimes say that a spot gets written to the screen or painted on the screen, but both mean the same thing as displayed on it.
但是仅在屏幕中央的发光点很无聊。缺少的是一种在管表面的任何地方绘制光的方法。我们需要弯曲阴极射线,使其电子落在屏幕上任何我们想要发光的地方,而不仅仅是中心。对于 Digital Light,我们需要能够绘制散布像素阵列。
But a glowing spot only at the center of the screen is boring. What’s missing is a way of painting light anywhere on the face of the tube. We need to bend the cathode ray so that its electrons land on the screen anywhere we want a glow, not just the center. For Digital Light we need to be able to paint an array of spread pixels.
幸运的是,移动电子的一个重要特性是它的路径会在它通过磁场时弯曲。就像光线通过玻璃透镜时会发生弯曲一样,阴极射线在通过磁铁的两极之间时也会发生弯曲。安装在阴极射线管电子枪附近的磁铁起到了作用。一个磁体使光线左右偏转,另一个磁体上下偏转。两者的结合可以将阴极射线弯曲到任何所需的位置——而且做得很快。通常使用电场代替磁场,但这是相同的想法。
Luckily, an important property of a moving electron is that its path will bend as it passes through a magnetic field. Just as a light ray bends when it passes through a glass lens, a cathode ray bends when it passes between the poles of a magnet. Magnets mounted near the electron gun of a cathode-ray tube do the trick. One magnet does the left-right deflection of the ray, and another the up-down. Combinations of the two can bend the cathode ray to any desired position—and do it fast. Electric fields are often used instead of magnetic fields, but it’s the same idea.
使用瞄准装置,无论是电动的还是磁性的,您都可以在管的表面上涂抹阴极射线,或者您可以画出漂亮的规则图案。在涂鸦模式下使用的阴极射线管——在任何你想写的地方,在任何方向——是一个书法显示器,来自希腊语,意思是漂亮的笔迹。阴极射线像您书写脚本一样绘制脚本S (图 4.8,左)。射线的强度一直很高。它也通过沿曲线滴落点来以书法方式绘制正确的S(图 4.8 中) ——特别是不在规则间隔的网格点上。在这种情况下,斑点不是散布像素。它们只是点,它们可以有各种形状和可变间距。采样定理没有说明它们。因为它没有,书法展示——尽管它们很优雅——并没有进入新的千年。
With the aiming mechanism, whether electric or magnetic, you can scribble the cathode ray over the face of the tube, or you can paint out a nice regular pattern. A cathode-ray tube used in scribble mode—write anywhere you wish, and in any direction—is a calligraphic display, from the Greek for beautiful handwriting. The cathode ray paints the script S (figure 4.8, left) just as you would write it. The intensity of the ray is constantly high. It paints the right S (in figure 4.8) calligraphically too, by dropping spots along the curve—and specifically not on regularly spaced grid points. The spots in this case aren’t spread pixels. They’re just spots, and they could have various shapes and variable spacings. The Sampling Theorem says nothing about them. And because it doesn’t, calligraphic displays—despite their grace—didn’t make it into the new millennium.
另一种显示器的工作原理是这样的:阴极射线有条不紊地绘制出一个矩形图——从左到右一排接着一排,从上到下,就像耕种田地一样。它被称为光栅显示,来自拉丁语rake。在图 4.9 中,光线以光栅顺序在左侧绘制S ,但沿着每一行平滑。老式模拟电视——“电子管”——使用了这种方法。但同样,没有涉及像素,所以这种方法也没有进入新的千年。但是对其进行了修改:光线只能在每个光栅行的规则网格位置上绘制。射线描绘了S在图 4.9 的右侧,带有特定形状的点和网格上的固定位置。实际上,它们是采样定理所要求的扩展像素。
Another kind of display works like this: the cathode ray methodically paints out a rectangular plot—one left-to-right row after another, top to bottom, like tilling a field. It’s called a raster display, from Latin for rake. In figure 4.9, the ray paints the S on the left in raster order, but smoothly along each row. Old analog television—“the tube”—used this method. But again, there were no pixels involved so this method also didn’t make it into the new millennium. But a modification of it did: The ray could only paint at regular grid locations along each raster row. The ray paints the S on the right in figure 4.9 with spots of specific shape and fixed locations on a grid. They are, in fact, spread pixels, as demanded by the Sampling Theorem.
图 4.8
Figure 4.8
图 4.9
Figure 4.9
书法与光栅的区别在早期的数码光中是一个很大的区别。你可以看到为什么。书法展示是诱人的优雅。但是尽管他们很优雅,但他们并没有使用像素的概念,这是未来的关键。媒体类型到一种位媒体的大数字融合也迫使显示类型融合到仅基于像素的一种媒体——光栅阵列或网格。从图片(右上方)中看不出这应该有效,但您正在阅读的文本就是它的一个例子。采样定理使具有散布像素的光栅显示与具有平滑笔触的书法显示一样美观。
The calligraphic versus raster distinction was a big one in early Digital Light. You can see why. The calligraphic displays are seductively graceful. But despite their grace, they didn’t use the concept of the pixel, which was key to the future. The Great Digital Convergence of media types into the one medium of bits also forced the convergence of display types into just the one based on pixels—the raster array or grid. It’s not at all obvious from the picture (above right) that this should work, but the text you’re reading is an example of how well it does. The Sampling Theorem made raster displays with spread pixels as beautiful as calligraphic display with smooth strokes.
值得记住的是,所有现代显示器本质上都是模拟的。尽管由数字和断开连接的像素驱动,但我们看到的是平滑和连续的。显示的行为是使分离的像素作为连续的光和颜色场可见的原因。正如我们在第 2 章的采样中看到的那样,在显示的时刻分散像素可以恢复这些像素所代表的原始视觉场景。
It’s worth remembering that all modern displays are intrinsically analog. What we see is smooth and continuous, despite being driven by digital and disconnected pixels. The act of display is what makes the separated pixels visible as a continuous field of light and color. As we saw in chapter 2 on sampling, spreading the pixels at the moment of display restores the original visual scene that those pixels represent.
现代数字世界的假设是,总会有一个光栅显示器可以让我们的像素可见。我们用户永远不需要知道实际显示设备的令人讨厌的细节。我们在这里关注这些细节的唯一原因是因为最初的展示是最初的记忆。
The enabling assumption of the modern digital world is that there’ll always be a raster display available to make our pixels visible. We users never need be aware of the nasty details of the actual display devices. The only reason we pay attention to those details here is because the first displays were the first memories.
英国人用威廉姆斯或威廉姆斯-基尔本管赢得了记忆竞赛。但严格来说,Williams 和 Kilburn 并没有发明一种新的管子。他们发明了一种使用标准阴极射线管的技术。他们的计算机内存是使用 Williams-Kilburn 技术进行位存储的 CRT。它存储了一个小点 (0) 或一个较大的点 (1),可以在管的表面上看到,用阴极射线画在那里(并用发光的荧光粉使其可见)。射线将以光栅或倾斜方式从左到右和从上到下扫描管的屏幕。这些比特位于光栅每一行的规则间隔位置——耕地中的种子。
The Brits won the memory race with the Williams, or Williams-Kilburn, tube. But strictly speaking, Williams and Kilburn didn’t invent a new kind of tube. They invented a technique for using a standard cathode-ray tube. Their computer memory was a CRT that used the Williams-Kilburn technique for bit storage. It stored a bit as a small spot (0) or a larger one (1) that could be seen on the face of the tube, painted there by a cathode ray (and made visible with glowing phosphors). The ray would scan the screen of the tube in raster, or raked, fashion, left to right and top to bottom. The bits were located at regularly spaced locations along each row of the raster—seeds in a tilled field.
洋基队并没有闲着。起初,冯诺依曼的团队并没有意识到威廉姆斯和基尔伯恩,而是赞助了一次认真的尝试来建造第一个记忆管。他们把希望寄托在 Selectron 上,这是一种由美国无线电公司的一个部门设计和交付的电子管。Vladimir Zworykin 是该部门的负责人,Jan Rajchman 是他的首席设计师和工程师。我们在第 3 章遇到了 Zworykin。他参加了与 von Neumann 的决定性会议,编程成为了一个词。事实上,会议是在 RCA 的 Zworykin 办公室举行的,Rajchman 也在场。Zworykin 在 1920 年代和 1930 年代的电视发明中已经发挥了重要作用。
The Yanks weren’t idle. Unaware of Williams and Kilburn at first, von Neumann’s team sponsored a serious attempt at building the first memory tube. They pinned their hopes on Selectron, a tube to be designed and delivered by a division of the Radio Corporation of America. Vladimir Zworykin headed the division, with Jan Rajchman his chief designer and engineer. We met Zworykin in chapter 3. He attended the fateful meeting with von Neumann where programming became a word. In fact, the meeting took place in Zworykin’s office at RCA, and Rajchman was there too. Zworykin had already played a major role in the 1920s and 1930s in the invention of television.
Zworykin 的小组设计 Selectron 以将位存储为点 (1) 或不存在点 (0)。并且这些位可以被视为通过点(或不是点)的光栅阵列管子的透明玻璃。但 Selectron 比普通的阴极射线管复杂得多。它的发展花了很长时间——致命的长。34
Zworykin’s group designed Selectron to store a bit as a spot (1) or the absence of a spot (0). And the bits could be seen as a raster array of spots (or not spots) through the clear glass of the tube. But Selectron was much more complex than an ordinary cathode-ray tube. Its development took a long time—fatally long.34
大西洋两岸的早期计算机计划使用可见的记忆,这是一个令人高兴的巧合。不必如此。位不必可见才能用作内存——大多数现代位都不是。值得注意的是,图灵的 Pilot Ace 具有不可见的记忆,即水银延迟线,其中 1 是声脉冲,就像声波一样,它相对缓慢地穿过装满水银的管道。它在旅行时被“记住”。在延迟线中,0 表示没有脉冲。延迟线中的脉冲序列通过管道循环。从管道末端出来的东西会自动重新引入到它的开头,使管道中的位记忆持续到需要的时间。今天计算机的庞大内存中的比特也是不可见的。它们深埋在硅芯片内部。
It’s a pleasing coincidence that early computers on both sides of the Atlantic planned to use memories that were visible. That didn’t have to be the case. A bit doesn’t have to be visible to work as memory—most modern bits aren’t. Notably, Turing’s Pilot Ace featured an invisible memory, a mercury delay line in which a 1 was an acoustic pulse, as in a sound wave, that traveled relatively slowly through a pipe filled with mercury. It was “remembered” while it traveled. In the delay line a 0 was no pulse. The sequence of pulses in a delay line recycled through the pipe. What came out of the end of the pipe was reintroduced automatically to its beginning, making the memory of the bits in the pipe last as long as they were needed. The bits in the vast memories of today’s computers are also invisible. They’re buried deep inside silicon chips. The fact that bits were sometimes visible and arranged in rectangular arrays in the first days of computers gave Digital Light an early launch.
威廉姆斯管是如此重要的一步,以至于两支球队最终都同意了。在 Baby 出生后的一个月内,Maniac 的主要硬件工程师 Yank Julian Bigelow 在曼彻斯特拜访了 Max Newman,并看到了 Williams 管的运行情况。冯·诺依曼团队长期支持 Zworykin 的 Selectron。但是,一旦毕格罗了解在阴极射线管上存储和读取数据是多么简单,他们就跳下 Zworykin 的船,完全使用威廉姆斯管。他们将其中的 40 个用于 Maniac 的主存储器。在 Yanks 方面,几乎所有 Edvac 报告的第一代后代都采用了威廉姆斯管,包括重要的 IBM 701,这是蓝色巨人计算机王朝的第一台。
The Williams tube was such an important step that both teams eventually went with it. Within one month of Baby’s birth, the Yank Julian Bigelow, Maniac’s main hardware engineer, visited Max Newman in Manchester and saw the Williams tube in action. The von Neumann team had held out for Zworykin’s Selectron for a long time. But once Bigelow understood how simple it really was to store and read a bit on a cathode-ray tube, they jumped Zworykin’s ship and went completely with Williams tubes. They used 40 of them for Maniac’s main memory. On the Yanks side, nearly all the first-generation progeny of the Edvac report adopted the Williams tube, including importantly, IBM 701, the first in Big Blue’s computer dynasty.
美国的 IBM(以冯诺依曼为顾问)刚刚涉足计算机世界,威廉姆斯管赢得了内存竞赛。Thomas J. Watson 准备接任公司董事长一职。他创造了著名的口号“THINK”,该口号现在在整个 IBM 中无处不在。1949 年 7 月,公司出于对 Baby 及其孩子 Mark I 的担忧,邀请威廉姆斯前往其纽约总部。他们问他,“两人和一条狗”组成的团队如何在曼彻斯特制造出比他们,强大的 IBM,所做的一切。威廉姆斯以他严肃的方式回答——可以想象他眼中闪烁的光芒:“嗯,我们有一个存储的想法,然后不顾一切地在那个商店周围建造了一台电脑,没有停下来想太多。” 聚集在一起的 IBM 人员倒吸一口凉气,
America’s IBM (with von Neumann as a consultant) was just getting its feet wet in the computer world as the Williams tube won the memory race. Thomas J. Watson was poised to assume the company’s chairmanship. He’d famously created the slogan “THINK” that was now pervasive throughout IBM. Concerned about Baby and its child Mark I, the company invited Williams to its New York headquarters in July 1949. They asked him how it was that a team of “two men and a dog” had managed to build a machine in Manchester more advanced than anything they, the mighty IBM, had done. Williams replied in his no-nonsense manner—one can imagine a twinkle in his eye: “Well, we had an idea for storage and then pressed on regardless and built a computer around that store without stopping to think too much.” The assembled IBM personnel gasped, then shrieked with hysterical laughter when they realized that Watson wasn’t in the room.
威廉姆斯讲述的故事是准确的。计算机相当简单——尤其是一台名为 Baby 的小型计算机。简单的威廉姆斯管已经超越了复杂的 Selectron。在这种情况下,英国人的大脑击败了扬克的肌肉。35
The story Williams told was accurate. Computers are rather simple—especially a small computer called Baby. And the simple Williams tube had outraced the complex Selectron. Brit brains had beat out Yank brawn in this case.35
使用威廉姆斯管内存的计算机上的实际显示不是威廉姆斯管本身。它本来可以——几乎没有。威廉姆斯管屏幕上的比特是来自电子枪的电荷,通过荧光粉可见。但是工作的威廉姆斯管需要一个“集电极板”覆盖屏幕。集电极板关闭电子电路中的电路,以便电荷(导致荧光粉发光的电荷)可以被电子电路检测并用于下一次计算。我们说电路读取隐形电荷的存在和数量。电路读取电荷但看不到荧光粉。我们人类读取发光的荧光粉,但看不到相应的电荷。
The actual display on a computer that used a Williams tube memory was not the Williams tube itself. It could’ve been—barely. The bits on a Williams tube screen are electric charges from the electron gun made visible with phosphors. But a working Williams tube requires that a “collector plate” cover the screen. The collector plate closes a circuit in the electronics so that the charge—the one that causes the phosphors to glow—can be detected by an electronic circuit and used in the next computation. We say that the circuit reads the presence and quantity of the invisible charge. The circuit reads the charge but can’t see the phosphors. We humans read the glowing phosphors but can’t see the corresponding charge.
Baby 主记忆管上的集电板由纱布或细金属丝网制成,因此您实际上可以通过它看到碎片——几乎看不到。没关系,因为珍贵的威廉姆斯管被隐藏起来,以保护它免受杂散电荷的影响——比如一辆路过的摩托车——这可能会破坏它。对工程师来说,集电板上不可见的电荷比屏幕上发光的荧光粉更重要。36
The collector plate on Baby’s main memory tube was made of gauze, or a fine wire mesh, so you could actually see the bits through it—barely. It doesn’t matter because the precious Williams tube was hidden away to protect it from stray electric charges—from a passing motorcycle say—that could corrupt it. The invisible electric charge on the collector plate was more important to the engineers than the glowing phosphors on the screen.36
另一个阴极射线管显示了存储在隐藏的威廉姆斯管表面上的比特。这很容易。每次读取一排威廉姆斯管时(例如每秒五次),它都会直接复制到显示管的相应行。显像管不是记忆,只是记忆中发光的、隐藏的屏幕的精确可见副本。由于它仅用于显示,而不是计算,因此不必保护它免受经过的摩托车的影响。我们用这样的显示器来观察或监视一段记忆,我们称之为监视器。
Another cathode-ray tube displayed the bits that were stored on the face of the hidden Williams tube. This was easy. Every time a row of the Williams tube was read (say, five times per second) it was directly copied to the corresponding row of the display tube. The display tube wasn’t a memory, just an exact visible copy of the glowing, hidden screen of the memory. Since it was for display only, not computation, it didn’t have to be protected from passing motorcycles. We use such a display to observe, or monitor, a memory, and we call it a monitor.
严格来说,第一个比特是第一个扩展的像素,但工程师将它们隐藏在电子保护罩下。散布的像素在那里但看不见——众所周知的树木在森林中倒下时闻所未闻。它们实际上只有在显示器上显示时才对人类可见。
Strictly speaking, the first bits were the first spread pixels, but the engineers hid them under electrically protective cover. The spread pixels were there but unseen—the proverbial trees falling unheard in a forest. They really only became visible to humans when they were displayed on the monitor.
威尔克斯在剑桥的 Edsac 是威廉姆斯管广泛胜利的一个显着例外。事实上,它根本没有使用可见内存——甚至是潜在可见的。与图灵的 Pilot Ace 一样,它使用了水银延迟线。
Wilkes’s Edsac at Cambridge was a notable exception to the broad Williams tube victory. In fact, it didn’t use a visible memory at all—not even potentially visible. Like Turing’s Pilot Ace, it used mercury delay lines.
但 Edsac 的工程师想看看汞延迟线中有什么,因此他们还设计了一个监视器。一个电子电路将通过延迟线的脉冲序列转换成一组绘制在阴极射线管屏幕上的点。电子设备将脉冲串放入延迟线中,并将它们折叠成多排点——从一排长排(512 位)到一个由较短排(每排 32 位)组成的矩形。然后,它以通常的阴极射线管方式(以光栅阵列形式)简单地在监视器屏幕上绘制斑点。这台显示器使英国剑桥的英国人 Edsac 成为 Digital Light 竞赛中的另一个参与者。请注意,监视器可以就像一排长长的灯一样,而不是二维数组。显示器技术导致光栅显示是一个令人愉快的意外。
But Edsac engineers wanted to see what was in the mercury delay lines, so they also devised a monitor. An electronic circuit converted the train of pulses proceeding through a delay line into a set of spots painted on a cathode-ray tube screen. The electronics took the string of pulses in a delay line and folded them into rows of spots—from one long row (512 bits) to a tilled rectangle of shorter rows (32 bits each). It then simply painted the spots on the monitor screen in the usual cathode-ray tube manner—in a raster array. This monitor made the Brits’ Edsac in England’s Cambridge another player in the race to Digital Light. Notice that the monitor could just as well have been a single long row of lights, not a two-dimensional array. It was a pleasant accident that the technology of monitors led to the raster display.
美国剑桥麻省理工学院的 Yanks' Whirlwind 是威廉姆斯管闪电战的另一个值得注意的例外。Jay Forrester 的团队改进了威廉姆斯管的想法,以满足旋风的更高速度要求。他们创造了一种竞争性存储器,但仍将比特存储在阴极射线管上,就像威廉姆斯管一样。然而,他们似乎从未打算将记忆管用于图片显示。37
The Yanks’ Whirlwind, at MIT in America’s Cambridge, was another notable exception to the Williams tube blitz. Jay Forrester’s team there improved on the Williams tube idea to meet the higher speed demands of Whirlwind. They created a competing memory that nevertheless stored bits on a cathode-ray tube, like a Williams tube. It seems, however, that they never intended to use the memory tubes for picture display.37
因为完善这种类似威廉姆斯的“静电存储器”需要很长时间,Forrester 和他的团队使用他们所谓的“测试存储”来存储 Whirlwind 的存储设备。其中大部分是拨动开关!人类“编写”了拨动开关。Whirlwind 可以读取它们但不能写入它们——用计算机术语来说是只读存储器。该团队设计了一个特殊的监视器来显示测试存储的内容。38
Because it took a long time to perfect this Williams-like “electrostatic memory,” Forrester and his team used what they called “test storage” for Whirlwind’s memory device. Most of it was toggle switches! Humans “wrote” the toggle switches. Whirlwind could read them but not write them—a read-only memory, in computer jargon. The team devised a special monitor to display the contents of the test storage.38
虽然不太像一台完整的计算机,而且编程繁琐,但 Whirlwind 的测试配置在 1949 年 8 月 19 日首次成功使用。我将测试配置称为 Whirlwind——(“Whirlwind 减号”),因为它比Whirlwind,它应该是一个完整的存储程序计算机。将其分开是不寻常的,但在 Digital Light 的历史上这样做很重要。
Although shy of being a full computer, and tedious to program, the test configuration of Whirlwind was first used successfully on August 19, 1949. I’ll call the test configuration Whirlwind– (“Whirlwind minus”), because it was less than the intended Whirlwind, which was supposed to be a full stored-program computer. It’s unusual to break it out separately but important to do so in the history of Digital Light.
在我的探索中,我发现了一个宝库——旋风摄影档案。它们不在麻省理工学院,我希望在那里找到它们,而是在贝德福德附近的秘密 MITRE 公司。2016 年 10 月 11 日,公司档案管理员 Krista Ferrante 迎来了我,这是我在研究这本书时度过的最激动人心、最有意义的日子之一。她为我准备了一辆装满了精心编目照片的手推车。他们有很多。早期的 Whirlwind 用户根本没有为拍照而道歉。克里斯塔和我愉快地整理了几个小时,我能够从中挑选出突破。
At this point in my quest, I discovered a treasure trove—the Whirlwind photographic archives. They weren’t located at MIT, where I expected to find them, but at the secretive MITRE Corporation in nearby Bedford. Krista Ferrante, a company archivist, welcomed me on October 11, 2016, to one of the most exciting and rewarding days I spent while researching this book. She’d prepared for me a cart filled with boxes of carefully catalogued photographs. There were lots of them. The early Whirlwind users hadn’t apologized at all about making pictures. Krista and I sorted through them delightedly for hours, and I was able to pick out the breakthroughs among them.
这是一个鲜为人知的例子(图 4.10),可能是 Whirlwind 项目的第一张数字图片。它是在 1949 年 6 月创建的,可能是手动切换的,因为即使是旋风——几乎是旋风,还没有准备好编程。缩写代表旋风一号,这是计算机的全称,于 1951 年 4 月正式宣布完成。
Here’s an unheralded example (figure 4.10), perhaps the first digital picture from the Whirlwind project. It was created in June 1949, with hand toggling probably, since even Whirlwind–, the almost Whirlwind, wasn’t quite ready to program. The initials stand for Whirlwind I, the full official name of the computer-to-be, which was declared officially complete in April 1951.
图 4.10
Figure 4.10
为了确定哪个内存位置与显示屏上的某个点相对应,麻省理工学院的工程师 Bob Everett 发明了一种“光枪”,它可以与显示屏交互并导致某个点关闭。它正在擦除(图 4.11)选定的点或散布像素,以制作稍晚一点的数码照片,这张照片的日期为 1952 年 4 月。这是 Yank 与数码照片的早期互动,但不像英国人那样早,我们将很快就会看到。39
To determine which memory location corresponded with a spot on the display, an MIT engineer, Bob Everett, invented a “light gun” that could interact with the display and cause a spot to turn off. It’s erasing (figure 4.11) selected spots, or spread pixels, to make a slightly later digital picture, this photo dated April 1952. It was an early Yank interaction with a digital picture, but not as early as the Brits, as we’ll see shortly.39
1949 年 9 月,Whirlwind– 添加了“特别展示”。它也是一个阴极射线管。这台示波器,正如他们所说的(借用电子工程师工具的名称),可以在其二维屏幕上的任何点绘制一个点。它不限于栅格网格位置。这些斑点写在管子的表面上,但旋风——无法阅读它们。也就是说,它们不是它的记忆的一部分。它们也不是它记忆碎片的图像。示波器不是像 Baby 或 Edsac 那样的显示器。它纯粹是一种图形显示设备——这是计算机上的第一个设备。图形显示设备上的每个图像都是有意的二维图片。
In September 1949 a “Special Display” was added to Whirlwind–. It was a cathode-ray tube too. This oscilloscope, as they called it (borrowing the name from an electronic engineer’s tool), could paint a spot at any point on its two-dimensional screen. It wasn’t restricted to raster grid locations. The spots were written on the face of a tube, but Whirlwind– couldn’t read them. That is, they weren’t part of its memory. And they weren’t an image of its memory’s bits either. The oscilloscope wasn’t a monitor like Baby’s or Edsac’s. It was purely a graphic display device—the first on a computer. Every image on a graphic display device is an intentional two-dimensional picture.
图 4.11
Figure 4.11
这是数字光的一个重大发展。它允许您从存储在计算机内存中的不可见描述或模型创建图片。这就是我们所说的计算机图形学。
This was a significant development in Digital Light. It allowed you to create a picture from an invisible description, or model, that was stored in a computer memory. This is what we mean by computer graphics.
由 Charlie Adams 领导的 Whirlwind 程序员于 1949 年底开始使用存储在大多数拨动开关的测试存储器中的程序来制作图片。图 4.12 是 1950 年 5 月 18 日制作的抛物线和带轴的四次曲线,是 Whirlwind– 早期图片的典型代表。这些图片中的每一张的模型都以数学方程的形式存储。40
Whirlwind– programmers, led by Charlie Adams, started to make pictures in late 1949 with programs stored in the test memory of mostly toggle switches. Figure 4.12, of a parabola and a quartic curve with axes, was made on May 18, 1950, and is typical of early pictures on Whirlwind–. The model for each of these pictures was stored in the form of a mathematical equation.40
大多数旋风 - 图片都是二维的。但是图 4.13 显示了两张描绘三维表面的图片,可能是第一次,1950 年 3 月 6 日。他们简要介绍了即将到来的照片,但值得注意的是,它们不是透视图。这一根本性的进步是十多年后的事,等待着它的布鲁内莱斯基。
Most of the Whirlwind– pictures were two-dimensional. But figure 4.13 shows two pictures depicting three-dimensional surfaces, probably for the first time, made on March 6, 1950. They give a brief glimpse of pictures to come, but it’s worth noting that they aren’t in perspective. That fundamental advance was over a decade away, awaiting its Brunelleschi.
图 4.12
Figure 4.12
图 4.13
Figure 4.13
图 4.14
Figure 4.14
图片由计算机历史博物馆提供。
Image courtesy of the Computer History Museum.
示波器是一种书法设备。它可以在屏幕上的任何点上绘制一个点,来自任何方向和任意间距,而不仅仅是沿着水平线的规则间隔的采样位置。这只是另一种说法,这些斑点既不是比特也不是散布像素。因此开始了数字光的书法与光栅分裂。计算机图形学的主线——Digital Light 的一个主要部门——将在大约十年后从这个书法分支发展而来。它将被千禧年的光栅分支和大数字融合所包含。41
The oscilloscope was a calligraphic device. It could paint a spot at any point on the screen, coming from any direction and with arbitrary spacing, not just at regularly spaced sampling locations along horizontal lines. That’s just another way of saying that these spots were neither bits nor spread pixels. Thus began the calligraphic versus raster split of Digital Light. The main line of computer graphics—a major division of Digital Light—would proceed from this calligraphic branch about a decade later. It would be subsumed by the raster branch at the millennium and the Great Digital Convergence.41
Harry Huskey 打算将图 4.14 中的数字图像作为图片。它来自另一台带有威廉姆斯管内存的计算机,但这是扬克斯的机器。它的工程师 Huskey 并不容易被认定为 Yank 或 Brit,因为他首先在美国从事 Eniac 工作,然后在英国从事 Turing 的 Pilot Ace 工作。然后他回到美国,按照冯·诺依曼的 Edvac 的模型,制造了一台他称之为 Zephyr 的机器——正如这里所宣传的那样。
Harry Huskey intended the digital image in figure 4.14 to be a picture. It’s from another computer with a Williams tube memory, but this one was a Yanks’ machine. Huskey, its engineer, isn’t easily pinned down as Yank or Brit because he first worked on Eniac in America, then on Turing’s Pilot Ace in England. Then he returned to America and built a machine that he called Zephyr—as advertised here—modeled on von Neumann’s Edvac.
我在 2013 年遇到了 Huskey 博士,当时他在加利福尼亚州山景城的计算机历史博物馆担任研究员。他已经 97 岁了。他回忆说,那是 1948 年末,他使用与 Kilburn 相同的技术手动将这张图像的位切换到威廉姆斯管存储器中。制作了第三张数码照片在 Zephyr 开发的早期。该计算机于 1950 年 8 月更名为 Swac 并专用。42
I met Dr. Huskey in 2013 when he was installed as a Fellow at the Computer History Museum in Mountain View, California. He was 97 years old. He recalled that it was late 1948 when he manually toggled the bits for this image into a Williams tube memory, using the same technique as Kilburn. This third digital picture was made early in the development of Zephyr. The computer was renamed Swac and dedicated in August 1950.42
图 4.15
Figure 4.15
洋基队在 1948 年的 Selectron 努力未能及时成功地成为冯诺依曼的疯子的记忆。但它仍然是早期数字光的参与者,因为一个不知名的人用手将图片(图 4.15)切换到 Selectron。它显示了 RCA 的首字母缩写,后面跟着一行四个点,代表 RCA 实验室,Zworykin 和 Rajchman 在那里开发了 Selectron。Rajchman 在这项工作中特别重要,所以他可能创造了这幅画。
The Yanks’ Selectron effort in 1948 didn’t succeed in time to serve as the memory for von Neumann’s Maniac. But it’s still a player in early Digital Light because an unknown person toggled a picture (figure 4.15) into Selectron by hand. It shows the initials RCA, followed by a line of four dots, for RCA Laboratories, where Zworykin and Rajchman developed Selectron. Rajchman was particularly important in the effort, so he might have created the picture.
1946 年,Eniac 和 Edvac 团队成员 J. Presper Eckert 又为 Yank 努力实现了可见记忆。他和他的团队试图将比特存储在阴极射线管上,并且成功了,但他们未能将这些位保持足够长的时间来构成一个严肃的记忆。埃克特的努力是美国佬与英国人争夺第一个电子存储器的又一次小冲突,而美国佬又输了。43
J. Presper Eckert, an Eniac and Edvac team member, made another Yank effort toward a visible memory in 1946. He and his team tried to store bits on a cathode-ray tube, and succeeded, but they failed to maintain the bits long enough to constitute a serious memory. The Eckert effort was yet another skirmish in the Yanks versus Brits battle for the first electronic memory, and the Yanks lost again.43
图 4.16
Figure 4.16
尽管 Eckert 未能为自己的设计建立一个可见的记忆,但他在得知 Williams 和 Kilburn 的结果后立即开始工作。Eckert 小组中的工程师 Herman Lukoff 按下按钮,将他的首字母“HL”输入到内存中,以进行耐力测试。Lukoff 在 1948 年 12 月至 1949 年 3 月之间的某个时间创作了这张照片,尽管我们没有它的照片。然而,这种内存从未在计算机中使用过。44
Although Eckert failed to build a visible memory of his own design, he got one working as soon as he learned of the Williams and Kilburn result. Herman Lukoff, an engineer in Eckert’s group, pushed buttons to enter his initials “H L” into the memory for an endurance test. Lukoff created this picture sometime between December 1948 and March 1949, although we have no photo of it. This memory, however, was never used in a computer.44
图灵 1951 年 3 月的 Ferranti Mark I 编程手册包含图 4.16 左侧所示的照片。Kilburn 在 1951 年 12 月举行的一次计算机会议上展示了它。这张照片的右半部分(带有台阶)可能是在程序控制下创建的数字图片,但它很粗糙,没有说服力。它的左半部分是偶然的废话,显示了内存位的状态,但没有二维连贯性,绝对不是数字图片。
Turing’s March 1951 programming manual for the Ferranti Mark I contains the photo shown on the left in figure 4.16. Kilburn presented it at a computer conference held in December 1951. The right half of this photo (with the stairsteps) is perhaps a digital picture created under program control, but it is crude and unconvincing. Its left half is incidental nonsense showing the state of memory bits but has no two-dimensional coherence and is definitely not a digital picture.
同一次会议的参与者还看到了 Whirlwind 的早期书法图片,如图 4.16 中的右侧照片所示。这张照片肯定是由程序生成的。这是会议记录中仅有的两张数字图像。他们公开宣布,实际上,书法与光栅分割已经开始。旋风图片至少可以作为计算机图形的示例,因为存储的计算机程序使用内部模型来驱动显示器(无论是书法还是光栅)。在这种情况下,模型是一个七阶多项式的数学方程——简洁、抽象、不可见。这张照片提供了进一步的证据,证明旋风团队在 1950 年代初开始拍照。45
Participants at the same conference were also treated to an early calligraphic picture from Whirlwind, as seen in the righthand photo in figure 4.16. This picture was definitely generated from a program. These were the only two digital images in the proceedings of the conference. They publicly announced, in effect, that the calligraphic versus raster split had begun. The Whirlwind picture, at least, qualifies as an example of computer graphics because a stored computer program used an internal model to drive a display (whether calligraphic or raster). The model in this case was the mathematical equation of a seventh-order polynomial—succinct, abstract, invisible. The photo provides further evidence that the Whirlwind team in the early 1950s was starting to make pictures.45
图 4.17
Figure 4.17
这两张图片的合成(图 4.17)及其标题来自 1952 年 12 月的 Ferranti Mark I 营销手册。标题清楚地表明,图片的商业潜力终于在这家早期制造商身上显现出来。图片毕竟是认真的。我们知道复选标记图片是程序生成的,因为最初曼彻斯特队的一员戴爱德华兹告诉我们。它可能是 1938 年从柏林到曼彻斯特的犹太移民迪特里希·普林茨(Dietrich Prinz)在紧要关头编写的。46
This composite of two images (figure 4.17), as well as its caption, comes from a December 1952 marketing brochure for the Ferranti Mark I. As the caption makes clear, the business potential of pictures was finally dawning on this early manufacturer. Pictures were serious after all. We know that the checkmarks picture was program-generated, because Dai Edwards, part of the original Manchester team, told us so. It was probably programmed by Dietrich Prinz, a Jewish immigrant from Berlin to Manchester in 1938, just in the nick of time.46
自从计算机出现以来,游戏就一直伴随着我们。更一般地说,交互性已经伴随我们很久了。令人惊讶的是,自 Digital Light 出现以来,游戏就推动了计算机的创新,而且自从我们第一次遇到最复杂的机器以来,我们一直坚持与它们进行交互。
Games have been with us since the beginning of computers. More generally, interactivity has been with us that long. It’s striking that play has driven innovation in computers since the dawn of Digital Light and that we’ve insisted on interacting with our most sophisticated machines since we first met them.
Christopher Strachey(“Stray chee”)是 Turing 在剑桥的同学,他试图在 Pilot Ace 上运行一个跳棋程序——用英式英语进行的跳棋程序。他在 1951 年 5 月 15 日的一封信中告诉图灵,它起作用了。然后 Strachey 得知在曼彻斯特的 Mark I 的记忆要大得多,Baby 的孩子。当然,记忆可见的事实也给他留下了深刻的印象。他为它重新编写了程序,最迟在 1952 年 7 月 9 日之前,它在商业版 Ferranti Mark I 上运行——使用图灵的编程手册。47
Christopher Strachey (“Stray chee”), a fellow student of Turing’s at Cambridge, tried to run a checkers program—draughts, in British English—on Pilot Ace. He told Turing that it worked in a letter on May 15, 1951. Then Strachey learned of the much larger memory on Mark I at Manchester, child of Baby. Surely the fact that the memory was visible also impressed him. He had his program recoded for it, and it was running on Ferranti Mark I, the commercial version, by July 9, 1952, at the latest—using Turing’s programming manual.47
“他自己写了这本手册,当我拿到一份副本时,我明白了为什么它以难以理解而闻名,”图灵的 Strachey 说。“人们只是不习惯阅读准确的描述,而艾伦略微烦躁的假设每个人都和他一样聪明,这加剧了这种情况。”
“He had written the manual himself and when I got a copy I could see why it was famed for its incomprehensibility,” said Strachey of Turing. “People just weren’t used to reading accurate descriptions and this was exacerbated by Alan’s slightly irritable assumption that everyone was as intelligent as himself.”
棋盘的连续状态显示在计算机的威廉姆斯管上。图 4.18 显示了 Strachey 的六张原始图片。它们来自存储程序控制下的计算机。
The successive states of the checkerboard were displayed on the computer’s Williams tube. Figure 4.18 shows six of Strachey’s original pictures. They came from a computer under stored-program control.
Strachey 的草稿程序是第一个视频游戏的竞争者——迄今为止记录的最好的程序。但是在 1950 年到 1952 年期间制造了几台计算机,其中任何一台都可能被编程用于游戏(或静态图片或动画)。正如我们将看到的,肯定有传闻的竞争者。
Strachey’s draughts program is a contender—the best so far documented—for the first videogame. But there were several computers built in the period from 1950 to 1952, and any one of them might have been programmed for games (or still pictures or animations). There are certainly anecdotal contenders, as we’ll see.
国际象棋从来都不是竞争者,尽管图灵是该游戏的知名粉丝。克劳德香农也是如此,他于 1950 年在曼彻斯特访问图灵并谈论它。迪特里希·普林茨(Dietrich Prinz)也是如此,他早年在曼彻斯特加入了费兰蒂(Ferranti)。斯特拉奇也是如此。当时这个游戏对计算机来说太难了,但是 Prinz 能够在 1951 年在 Ferranti Mark I 上编写它的一部分,即残局(在将死的两步内)。尽管他可能是生成复选标记图像的程序员(图 4.17),没有证据表明他的国际象棋程序使用了视觉显示。
Chess was never a contender, although Turing was a well-known fan of the game. So was Claude Shannon who visited Turing in Manchester in 1950 to talk about it. So was Dietrich Prinz, who joined Ferranti early in Manchester. And so was Strachey. The game was too hard for computers then, but Prinz was able to program a part of it, the endgame (within two moves of a checkmate), in 1951 on Ferranti Mark I. Although he was probably the programmer who generated the checkmarks image (figure 4.17), there’s no evidence that his chess program used a visual display.
第一个电子游戏的两个紧密竞争者出现在剑桥的 Edsac 上。Stanley Gill 在 1952 年 11 月的剑桥博士论文中描述了一个简单的程序一只羊靠近栅栏上的一对门。Edsac 为栅栏展示了一条垂直线,我们被告知,大门有一个上间隙或下间隙。在程序预测将打开的大门对面画了一条水平线。Edsac 的纸带阅读器的光束可能会被玩家挥手打开顶门打断。否则下层门打开了。绵羊和大门的图形(如果不是游戏的话)将与后来的 Pong 电子游戏一样简单。唉,没有人拍照。48
Two close contenders for the first videogame appeared on Cambridge’s Edsac. A November 1952 Cambridge PhD thesis by Stanley Gill described a simple program in which a sheep approaches a pair of gates in a fence. Edsac displayed a vertical line for the fence, we’re told, with an upper gap or a lower gap for the gates. A horizontal line was drawn opposite the gate that the program predicted would open. The light beam of Edsac’s paper tape reader could be interrupted by a player’s hand wave to open the top gate. Otherwise the lower gate opened. The graphics—if not the play—of sheep and gates would have been about as unsophisticated as that of the much later Pong videogame. Alas, nobody took photos.48
图 4.18
Figure 4.18
Alexander Shafto “Sandy” Douglas 确实为他的游戏创作拍摄了照片(图 4.19)。大约在 1952 年,但在 1953 年 3 月之前,他将井字游戏(英式英语的 noughts 和 crosss)编入了 Edsac。这三张图片是他从电脑显示器上拍摄的原件。使用类似于我在其他软日期情况下所做的保守估计,Gill 的 1952 年 11 月战胜了道格拉斯的 1953 年 3 月,使他们成为第二和第三知名电子游戏的创造者。以同样的论点,跳棋优先于羊和门(美式英语),而草稿则轻推noughts(英式)。49
Alexander Shafto “Sandy” Douglas did take photos (figure 4.19) of his game creation. He programmed tic-tac-toe—noughts and crosses, in British English—into Edsac circa 1952 but before March 1953. These three pictures are originals that he took from the computer’s monitor. Using conservative estimates similar to ones I’ve made in other soft date circumstances, Gill’s November 1952 wins over Douglas’s March 1953, making them the creators of the second- and third-known videogames. With the same argument, checkers takes priority over sheep and gates (American English), and draughts nudges out noughts (British).49
图 4.19
Figure 4.19
图 4.20
Figure 4.20
英国人拥有第一个记录在案的数字图片和交互式视频游戏。当然他们也有早期的动画,因为很明显Baby可以动画。但奇怪的是,没有任何关于早期婴儿动画的证据浮出水面——甚至没有轶事。Baby和Edsac都显示了数字图像序列,但它们只是记忆中的偶然内容。50
The Brits had the first documented digital pictures and interactive videogames. Surely they had early animations too, because it’s clear that Baby could animate. But oddly no evidence of any animations on early Baby has surfaced—not even anecdotes. Both Baby and Edsac did display sequences of digital images, but they were only incidental contents of memory.50
Edsac 上可能有一位动画高地舞者,但唯一的证据是轶事报道。据我们所知,美国佬拥有第一个记录在案的二维图片时间序列意义上的计算机动画。这是麻省理工学院的旋风。51
There may have been an animated Highland dancer on Edsac, but the only evidence is an anecdotal report. As far as we know, the Yanks had the first documented computer animation in the sense of intentional temporal sequences of two-dimensional pictures. This was on MIT’s Whirlwind.51
1951 年 6 月 11 日出版的 Whirlwind 编程手册以“弹跳球显示”为特色。示波器显示的示意图(图 4.20)如下程序本身的文本列表,由 Charlie Adams 编写。根据标题,这些点是按时间连续显示的。这显然是第一个记录在案的计算机动画,但它可能只是一张缓慢渲染的静止画面——没有仔细控制时间。每个点一旦显示出来,就会简单地衰减以呈现一个弹跳球的外观——好吧,无论如何都是一个弹跳点。
The Whirlwind programming manual, published on June 11, 1951, featured a “bouncing ball display.” A sketch (figure 4.20) of the oscilloscope display follows a textual listing of the program itself, written by Charlie Adams. The dots were displayed in time succession, according to the caption. This was apparently the first documented computer animation, but it might have been just a still picture rendered slowly—without careful control of time. Each dot, once displayed, simply decayed to give the appearance of a bouncing ball—well, a bouncing dot anyway.
图 4.21
Figure 4.21
像往常一样,我会选择保守的出版日期 1951 年 6 月 11 日,作为这张照片的“官方”日期,可能还有第一部动画。它得到 1951 年 12 月 13 日的官方旋风照片(图 4.21)的支持。52
I’ll go with, as usual, the conservative publication date June 11, 1951, for the “official” date of this picture, and possibly the first animation. It’s supported by an official Whirlwind photograph (figure 4.21) dated December 13, 1951.52
我为这张照片而烦恼,因为它的影响力。亚当斯表示,这可能是“在静电存储投入使用之前,Whirlwind 最广为人知的演示”。意思是旋风——,换句话说。亚当斯和他的同事杰克吉尔摩(Jack Gilmore)于 1950 年 10 月加入他的行列,将弹跳点(“球”)修改为一种游戏(图 4.22)。而且他们在每次弹跳时都添加了“砰”的一声,所以这个版本绝对是一个动画。53
I bother with this picture because of its influence. Adams stated that it was “probably the most widely seen demonstration of Whirlwind, before electrostatic storage became operational.” Meaning Whirlwind–, in other words. Adams and his colleague Jack Gilmore, who joined him in October 1950, modified the bouncing dot (“ball”) into a sort of game (figure 4.22). And they added a “thunk” sound at every bounce, so this version was definitely an animation.53
玩家将交互式地改变反弹的频率,获胜者是第一个让“球”穿过地板上的一个洞——沿着水平轴的一个缺口——发出不同的声音。这种“游戏”的最早已知照片是 1953 年 6 月的旋风照片。54
The players would interactively alter the frequency of the bounces with the winner being the first to make the “ball” go through a hole in the floor—a gap along the horizontal axis—with a different sound. The earliest known picture of this “game” is this Whirlwind photograph dated June 1953.54
公开的代码并没有表明这是一个等待下一个玩家移动的循环程序——换句话说,它是真正的交互式程序。相反,它似乎一直是一个程序,每次重新启动时都会通过拨动开关输入一组不同的三个初始条件(如图 4.21 中的手绘图所示)。无论如何,这构成交互性并称之为早期视频游戏是很诱人的。有些有。这当然是一种游戏形式。这个“游戏”鼓励麻省理工学院的学生坚持编写 Whirlwind- 的繁琐过程。55
The published code doesn’t show that this was a cycling program that awaited the next player’s move—in other words, that it was truly interactive. It appears instead to have been a program that was restarted each time with a different set of three initial conditions (the set shown in the hand-drawn figure in 4.21) entered via toggle switches. It’s tempting to make the stretch that this constitutes interactivity anyway and call this an early videogame. Some have. It’s certainly a form of play. The “game” encouraged MIT students to persist in the tedious process of programming Whirlwind–.55
图 4.22
Figure 4.22
弹跳点最终是动画,如果不是在 1951 年 6 月,那么到 1953 年 6 月。但前两个经过验证和注明日期的计算机动画确实出现在旋风上,在 1951 年。一个是光栅,另一个是书法。
The bouncing dot was eventually an animation, if not in June 1951 then by June 1953. But the first two verified and dated computer animations did appear on Whirlwind, in 1951. One was raster and the other calligraphic.
Edward R. Murrow 于 1951 年 12 月 16 日的电视节目See It Now以两部旋风动画为特色。节目以图 4.23 所示的光栅动画开始。单词HELLO MR. MURROW以散布像素呈现。单词中的每一列斑点依次变亮,然后变暗,大概是在计算机控制下。(右图是模拟。)另一个动画(未显示)显示了一个移动点,它描绘了导弹的抛物线轨迹。这幅画是用书法方式绘制的,沿着曲线一次一点,没有留下任何痕迹。这是移动“球”的第一次反弹。56
Edward R. Murrow’s television show See It Now on December 16, 1951, featured two Whirlwind animations. The show began with the raster animation shown in figure 4.23. The words HELLO MR. MURROW were rendered in spread pixels. Each column of spots in a word successively brightened and then darkened, presumably under computer control. (The picture at right is a simulation.) The other animation (not illustrated) showed a moving dot that traced out the parabolic trajectory of a missile. The picture was painted calligraphically, one spot at a time along the curve, and left no trail. It was the first bounce of a moving “ball.”56
图 4.23
Figure 4.23
数学家马丁戴维斯告诉我一个故事,它建立了洋基队的另一个早期动画,肯定是在基于像素的显示器上。1952 年春天,戴维斯在伊利诺伊大学短暂调试代码。他使用的计算机是 Ordvac,它是 Edvac 的另一个孩子。它于 1951 年春天投入使用。就像 Maniac 一样,它有 40 个威廉姆斯管和一个可以切换以显示其中任何一个的显示器。戴维斯报告说,得到他的妻子弗吉尼亚的证实,有人编写了一个程序来显示该信息HELLO VISITOR! THIS IS THE ORDVAC.字母是显示器的高度,所以消息太长,无法一次看到。相反,当消息在监视器上滚动时显示出来。因此,这部早期的电脑动画创作于 1951 年春季和 1952 年春季之间的某个时间。保守的约会时间将其定为 1952 年春季。57
The mathematician Martin Davis told me a story that establishes another early animation by the Yanks, definitely on a pixel-based display. Davis was briefly debugging code at the University of Illinois in the spring of 1952. The computer he worked on was Ordvac, yet another child of Edvac. It became operational in the spring of 1951. Just like Maniac, it had 40 Williams tubes and a monitor that could be switched to display any one of them. Davis reports, corroborated by his wife Virginia, that someone had written a program that displayed the message HELLO VISITOR! THIS IS THE ORDVAC. The letters were the height of the monitor, so the message was too long to be seen at one time. Instead, it was revealed as the message scrolled across the monitor. This early computer animation was therefore created sometime between spring 1951 and spring 1952. Conservative dating puts it at spring 1952.57
在同一轶事类别中还有一份来自 Richard Merwin 的报告,他曾在 Eniac 工作,然后在 Los Alamos 的 Maniac(Edvac 报告的另一个后代),然后是 IBM 702。Dick 和我是 IEEE 计算机科学家代表团的成员1978 年,尼克松在中国进行开创性访问后不久,中国对旅游业敞开大门之前不久,他们被邀请到中国呆一个月。在一个令人难忘的时刻,当我们的公共汽车经过紫禁城时,迪克告诉我他见过的第一部电脑动画——一个酒瓶将里面的东西倒入酒杯——在 1950 年代初在威廉姆斯管上展示。他描述的动画可能是在 Maniac 上,但可能是在 1952 年或 1953 年的某个时候在 IBM 701 上,或者后来在他工作的 IBM 702 上。可悲的是不再活着来证实他们。也许它与我从劳伦斯利弗莫尔国家实验室的图形先驱乔治迈克尔那里听到的另一个版本混为一谈:1950 年代初期的 IBM 701 计算机使用了啤酒瓶将其内容物倒入玻璃杯中的动画作为其威廉姆斯管的内存检查记忆。计算机图形学先驱 Robin Forrest 报告了另一个变体:“据称,一位聪明的程序员设法编写了一个程序,该程序可以显示水流入玻璃杯的动画。” 58
In the same anecdotal category is a report from Richard Merwin, who had worked on Eniac, then on Maniac (another descendant of the Edvac report) at Los Alamos, then on IBM 702. Dick and I were members of an IEEE delegation of computer scientists who were invited to spend a month in China in 1978, not long after Richard Nixon’s groundbreaking visit there and before China opened its doors to tourism. At a memorable moment, as our bus was passing the Forbidden City, Dick told me about the first computer animation he’d ever seen—a wine bottle pouring its contents into a wine glass—displayed on a Williams tube in the early 1950s. The animation he described could have been on Maniac but was probably on an IBM 701 sometime in 1952 or 1953, or later on the IBM 702, the version he worked on. I call this an anecdote because at the distance of 40 years I suspect my memory of the fine details, and Merwin is sadly no longer alive to confirm them. Perhaps it’s conflated with another version I heard from the graphics pioneer George Michael of the Lawrence Livermore National Laboratory: the IBM 701 computer in the early 1950s used an animation of a beer bottle pouring its contents into a glass as a memory check for its Williams tube memory. And the computer graphics pioneer Robin Forrest reported yet another variation: “It is claimed that one clever programmer managed to write a program which caused an animation of water flowing into a glass to be displayed.”58
您可能会反对 First Light 不是图片,因为它是文本:C.R.T. STORE。但是文本是任何合理定义的图片。每张图像都准确地——用我们将熟悉的术语——将几何定义的字母和数字渲染成像素,就像现代动画电影是将几何定义的字符渲染成像素一样。
You might object that First Light isn’t a picture, because it is text: C.R.T. STORE. But text is a picture by any reasonable definition. Each image is exactly—in terms that will become familiar as we proceed—a rendering of geometrically defined letters and numerals into pixels, just as a modern animated movie is a rendering of geometrically defined characters into pixels.
图片的锯齿状性质令人不快。Kilburn 在没有采样定理的情况下天真地制作了它们。怀疑他是否听说过。Kotelnikov 在 1933 年的第一次陈述是用俄语,而香农的英语普及直到 1948 年才出现。图灵早在 1943 年就知道采样定理——这与香农声称它在该领域众所周知——但图灵没有当 Kilburn 创作第一张数码照片 First Light 时,他们还没有抵达曼彻斯特。并且没有理由认为图灵,无论他多么聪明,曾经想过将采样定理应用于视觉领域。
The jagged nature of the pictures is unpleasant. Kilburn made them naively, without the Sampling Theorem. It’s doubtful he’d ever heard of it. Kotelnikov’s first statement of it in 1933 was in Russian, and Shannon’s English popularization of it wouldn’t appear until 1948. Turing knew the Sampling Theorem as early as 1943—consistent with Shannon’s claim that it was generally known in the field—but Turing hadn’t yet arrived at Manchester when Kilburn created First Light, the first digital picture. And there’s no reason to think that Turing, no matter how smart he was, ever thought about applying the Sampling Theorem to visual fields.
每个像素只有一位或两个值,无论是否天真,Kilburn 的尝试都已尽善尽美。在他的威廉姆斯管内存中根本没有足够的像素——也没有足够的比特位——来准确地表示一个定义平滑、边缘锐利的物体,比如一个字母。在频率峰值中,像素的位置远不接近(两倍)字母中的最高空间频率。这些不仅是第一张照片,而且还首次展示了要使 Digital Light 成功必须解决的“锯齿”难题。
With only one bit, or two values, per pixel, Kilburn’s attempt was as good as you could do, naively or not. There simply weren’t enough pixels—and not enough bits per pixel—in his Williams tube memory to accurately represent a smoothly defined, sharp-edged object like a letter. In frequencyspeak, the placing of the pixels was nowhere near (twice) the highest spatial frequency in the letters. Not only were these the first pictures, but they first demonstrated the difficult problem of “jaggies” that had to be solved to make Digital Light successful.
所有最初的图片、电子游戏和动画——除了麻省理工学院的书法图片——都是将简单的几何对象——字母、数字、线条、曲线和正方形——临时转换为一位像素。它们是幼稚的渲染——不知道采样定理。还没有人意识到采样的最终重要性,这个想法最终将实现大数字融合。这就是为什么我不介意在这个早期阶段混淆旋风人单独使用的书法显示与其他人使用的光栅显示。书法展示是我们幼稚童年的一部分。
All of the first pictures, videogames, and animations—except the calligraphic pictures at MIT—were ad hoc conversions of simple geometrical objects—letters, numerals, lines, curves, and squares—into one-bit pixels. They were naive renderings—with no awareness of the Sampling Theorem. Nobody was yet aware of the ultimate importance of sampling, the idea that would eventually allow the Great Digital Convergence. That’s why I don’t mind confusing, at this early stage, the calligraphic display used discretely by Whirlwind people with raster displays used by the others. Calligraphic displays were part of our naive childhood.
图 4.24
Figure 4.24
考虑到天真,图 4.24(左)中的 1760 采样器暗示了对此处勾画的数字光的早期历史的反对。(顺便说一句,sampler似乎非常合适,但来自这个词的完全不同的含义——一个人的工作样本,在这种情况下是 Elizabeth Laidman 的针线活。)为什么这不是 Digital Light 的前身?为什么没有任何带有图片的纺织品或挂毯?还是任何马赛克,例如图 4.24(右)中的马赛克,它描绘了由规则间隔的瓷砖构成的图像?这些中的任何一个都是由天真的采样形成的——没有采样定理——就像第一光一样。
With naivete in mind, the 1760 sampler in figure 4.24 (left) suggests an objection to the early history of Digital Light sketched here. (By the way, sampler seems eerily appropriate but comes from an entirely different meaning of the word—a sample of one’s work, Elizabeth Laidman’s needlework in this case.) Why isn’t this a precursor of Digital Light? Why isn’t any textile or tapestry that carries a picture? Or any mosaic, such as the one in figure 4.24 (right) that portrays an image built of regularly spaced tiles? Any of these is a picture formed from a naive sampling—without the Sampling Theorem—just like First Light.
嗯,它们是数码照片的前身和数码光的前身。毫无疑问。一方面,它们被铭记在线或瓷砖的永久记忆中。几个世纪甚至数千年的时间里,肯定有成千上万个类似的前身。但是从他们的离散样本到今天的现代图片(比如你现在正在阅读的文字)没有明显的技术路径。下一部分是关于第一个像素的更重要的竞争者。
Well, they were antecedents to digital pictures and precursors of Digital Light. There’s no question about that. They were remembered, for one thing, in permanent memories of thread or tile. There were surely thousands of similar precursors spread over centuries, even millennia. But there was no obvious technological path from their discrete samples to today’s modern pictures—such as the words you are currently reading. The next section is about a more serious contender for the first pixels.
图 4.25
Figure 4.25
电传打字机——一种远距离打字的机器——是一个古老的概念,也被称为电传打字机或电传打字机。(严格来说,电传打字机是一个商品名称。)基本上,当电信号传输到类似打字机的机器时,它就会起作用,该机器通过在一张纸上键入其键将信号转换为字母。每个可用字母都有一个独特的信号。
The teletype—a machine for typing at a distance—is an old idea, also known as a teleprinter or a teletypewriter. (Strictly speaking, Teletype is a trade name.) Basically, it works when an electrical signal is transmitted to a typewriter-like machine that turns the signal into a letter by typing its key on a sheet of paper. There is a unique signal for each available letter.
根据我们对数字图片的定义,任意类型的消息不是数字图片,因为它无意成为连贯的二维图片。但是,如果将打字的字母以二维方式排列,并且完全有意将结果视为图片,那又会怎样呢?图 4.25 显示了两个例子,一个是麦当娜和孩子,另一个是达格·哈马舍尔德,他在 1953 年成为最年轻的联合国秘书长。注意叠印字符,这很容易用电传打字机完成。59
By our definition of a digital picture, an arbitrary typed message isn’t a digital picture because there is no intent that it be a coherent two-dimensional picture. But what about the case where the typed letters are arranged in two dimensions with full intention that the result be perceived as a picture? Figure 4.25 shows two examples, one of the Madonna and Child and the other of Dag Hammarskjöld, who became the youngest UN secretary-general in 1953. Note the overprinted characters, which were easy to accomplish with a teletype.59
问题是:如果唯一信号是数字位,那么我们可以将其解释为一个像素,然后将输入的字母解释为该像素的显示元素吗?这不是一个随意的问题,因为可以说信号在 1874 年变成了数字信号,当时 Émile Baudot(发音为“boh Doh”)设计了一个我们可以识别的“五单元”系统今天作为 5 位编码方案。上面两张图片最初可能是在 Baudot 代码中指定的。一个字形显示元素的灰度值(包括由叠印字母字符形成的那些)大致是该字形占据的矩形区域中黑到白的相对量。60
The question is: If the unique signal is digital bits, then can we construe it as a pixel, and then construe the typed letters as a display element for that pixel? This is not a casual question because the signals arguably became digital in 1874 when Émile Baudot (pronounced “boh Doh”) designed a “five-unit” system that we would identify today as a 5-bit coding scheme. Both pictures above were probably specified in Baudot code originally. The gray value of a glyph display element (including those formed by overprinting alphabetic characters) is roughly the relative amount of black to white in the rectangular area occupied by the glyph.60
这些年来,人们制作了成百上千张这样的照片——其中很大一部分是裸体照片——并在粉丝之间传播,首先是通过电报,然后是业余无线电。业余爱好者会用输入信号驱动电传打字机,打印图片,同时在纸带上打孔。纸带变成了记忆,可以从中复制多份副本或发送给朋友——比如圣诞节问候。因此,在计算机出现之前(即 1948 年之前)以及之后的十多年里,计算机仍然稀有且昂贵,这是一种常见的地下拍照方法。例如 1947 年的麦当娜和儿童以及 1962 年的哈马舍尔德。61
Hundreds, perhaps thousands, of such images were produced over the years—a goodly percentage of them nudes—and passed around among fans, first via telegraph and then via ham radio. Ham operators would drive a teletype with the incoming signals, print the picture, and simultaneously punch a paper tape. The paper tape became the memory from which multiple copies could be struck or sent to friends—for a Christmas greeting, say. So this was a common underground method for making pictures before there were computers—that is, before 1948—and for more than a decade after, when computers were still rare and expensive. Examples are the Madonna and Child from 1947 and the Hammarskjöld from 1962.61
电传艺术时代跨越了计算机的诞生,并迅速轻松地适应了计算机世界。为取代鲍多代码的电传打字机开发了新代码,并成为计算机与打印机终端(例如电传打字机)对话的代码。重叠的历史迫使我们思考数字光的定义。它提出了这个定义延伸的问题:在计算机出现之前,电传打字机编码是第一个像素吗?
The teletype art era straddled the birth of the computer and was quickly and easily adapted to the computer world. New codes were developed for teletypes that supplanted the Baudot code and became the codes with which computers talked to printer terminals—such as teletypes. That overlapping history forces us to contemplate the definition of Digital Light. It raises this definition-stretching question: Before computers existed, were the teletype codes the first pixels?
不完全的。由于朴素的采样和粗略的重建,我们可以将它们视为数码光像素的早期前身。但因为记忆系统是纸带,而不是电子记忆,它们不符合数码光的定义。为了与本书中的其他定义保持一致,我们坚持涉及电子计算机内存。
Not quite. Because of the naive sampling and the crude reconstruction, we can think of them as early predecessors of the pixels of Digital Light. But because the memory system was paper tape, not electronic memory, they don’t fit the definition of Digital Light. To be consistent with the other definitions in this book, we insist that electronic computer memory be involved.
在 1950 年代、1960 年代、1970 年代,甚至 1980 年代,幼稚的抽样非常猖獗——根本不基于抽样的书法展示也是如此。直到 1960 年到 1970 年的数字光时代,我们才开始看到将采样定理应用于像素计算的第一个提示。这些早期努力的特点是在用于注释图片的几何形状或字形的边缘进行水平软化。用行话来说,这是水平抗锯齿。62
In the 1950s, 1960s, 1970s, and even the 1980s naive sampling was rampant—and so were calligraphic displays that weren’t based on sampling at all. It wasn’t until the 1960 to 1970 era of Digital Light that we began to see the first hints of the Sampling Theorem applied to the computation of pixels. These early efforts featured horizontal softening at the edges of geometric shapes, or glyphs, that were used to annotate pictures. In jargon, this was horizontal antialiasing.62
如果采样的速率低于采样定理所需的速率,则未表示的较高频率会在结果中显示为称为混叠的视觉噪声。抗锯齿是锯齿问题的一种解决方案,一种消除令人不快的锯齿的方法,因为锯齿被人们熟悉地称为锯齿。采样定理的正确应用需要计算能力,这就是为什么早期使用它内置在硬件中。在软件中实现它等待摩尔定律的进一步力量。
If sampling is done at less than the rate required by the Sampling Theorem, then the unrepresented higher frequencies appear in the result as a visual noise called aliasing. Antialiasing is a solution to the aliasing problem, a way of getting rid of the unpleasant jaggies, as aliasing is familiarly called. The correct application of the Sampling Theorem requires computational horsepower, which is why early uses of it were built into hardware. Implementing it in software awaited further power from Moore’s Law.
图 4.26
Figure 4.26
图 4.27
Figure 4.27
几何模型的第一个显式和完全抗锯齿(在两个维度上)可能是我们在 1973 年施乐帕洛阿尔托研究中心的 Richard Shoup 在图 4.26 中看到的(但请参阅注释以了解可能的 1971 年前身)。锯齿线位于顶部,抗锯齿版本位于底部。63
The first explicit and full antialiasing—in both dimensions—of a geometric model was probably what we see in figure 4.26 by Richard Shoup at Xerox Palo Alto Research Center in 1973 (but see the annotation for a possible 1971 predecessor). The jagged lines are at the top, and the antialiased versions at the bottom.63
Shoup(听起来像呐喊)也在 1973 年制作了图 4.27 所示的巡回赛马车车轮图片(左侧为锯齿状,右侧为抗锯齿)。他没有明确地对这些图片中的任何一张使用采样定理,但平滑的结果证明他的方法是等效的。它们由 8 位灰度像素组成,具有老式的视频分辨率(每个大约 500 像素宽)。64
Shoup (sounds like shout) also made in 1973 the tour-de-force wagon wheel pictures shown in figure 4.27 (jagged on left, antialiased on right). He didn’t explicitly use the Sampling Theorem for any of these pictures, but the smooth results attest that his method was equivalent. They are composed of 8-bit grayscale pixels and have an old-fashioned video resolution (roughly 500 pixels wide each).64
在犹他大学首次明确使用采样定理进行空间抗锯齿。那里的数字音频专家 Thomas Stockham 在 1970 年代向一代早期计算机图形学先驱教授了采样定理。犹他州学生 Ed Catmull 在 1974 年的博士论文中展示了抗锯齿图片。那里的另一位学生 Frank Crow 在 1976 年的博士论文和随后的出版物中将 Stockham 的教学带到了计算机图形学界。65
The first explicit use of the Sampling Theorem for spatial antialiasing was at the University of Utah. Thomas Stockham, a digital audio expert there, taught the Sampling Theorem to a generation of early computer graphics pioneers in the 1970s. Utah student Ed Catmull showed antialiased pictures in his 1974 doctoral dissertation. Another student there, Frank Crow, brought Stockham’s teaching to the computer graphics community in his 1976 doctoral dissertation and subsequent publications.65
无论你如何解析历史,很明显,Digital Light 是与计算机的诞生同时诞生的。First Light 是在婴儿的子宫内创建的。第一个像素实际上是第一台计算机内存的位。关键的年份是从 1947 年到 1952 年。婴儿记忆管上的第一张测试图片和存储程序计算机上的第一张故意程序生成的图片之间可能有一两年的间隔。即便如此,到 1951 年,计算机上仍能用存储程序控制的像素制作图片。这些像素天真地来源于几何模型,通常是字母、数字或其他简单形状。有些模型是交互式的,有些是动画的。采样定理的真正和充分使用可能始于 1970 年代初期。
No matter how you parse the history, it’s clear that Digital Light was born simultaneously with the birth of computers. First Light was created in utero with Baby. The first pixels were literally bits of the first computer memories. The crucial years were from 1947 to 1952. There may have been a hiatus of one or two years between the first test pictures on Baby’s memory tube and the first intentionally program-generated pictures on a stored-program computer. Even so, by 1951 pictures were being made on computers with pixels under stored-program control. These pixels were derived, naively, from geometric models, typically of letters, digits, or other simple shapes. Some of the models were interactive, and some were animated. The true and full use of the Sampling Theorem probably began in the early 1970s.
像素统一了所有数字光的历史,包括计算机图形、视频游戏、图像处理、数字摄影、应用程序或操作系统界面、数字电视、动画电影、虚拟现实等。从这个有利的角度来看,几十年来在计算机图形学中使用书法显示可以被视为绕道而行。显示器上显示元素密度的大幅增加以及摩尔定律在计算速度方面的巨大改进允许光栅显示包含书法显示并将数字光返回到其光栅根。显示器向单一光栅类型的崩溃最终实现了各种视觉媒体的大数字融合。采样定理是像素的基础。
The pixel unifies the history of all Digital Light, including computer graphics, videogames, image processing, digital photography, apps or operating systems interfaces, digital television, animated movies, virtual reality, and so forth. From this vantage point the several decades-long use of calligraphic displays in computer graphics can be seen as a detour. The large increase in density of display elements on displays and the vast Moore’s Law improvements in computation speed permitted raster displays to subsume calligraphic displays and return Digital Light to its raster roots. The collapse of displays into the single raster kind finally enabled the Great Digital Convergence of various visual media. And the Sampling Theorem is the magic that underlies the pixel.
我们现在已经准备好将三个伟大的想法——频率、采样和计算——应用并投入到两种技术中,一种是旧的,一种是新的。旧的是电影。重温电影历史的一个原因是为我们提供 Digital Light 将采用的词汇。制作一部数字电影不可避免地依赖并衍生于现有的电影和动画技术。但主要的原因是为了展示采样这一伟大想法如何不仅可以理解图片,还可以理解移动的图片流。事实证明,电影技术也依赖于采样定理,尽管当时没有人知道。采样定理为我们提供了一种更好的方式来思考电影。我们将遇到几个新的英雄和暴君,并重温被误传的故事。
We are now ready to apply and devote the three great ideas—frequencies, samplings, and computations—to two technologies, one old and one new. The old one is the movies. One reason to revisit the history of film movies is to give us the vocabulary that Digital Light would adopt. Creating a digital movie inevitably depended on and derived from the existing technology of film and animation. But the principal reason is to demonstrate how the great idea of sampling works for understanding not only pictures but also moving streams of pictures. It turns out that movie technology depends on the Sampling Theorem too, even though nobody knew it at the time. The Sampling Theorem gives us a better way to think about film. And we’ll meet several new heroes and tyrants and revisit mistold stories. The second application of our fundamental ideas will be to Digital Light itself, the new technology of the single new medium.
运动的绝对连续性是人类思维无法理解的。任何种类的运动定律只有在人检查运动中任意选择的元素时才能理解。但与此同时,很大一部分人为错误来自于将连续运动任意划分为不连续的元素。
Absolute continuity of motion is not comprehensible to the human mind. Laws of motion of any kind only become comprehensible to man when he examines arbitrarily selected elements of that motion; but at the same time, a large proportion of human error comes from the arbitrary division of continuous motion into discontinuous elements.
——列夫·托尔斯泰,战争与和平1
—Leo Tolstoy, War and Peace1
起源是滑溜溜的东西,比喻和字面意义上的,电影可能是有史以来最滑溜的媒体。. . . 起源笼罩在令人生畏的禁忌和驱使好奇心的混合物中,构成了权力和所有权要求的令人不安的混合物(通常是虚假的,总是简化的):不可避免的进步的神话;民族自豪感;和简单的错误信息。面对索赔和反索赔的蛇坑,标志着电影起源的纯粹自我主义和混淆可能会举手投降。
Origins are slippery things, figuratively and literally, and the cinema is possibly the most slippery medium that has ever existed. . . . Origins are shrouded in a mixture of forbidding taboos and driving curiosity, and constitute a troubling concoction of claims to power and ownership (often spurious, always simplified): myths of inevitable progress; national pride; and simple misinformation. Faced with the snake-pit of claims and counterclaims, pure egotism and obfuscation that marks accounts of the origins of cinema one might just throw up one’s hands.
——汤姆·冈宁,曼诺尼《光与影的伟大艺术2 》简介
—Tom Gunning, introduction to Mannoni’s The Great Art of Light and Shadow2
电影史比计算机史更具争议性。许多美国人相信托马斯·爱迪生发明了电影——否则就是那个不发音的埃德沃德·迈布里奇。法国人确信这是他们自己的卢米埃兄弟。将如此复杂的技术成果简单化当然是错误的。就像电影结尾的电影片尾字幕一样,总有许多贡献者对一部精彩的作品至关重要。说,不仅仅是导演、男主角或编剧。当然不是钱人或首席营销人员。不,电影的真实故事是一片荆棘,比电脑更棘手。
Movie history is even more contentious than computer history. Many Americans believe that Thomas Edison invented the movies—else it was that unpronounceable Eadweard Muybridge. The French are convinced it was their own Lumière brothers. What’s certainly wrong is to simplify so complex a technological achievement. Like movie credits at the end of a film, there are always many contributors who are fundamental to a magnificent production. It’s never just the director, lead actor, or screenwriter, say. And certainly not the money man or chief marketer. No, the true story of cinema is a briar patch, thornier than that of computers.
这两个世界之间有几个隐喻的联系,但真正的联系是采样。Kotelnikov 教我们如何将音频流采样为索像素,将视野采样为像素。但是也可以对流入我们眼睛的视野进行采样。视觉流示例的熟悉名称是frame。我们将一系列帧称为电影或电影。视觉流——随时间变化的视野时间——也是所有的音乐。波和采样的伟大想法适用。然后将计算的概念——图灵的好主意——应用于帧(以及像素和索素),为我们带来了数字光的全部荣耀。
There are several metaphorical connections between those two worlds, but the real connection is sampling. Kotelnikov taught us how to sample an audio stream into soxels and a visual field into pixels. But the flow of visual fields into our eyes can be sampled too. The familiar name for a sample of visual flow is frame. And we call a sequence of frames a movie, or a motion picture. Visual flow—visual fields that change in time—is all music too. The great ideas of waves and sampling apply. Then the notion of computation—Turing’s great idea—applied to frames (and pixels and soxels) brings us the full glory of Digital Light.
简而言之,我们可以通过定期拍摄的离散快照准确地表示不断变化的视野——我们的眼睛实际看到的东西。每个样本都是那一刻呈现在我们眼前的静止画面。我们可以忽略帧之间发生的所有事情,因为在显示时,样本被电影放映机传播成一个连续的流,准确地代表了原始的视觉流。
In short, we can accurately represent changing visual fields—what our eyes actually see—with discrete snapshots taken at regular intervals. Each sample is the still picture presented to our eyes at that instant. We can ignore everything that happens between the frames because, upon display, the samples are spread by a movie projector into a continuous flow that accurately represents the original visual flow.
问题是,发明电影的男人(他们都是男人)都不知道这一点。他们创建的系统也没有以这种漂亮的方式工作。采样定理不存在——再过半个世纪。因此,发明者完全天真地创造了电影技术,并带有伤痕来证明这一点。那个笨拙的年轻人的缺陷,一个世纪前被锁定在系统中,仍然存在。Digital Light 并非一蹴而就。它继承了它的历史。
The catch is that none of the men (they were all men) who invented the movies knew this. Nor does the system that they created work in quite this beautiful way. The Sampling Theorem didn’t exist—not for another half century. So the inventors created movie technology entirely naively, and it bears the scars to prove it. Flaws from that clumsy youth, locked into the system a century ago, still abide. Digital Light didn’t just spring into existence. It inherited its historical past.
在本章中,我们从电影史中抽取离散样本,并从它们中重建出一部更加连贯的历史——一部更加诚实、不那么具有传奇色彩的历史。电影史上的暴君是商人,而不是皇帝或独裁者:利兰·斯坦福到爱德华·迈布里奇,托马斯·爱迪生到威廉·肯尼迪·劳里·迪克森,沃尔特·迪斯尼到 Ub Iwerks。在所有这些情况下(还有更多),支配者是被支配者成功的基础——反之亦然。两者都很重要。我们发现许多神话——迈布里奇是电影之父,爱迪生如何发明电影,迪斯尼如何创造米老鼠——被证明是错误的。
In this chapter we take discrete samples of the history of cinema and reconstruct from them a more coherent history—a more honest, less hagiographic one. The tyrants of movie history were businessmen instead of emperors or dictators: Leland Stanford to Edward Muybridge, Thomas Edison to William Kennedy Laurie Dickson, and Walt Disney to Ub Iwerks. In all these cases (and there are more), the dominator was fundamental to the success of the dominated—and vice versa. Both mattered. And we find that many myths—how Muybridge fathered the cinema, Edison invented the movies, and Disney created Mickey Mouse—turn out to be wrong.
他起初是泰迪马格里奇。或者也许是艾迪。我们不知道他妈妈真正的喜爱,但直到很久以后他肯定不是 Eadweard Muybridge。这个名字是他众多别名中的最后一个,也是最奇怪的一个。他的正式名字是爱德华·詹姆斯·马格里奇,出生在伦敦附近的泰晤士河畔金斯敦。这张表记录了这位著名表演者在公众面前进行的名字游戏——他的名字的变体与他的姓氏的变体一起使用:3
He was Teddy Muggeridge at first. Or perhaps Eddy. We don’t know his mum’s actual endearment, but he certainly wasn’t Eadweard Muybridge until much later. That name was the last—and the weirdest—of his many aliases. Officially he was Edward James Muggeridge, born in Kingston upon Thames near London. This table captures the name game that this notable showman worked on the public—with variations of his first name used with variations of his surname:3
|
1830–55 1830–55 |
1855–56 1855–56 |
1856–62 1856–62 |
1862–65 1862–65 |
1866–68 1866–68 |
1869–1904 1869–1904 |
|---|---|---|---|---|---|
|
马格里奇 Muggeridge |
马格里奇 Muggridge |
麦格里奇 Muygridge |
迈布里奇 Muybridge |
赫利俄斯 Helios |
迈布里奇 Muybridge |
|
爱德华·詹姆斯泰德·爱德华 Edward James Ted Edward |
EJ E. J. |
EJ爱德华詹姆斯 E. J. Edward James |
EJ E. J. |
爱德华·爱德华多·圣地亚哥·埃德沃德 ('82–'04) Edward Eduardo Santiago Eadweard (’82–’04) |
他在这里永远是 Edward Muybridge(简称为“我的桥”),因为他在这个别名下完成了他最伟大的工作——对 Digital Light 很重要的工作。
He’ll always be Edward Muybridge (pronounced simply “My bridge”) here because he did his greatest work—the work that matters to Digital Light—under that alias.
他以 EJ Muggridge 的身份来到美国——带着一个gg。到1860 年,当他登上一辆从加利福尼亚开往东部的巴特菲尔德陆路驿马车时,他已成为 EJ Muygridge(拥有yg )。他没有成功。对他的未来如此重要的横贯大陆铁路将是一个更好的选择——但它还不存在。事实上,六匹巴特菲尔德马在德克萨斯州的某处沿着著名的舞台线吓坏了,他被从马车上扔了下来。他遭受了足够的身体——也许是精神——的伤害,以至于起诉巴特菲尔德并赢得了和解。1861 年,他仍然是 Muygridge,现在回到英国,当时他试图为洗衣机申请专利。他是第一个迈布里奇——与yb——1862 年在另一项英国专利申请中,这一项用于印刷工艺。奇怪的是,他从未尝试为他最重要的发明——Zoöpraxiscope——申请专利,而这项发明尚未到来。(电影设备的名字和电脑的名字一样有趣。)
He had come to America as E. J. Muggridge—with a gg. He had become E. J. Muygridge—with a yg—by 1860 when he boarded a Butterfield Overland stagecoach from California bound for the East. He didn’t make it. The transcontinental railroad that was so important to his future would’ve been a far better choice—but it didn’t exist yet. As it was, the six Butterfield horses spooked somewhere in Texas along the famous staged line, and he was thrown from the coach. He suffered sufficient bodily—and perhaps mental—damage to sue Butterfield and win a settlement. He was still Muygridge in 1861, now returned to England, when he tried to patent a washing machine. He was first Muybridge—with the yb—in 1862 in another English patent application, this one for a printing process. Oddly, he never tried to patent his most important invention—the Zoöpraxiscope—which was yet to come. (The names of movie devices are as much fun as those of computers.)
他最丰富多彩的别名是 Helios(只有一个字)。在约翰·缪尔(John Muir)首次支持加利福尼亚奇妙的优胜美地山谷(Yosemite Valley)时,他开始成为一种新的艺术家,摄影艺术家,在旧金山取得了这个名字。赫利俄斯(太阳神摄影师)拍摄了一些最早且广受好评的强大优胜美地照片。
His most colorful alias was Helios (just the one word). He assumed the name in San Francisco as he set out to be a new kind of artist, a photographic artist, near the time when John Muir first championed California’s marvelous Yosemite Valley. Helios—the photographer as sun god—made some of the earliest, and acclaimed, photographs of mighty Yosemite.
正是他的谋杀案审判让他声名狼藉——又是迈布里奇先生,现在是爱德华迈布里奇。一个全是男性的陪审团裁定他在旧金山附近枪杀了他妻子的情人——以及他孩子可能的父亲——无罪。毫无疑问,他杀死了这个人——用一把他完全打算用于此目的的手枪直指胸膛。尽管有法官的告诫,陪审团并不打算在加州淘金热之后找到一个捍卫自己“荣誉”(!?)的人犯有谋杀罪。4
It was his murder trial that brought him notoriety—as Mr. Muybridge again, now Edward Muybridge. An all-male jury acquitted him of gunning down his wife’s lover—and his child’s probable father—near San Francisco. There’s no question that he killed the man—point blank to the chest with a pistol that he fully intended for the purpose. Despite the judge’s admonition, the jury wasn’t about to find a man defending his “honor” (!?) guilty of murder in post–Gold Rush California.4
迈布里奇只是在晚年 52 岁时才影响了古怪的 Eadweard,因为他在巴黎的艺术界声名鹊起。他肯定是从家乡泰晤士河畔金斯敦著名的加冕石(图 5.1)中得到的。900 年代,两位名叫爱德华的国王在这块石头上加冕。在它的底部两次浮雕是Eadweard - 古英语拼写。所以迈布里奇的最终名字只是“Ed ward”,尽管转录很容易起皱。
Muybridge affected the weird Eadweard only later in life, at age 52, as he made a name for himself in the art world of Paris. He took it surely from the famous coronation stone (figure 5.1) in his hometown, Kingston upon Thames. Two kings named Edward had been crowned on that stone in the 900s. Embossed in its base twice is Eadweard—the Old English spelling. So Muybridge’s final first name was just “Ed ward,” despite the pucker-provoking transcription.
在 Helios 和 Eadweard 之间,普通的爱德华完成了他令人难忘的工作。他的赞助人利兰·斯坦福(Leland Stanford)从建造第一条横贯大陆的铁路中获得了令人发指的强盗大亨财富——这些铁马将巴特菲尔德驿马车及其多肉的马带入了遗忘(或修剪整齐的椭圆形轨道)。当然,他巨额财富的主要遗产是斯坦福大学,硅谷将在斯坦福大学(在 1960 年代)成为摩尔定律的温床。但在他自己的时代,斯坦福大学在赛马——他的热情——尤其是猪身上投入了大量资金。
Between Helios and Eadweard, plain Edward did his memorable work. His patron, Leland Stanford, gained outrageous, robber-baron wealth from construction of the first transcontinental railroad—the iron horses that railroaded the Butterfield stagecoach and its fleshy horses into oblivion (or onto a manicured oval track). The major legacy of his vast fortune was, of course, Stanford University, from which Silicon Valley would spring (in the 1960s) as a hotbed of Moore’s Law. But in his own time, Stanford spent heavily on racehorses—his passion—particularly trotters.
图 5.1
Figure 5.1
图 5.2
Figure 5.2
爱德华·迈布里奇 (Edward Muybridge) 以这个名字着称,他在中途小跑时拦住了斯坦福最喜欢的小跑之一,一张照片显示所有四只蹄子都离地。公认的智慧是迈布里奇从那里开始发明电影。这归功于他第一次演示,当以相似的速度投影时,一系列快速连续拍摄的运动物体(例如马或裸体男人或女人)的静止照片似乎显示了运动中的物体。但这个故事并非如此。5
Edward Muybridge, under that name, famously stopped one of Stanford’s favorite trotters in mid-trot with a single photograph showing all four hooves off the ground. Received wisdom is that Muybridge proceeded from there to invent movies. It credits him with the first demonstration that a sequence of still photographs of a moving object, such as a horse—or a naked man or woman—taken in quick succession appears to show the object in motion, when projected at similar speed. But this story isn’t quite so.5
他实际上所做的是这样的。他在斯坦福的农场上建造了一个 24 摄像头的设备——The Farm,这是斯坦福学生今天对校园的称呼。他使用了一个巧妙的触发机制,当一匹马疾驰而过时,快速连续地打开每个相机的快门。每个照相机在涂有化学乳剂的玻璃板上形成一个单一的摄影图像。这些印版必须立即在现场开发。6
What he actually did was this. He built a 24-camera apparatus on Stanford’s farm—The Farm, as Stanford students call the campus today. He used a clever triggering mechanism to open the shutter of each camera in quick succession as a horse raced by. Each camera formed a single photographic image on a glass plate coated with a chemical emulsion. The plates had to be developed immediately on site.6
为了展示结果,他使用了公共演讲者用来投射静止图像的著名魔术灯——当时的 PowerPoint。他在其中添加了一个比旧的长播放 (LP) 唱片更大的旋转磁盘。他在圆盘的边缘放置了小画,每幅画都来自连续的马照片,如图 5.2 所示(左,快门在右)。当圆盘以或多或少均匀的速度旋转时,投影图像似乎在移动,再现了马的运动。一个完整的循环大约需要一两秒。7
To show the results he took the well-known magic lantern that public speakers used to project still images—the PowerPoint of its time. He added to it a rotating disk larger than an old long-playing (LP) record. He placed small paintings, each derived from successive horse photographs, around the edge of the disk, as shown in figure 5.2 (left, with the shutter at right). As the disk rotated at a more-or-less uniform speed, the projected images appeared to move, recreating the movement of the horse. One complete cycle took about one or two seconds.7
1880 年 1 月 16 日,迈布里奇在 Leland Stanford 位于旧金山的豪宅中放映了这部假定的第一部电影。但这种说法存在几个问题。为了例如,他没有投影相框。它们是从照片中衍生出来的画作。他用一定程度的扭曲修改了画作——水平拉长的腿和身体——以适应他的投影系统的扭曲伪影。而且他没有电影摄影机,只有一系列静态摄影机,每个摄影机的视角略有不同。最后,只有他可以使用该系统,因为它已经固定到位。说一个没有电影摄影机、不使用胶卷、不投影照片的系统是一个电影系统,这是一个太大的飞跃。就像几乎是计算机一样,他的系统充其量也就是电影,这是一个延伸。8
Muybridge showed this supposed first movie in Leland Stanford’s San Francisco mansion on January 16, 1880. But there are several problems with this claim. For instance, he didn’t project photographic frames. They were paintings derived from photographs. And he modified the paintings with a certain amount of distortion—horizontally elongated legs and bodies—to accommodate a distortion artifact of his projection system. And he didn’t have a movie camera, only a sequence of still cameras, each with a slightly different point of view. And, finally, only he could use the system, as it was fixed in place. It’s too large a leap to say that a system that didn’t have a motion-picture camera, didn’t use film, and didn’t project photographs was a movie system. Like the almost-computer, his system was at best almost-cinema, and that’s a stretch.8
迈布里奇并不是第一个展示静止图像运动的人,无论是摄影静止图像还是从中衍生出的轮廓。在 1860 年代和 1870 年代流行的 Zoëtrope 做到了这一点(图 5.3)。想象一个大约半英尺高、直径两英尺的纸板圆筒。如果你打开盒子里的灯,如果你足够小,可以放进盒子里,你会看到围绕圆柱体圆周的一系列图片,它们的顶部对齐。每张图片都是一个序列中的一张,比方说一匹马在小跑中连续走几步。当然,你不能装在圆柱体里面,所以为了让你从外面窥视,每张照片之间的墙壁上都开有缝隙。通过每个狭缝,您可以看到对面墙上的一张图片。如果你要在圆柱体外面走来走去,你会看到每个缝隙都显示下一张图片,即马小跑的下一部分。现在想象一下,当圆柱体转动时,您从外部固定位置观察圆柱体。在狭缝之间,你看到了黑暗。只有当狭缝旋转到位时,您才能看到图片。就是正对面的图片,是马的下一段小跑。因此,当圆柱体以适当的速度旋转时,您会看到一系列照片,显然都在同一个位置,从您的眼睛穿过圆柱体。从这一系列样本中,您可以看到一匹马在小跑。您可能已经意识到这或多或少也是电影电影的工作方式,鼓的黑暗部分用作快门。图 5.3 由 William Kennedy Laurie (WKL) Dickson 绘制——这个名字值得记住。现在想象一下,当圆柱体转动时,您从外部固定位置观察圆柱体。在狭缝之间,你看到了黑暗。只有当狭缝旋转到位时,您才能看到图片。就是正对面的图片,是马的下一段小跑。因此,当圆柱体以适当的速度旋转时,您会看到一系列照片,显然都在同一个位置,从您的眼睛穿过圆柱体。从这一系列样本中,您可以看到一匹马在小跑。您可能已经意识到这或多或少也是电影电影的工作方式,鼓的黑暗部分用作快门。图 5.3 由 William Kennedy Laurie (WKL) Dickson 绘制——这个名字值得记住。现在想象一下,当圆柱体转动时,您从外部固定位置观察圆柱体。在狭缝之间,你看到了黑暗。只有当狭缝旋转到位时,您才能看到图片。就是正对面的图片,是马的下一段小跑。因此,当圆柱体以适当的速度旋转时,您会看到一系列照片,显然都在同一个位置,从您的眼睛穿过圆柱体。从这一系列样本中,您可以看到一匹马在小跑。您可能已经意识到这或多或少也是电影电影的工作方式,鼓的黑暗部分用作快门。图 5.3 由 William Kennedy Laurie (WKL) Dickson 绘制——这个名字值得记住。只有当狭缝旋转到位时,您才能看到图片。就是正对面的图片,是马的下一段小跑。因此,当圆柱体以适当的速度旋转时,您会看到一系列照片,显然都在同一个位置,从您的眼睛穿过圆柱体。从这一系列样本中,您可以看到一匹马在小跑。您可能已经意识到这或多或少也是电影电影的工作方式,鼓的黑暗部分用作快门。图 5.3 由 William Kennedy Laurie (WKL) Dickson 绘制——这个名字值得记住。只有当狭缝旋转到位时,您才能看到图片。就是正对面的图片,是马的下一段小跑。因此,当圆柱体以适当的速度旋转时,您会看到一系列照片,显然都在同一个位置,从您的眼睛穿过圆柱体。从这一系列样本中,您可以看到一匹马在小跑。您可能已经意识到这或多或少也是电影电影的工作方式,鼓的黑暗部分用作快门。图 5.3 由 William Kennedy Laurie (WKL) Dickson 绘制——这个名字值得记住。从这一系列样本中,您可以看到一匹马在小跑。您可能已经意识到这或多或少也是电影电影的工作方式,鼓的黑暗部分用作快门。图 5.3 由 William Kennedy Laurie (WKL) Dickson 绘制——这个名字值得记住。从这一系列样本中,您可以看到一匹马在小跑。您可能已经意识到这或多或少也是电影电影的工作方式,鼓的黑暗部分用作快门。图 5.3 由 William Kennedy Laurie (WKL) Dickson 绘制——这个名字值得记住。9
And Muybridge wasn’t anywhere near the first to show movement from stills, either photographic stills or silhouettes derived from them. The Zoëtrope, popular in the 1860s and 1870s did that (figure 5.3). Imagine a cardboard cylinder about a half foot high and two feet in diameter. If you turned on a light inside the box, and if you were small enough to fit inside, you would see a sequence of pictures around the circumference of the cylinder, their tops aligned. Each picture would be one from a sequence, let’s say of a horse taking successive steps during a trot. Of course, you can’t fit inside the cylinder, so to allow you to peer in from the outside, slits are cut in the walls between each picture. Through each slit you see one picture positioned on the opposite wall. If you were to walk around outside of the cylinder, you would see that each slit reveals the next picture, the next part of the horse’s trot. Now imagine that you view the cylinder from a fixed position outside as it turns. Between the slits, you see darkness. You see a picture only when a slit rotates into position. It’s the picture directly opposite, which is the next part of the horse’s trot. So, as the cylinder rotates at the proper speed you see a succession of pictures, all apparently in the same location, across the cylinder from your eye. From this succession of samples, you perceive a horse moving in a trot. You probably recognize that this is more-or-less how film movies work, too, with the dark parts of the drum serving as the shutter. Figure 5.3 was drawn by William Kennedy Laurie (W.K.L.) Dickson—a name worth remembering.9
Zoëtrope 中的图片可以是照片或源自照片的绘画。如果你忽略图像来源于照片的要求,那么中国人在大约两千年前就发明了西洋镜。西洋镜中的图像不仅限于马。10
The pictures in a Zoëtrope could be photographs or paintings derived from photographs. If you omit the requirement that the images originate as photographs, then the Chinese invented the Zoëtrope almost two millennia ago. And the images in a Zoëtrope weren’t restricted to horses.10
迈布里奇也不是第一个投影图像序列的人。Athanasius Kircher 在 1671 年就这样做了,或者至少写过它。关于写作的附带条件是必要的,因为 Kircher 将镜头放在幻灯片的错误一侧(图 5.4),如果他实际制造了投影仪,他会注意到这一点。实施是橡胶与创意之路相遇的地方。11
Nor was Muybridge the first to project sequences of images. Athanasius Kircher was doing that in 1671, or at least writing about it. The proviso about writing is necessary because Kircher placed the lens on the wrong side of the slides (figure 5.4), something he would’ve noticed had he actually built the projector. Implementation is where the rubber meets the road for ideas.11
图 5.3
Figure 5.3
在本章的后面,我们将从现实世界中拍摄的真人电影到由虚幻世界制作的动画电影。令人惊讶的是,迈布里奇的原创贡献与动画电影更为相关。上个世纪的动画师通过用墨水逐帧追踪在摄影胶片上运动中捕捉到的人或动物,从电影中衍生出卡通片。这种技术,称为rotoscoping,是迈布里奇为他所谓的第一部电影所做的。
Later in this chapter we’ll proceed from live-action films taken in the real world to animated movies made of unreal worlds. Muybridge’s original contributions are more pertinent, surprisingly, to animated movies. Animators of the last century derived cartoons from film by tracing in ink, frame by frame, over humans or animals captured in motion on photographic film. This technique, called rotoscoping, is what Muybridge did for his supposed first movie.
动画师也以扭曲他们的卡通而闻名——使用称为挤压和拉伸、夸张和预期的技术——以适应低幼稚的采样电影率。迈布里奇在那部所谓的第一部电影中拉伸了马匹(或为他完成了工作)。仔细查看迈布里奇光盘上的图像。因此,他可以更恰当地被人们铭记为第一个使用转描和拉伸的人,这一成就有点羞于发明电影。12
Animators also famously distort their cartoons—with techniques called squash and stretch, exaggeration and anticipation—to accommodate for the low naive sampling rate of movies. Muybridge stretched the horses in that supposed first movie (or had the work done for him). Look carefully at the images on the Muybridge disc. So he can more properly be remembered as the first to use rotoscoping and stretch, an accomplishment a bit shy of inventing cinema.12
图 5.4
Figure 5.4
如果你想一想,迈布里奇最真正令人难忘的遗产是那些移动的裸体和动物的连续照片的奇妙静态阵列,今天仍然普遍作为他的作品集的明信片、海报或专辑。它们像数字图像中的像素光栅一样从左到右和从上到下排列。
If you think about it, Muybridge’s most truly memorable legacy are those marvelous static arrays of sequential photographs of moving nudes and animals, still pervasive today as postcards, posters, or albums of his collected works. They are arrayed left to right and top to bottom like the raster of pixels in a digital image.
动画师高度重视这些迈布里奇光栅。在 1920 年代初期,两个年轻的朋友,Ub Iwerks 和 Walt Disney,在他们推出了他们刚刚起步的动画业务时向他们学习。动画师今天仍然尊重他们。图 5.5 是 Pixar 动画师的恶搞和高度赞扬。迈布里奇为斯坦福大学著名地证明了一匹马的所有四英尺都在一帧内离开地面,而这项“最近重新发现的工作”确定了 Luxo 台灯的一英尺离开地面四帧。
Animators hold these Muybridge rasters in high regard. In the early 1920s two young pals, Ub Iwerks and Walt Disney, learned from them as they launched their fledgling animation business. And animators still honor them today. Figure 5.5 is a spoof—and high tribute—by Pixar animators. Muybridge famously proved for Stanford that all four feet of a horse leave the ground in one frame, while this “recently rediscovered work” establishes that the one foot of a Luxo desk lamp leaves the ground for four frames.
一些作家指责强盗男爵斯坦福从迈布里奇那里窃取信用,但检查记录表明并非如此。几十年前,在浏览在一家古董书店,我发现了一本 1882 年的大型毛绒书,名为《奔跑的马》。我相信这是最初的迈布里奇研究,对任何对动画感兴趣的人都很有名。
Some writers have accused robber-baron Stanford of stealing credit from Muybridge, but inspection of the record indicates otherwise. Several decades ago, while browsing an antique bookstore, I discovered a large plush book from 1882 titled The Horse in Motion. I leapt at it believing it to be the original Muybridge study that was famous to anyone interested in animation.
图 5.5
Figure 5.5
©皮克斯。
© Pixar.
但事实并非如此——反正也不完全是。首先,作者不是迈布里奇。是我从未听说过的 JDB Stillman。打开扉页,我发现 Leland Stanford 确实资助了该出版物,正如预期的那样。迈布里奇在哪里?我很快就找到了他,作为“先生。迈布里奇,”在第一段中突出显示。“由 EJ Muybridge 先生提供”的附录描述了他的技术。和“先生。迈布里奇”也出现在最后一段,从而包含了整本书。13
But it wasn’t—not exactly anyway. For starters, the author wasn’t Muybridge. It was J. D. B. Stillman, whom I’d never heard of. Opening to the title page, I found that Leland Stanford had indeed funded the publication, as expected. Where was Muybridge? I soon found him, as “Mr. Muybridge,” prominently displayed in the very first paragraph. An appendix “furnished by Mr. E. J. Muybridge” described his technique. And “Mr. Muybridge” appeared in the very last paragraph too, thus embracing the entire book.13
从正文中可以清楚地看出,斯坦福和斯蒂尔曼根本不关心摄影。马的运动对他们来说很重要。迈布里奇的照片与其说是艺术品,不如说是出租作品——称它们为意味着结束。斯蒂尔曼确实提到了作品的艺术意义,但他的意思只是艺术家对马的准确演绎。马就是问题。那么,为什么迈布里奇会因为这本书起诉斯坦福?
It’s clear from the main text that Stanford and Stillman simply didn’t care about photography. The movement of horses was the important thing to them. Muybridge’s photographs served less as works of art than they did as works for hire—call them a means to an end. Stillman does mention the artistic import of the work, but he meant only the accurate rendition of horses by artists. The horses were the thing. So why did Muybridge sue Stanford over this book?
图 5.6
Figure 5.6
到其出版时,他已前往巴黎并为自己加冕为高贵的 Eadweard(图 5.6,右)。他向那里的艺术界宣布,他发明了一种新的艺术形式,并且是大亨斯坦福的好友(图 5.6,左)。他用马和人在运动中让他们惊叹不已。他是预测运动的雄狮营销者,他受到了崇拜。他还说服了艾萨克·牛顿在英国的皇家学会接受他的论文《运动中动物的态度》并安排出版。但随后斯蒂尔曼的书出现了,仅仅提到了受雇工作,斯坦福声称拍摄一匹运动的马是他自己的想法。重要的是,迈布里奇的名字不在扉页上。皇家学会拒绝发表这篇论文,怀疑是抄袭。迈布里奇被羞辱了。他的一些新粉丝认为他是个骗子。14
By the time of its publication he had gone to Paris and crowned himself the noble Eadweard (figure 5.6, right). He announced to the artistic community there that he had invented a new artform and was a buddy of tycoon Stanford (figure 5.6, left). He wowed them with horses and men in motion. He was a leonine marketer of projected movement, and he was lionized. He also had convinced Isaac Newton’s Royal Society in England to accept his paper On the Attitudes of Animals in Motion and schedule it for publication. But then Stillman’s book appeared with the mere work-for-hire mention and Stanford’s claim that it was his own idea to film a horse in motion. Importantly, Muybridge’s name wasn’t on the title page. The Royal Society reneged on the offer to publish the paper, suspecting plagiarism. Muybridge was humiliated. Some of his new fans thought he was a fraud.14
他把西装弄丢了。现在这一切似乎都被误导了。斯坦福的一切都是关于马的。迈布里奇是关于摄影技术的。拍摄运动中的马是斯坦福在 1872年的想法——这一想法受到 1874 年科普文章的重新启发关于 Étienne-Jules Marey 在法国的工作。但正是迈布里奇的发明使之成为可能。这是一场不同形式的塔楼与恶臭之战——理念与工程。斯坦福将这些照片全部归功于他为这项任务聘请的人。事实上,他以一美元的价格将这项技术的知识产权转让给了迈布里奇。他完全错过了这项技术的潜在进口,无论是在艺术上还是在经济上。15
And he lost the suit. It all seems so misguided now. Stanford was all about the horses. Muybridge was all about the photographic technique. It was Stanford’s idea in 1872 to film the horse in motion—an idea re-inspired by an 1874 Popular Science article about the work of Étienne-Jules Marey in France. But it was Muybridge’s invention that made it possible. It’s a tower versus stinks battle in a different guise—the idea versus the engineering. Stanford gave full credit for the photographs—to the man he had hired for the task. In fact, he signed away the intellectual property rights for the technique to Muybridge—for a dollar. He completely missed the potential import of the technique, both artistically and financially.15
然而,富有的斯坦福大学凭借知名度、金钱、设备和空间,让发明家迈布里奇向世界展示了快速拍摄以相同快速序列投影的连续照片给人一种运动的错觉。斯坦福为此付出了代价——付出了很多——却从来不知道他到底资助了什么。这不是关于马的。华丽的迈布里奇成功地将这个想法推向了广泛的领域——这也许是他对电影最重要的贡献。“电影之父”对他来说似乎离谱,但“电影的约翰尼苹果种子”却很合适。特别是,他的节目激发了托马斯·阿尔瓦·爱迪生对美国电影的兴趣,并影响了法国的马雷。这就是即将到来的洋基队与法兰克队比赛的第一缕曙光。16
Nevertheless, the wealthy Stanford made it possible—with name recognition, money, equipment, and space—for Muybridge the inventor to show the world that rapidly shot sequential photographs projected in the same quick sequence give the illusion of motion. Stanford paid for it—paid a lot—without ever understanding exactly what it was that he had funded. It wasn’t about the horses. And flamboyant Muybridge successfully marketed the idea far and wide—perhaps his most important contribution to cinema. “The father of cinema” seems way off the mark for him, but “the Johnny Appleseed of cinema” fits nicely. In particular, his show inspired Thomas Alva Edison’s interest in motion pictures in America and influenced Marey in France. And that’s the first glimmer of the Yanks versus Franks contest to come.16
对计算机的仔细定义帮助我们修剪了计算机故事中的历史主张。它扫清了通往 Digital Light 的道路。我们可以对电影史采用相同的技术。
A careful definition of computer helped us prune the thicket of historical claims in the story of computers. It cleared the path to Digital Light. We can employ the same technique for cinema history.
让我们也使用另一种适用于计算机的方法:将硬件与软件分开。对于电影院来说,电影本身就是软件。事实上,软件本身就是我们通常所说的“电影院”。我们可以在电影、电视或手机上看到《公民凯恩》。像往常一样,神奇之处在于软件——钢琴中的肖邦练习曲。但这本书的一个基本概念建立在对我们现代媒体文化的欣赏之上,而现代媒体文化本身依赖于对其技术基础的直观理解——在这两个领域中看到奇迹和美景。由于有大量关于电影软件(电影)的书籍,我们专注于未被充分认识的硬件。
Let’s also use another approach that worked for computers: separate hardware from software. For cinema, the movies themselves are the software. In fact, the software alone is what we usually mean by “the cinema.” We can see Citizen Kane on film, television, or cellphone. As usual, the magic lies in the software—the Chopin étude in a piano. But a fundamental notion of this book rests on an appreciation of our modern media culture that itself depends on an intuitive understanding of its technological underpinnings—on seeing marvels and beauties in both realms. Since there are a host of books on movie software—the cinema—we concentrate on the underappreciated hardware.
但在过于仓促地转向硬件之前,让我们先看看电影软件的一个奇怪之处。尽管电影放映机只能沿电影的一个方向移动,但存储在电影上的软件可以让观众感知时间倒退(倒叙,爱尔兰人)或向前(比如十年后,甚至千年,2001:太空漫游)的事件),或者无限循环(土拨鼠日),或者随着变化的重复(罗生门)。就好像电影软件在我们的大脑上计算了它在电影硬件上无法计算的东西。
But before heading too hastily toward hardware, let’s notice a curious thing about cinema software. Although a movie projector moves along film in one direction only, software stored on the film can make viewers perceive events that jump backward in time (flashbacks, The Irishman) or forward (say ten years later, or millennia even, 2001: A Space Odyssey), or in infinite loops (Groundhog Day), or as repetition with change (Rashomon). It’s as if movie software computes on our brains what it can’t compute on movie hardware.
没有一个词可以形容那种硬件,电影院的硬件。经典电影具有三个可分离的部分:相机、胶卷和投影仪。通过说电影机器,我们指的是所有三个——就好像它们在一个黑盒子里一样——这就是我们的定义。电影机器之于电影就像计算机之于计算。少了任何东西,充其量就是一台电影机器——就像上一章的电脑一样。由于硬件在这里是隐含的,所以我经常放弃机器这个词,并将电影和电影这两个术语与电影互换使用。17
There’s no single word for that hardware, the hardware of cinema. Classic cinema has three separable pieces: camera, film, and projector. By saying movie machine, we mean all three—as if they were in one black box—and that’s our definition. A movie machine is for cinema what a computer is for computation. Anything less is, at best, an almost movie machine—like the almost-computer of the last chapter. Since hardware is implicit here, I often drop the word machine and use the terms motion picture and cinema interchangeably with movie.17
所以,当我们问谁制作了第一部电影时,我们并不是指第一个内容。我们指的是谁拥有第一台电影机——第一台相机、胶片和投影仪作为一个系统协同工作。这就是上世纪大部分时间我们所说的电影,硬件方面的意思,今天仍然如此。在数码光中,我们有数码相机,存储数码相框,并用数码投影仪进行投影。
So, when we ask who made the first movie, we don’t mean the first content. We mean who had the first movie machine—the first camera, film, and projector working together as one system. That’s what we meant by a movie, hardware-wise, most of last century, and it still means that today. In Digital Light, we have digital cameras, store digital frames, and project them with digital projectors.
电影应该起作用并不明显。电影并不像进入我们眼睛的视觉那样流畅。相机每秒只记录 24 个视觉流的快照,并丢弃帧之间发生的一切——但我们还是感知到了流。我们看到静止,但我们感知到运动。我们该如何解释呢?
It’s not obvious that movies should work. Movies are not smooth like the visual flow into our eyes. The camera records only 24 snapshots of each second of visual flow, and discards everything that happens between frames—but we perceive flow anyway. We see stills, but we perceive motion. How can we explain this?
如果我们今天从采样定理开始作为数字光的一部分发明电影系统,它会是什么样子?答案似乎很简单:以视觉流中最高时间频率的两倍将视觉流采样到帧中,然后在投影期间使用良好的扩展器将帧扩展回平滑的视觉流——就像我们将像素变成单个静止图片一样.
What could a movie system be like if we invented it today, as part of Digital Light, starting with the Sampling Theorem? The answer seems straightforward: sample a visual flow into frames at twice the highest temporal frequency in the visual flow, then use a good spreader during projection to spread the frames back into a smooth visual flow—just as we turned pixels into a single still picture.
让我们把这个描述分开。首先,视觉流中的频率是多少?傅里叶用来表示它的波是什么?我们必须先了解这一点,然后才能应用采样定理——最高频率两倍的采样业务。我们还需要确定视觉流中的“最高频率”是什么意思。然后我们必须弄清楚投影帧的“好的吊具”是什么。展开框架是什么意思?
Let’s take that description apart. First, what are the frequencies in a visual flow? What are the waves that Fourier would use to represent it? We have to understand that before we can apply the Sampling Theorem—the sample-at-twice-the-highest-frequency business. We also need to decide what “the highest frequency” in a visual flow means. Then we have to figure out what “a good spreader” is for projected frames. What does spreading a frame mean?
对于音频,波是声波。对于静止的视觉场景,波浪是傅里叶章节中显示的光强度的起伏波纹。回想一下我对伯克利多肉花园的直观分析。需要一些练习才能开始“看到”构成该视觉场景的有节奏的空间波。在视觉流中“看到”波浪也需要练习。
For audio the waves are sound waves. For a still visual scene the waves are the undulating corrugations of light intensity shown in the Fourier chapter. Recall the intuitive analysis of my succulent garden in Berkeley. It took some practice to start “seeing” the rhythmic spatial waves that make up that visual scene. It takes practice to “see” the waves in a visual flow too.
这里有一些练习可以帮助你看到它们。看着一个人走过。或者一个女人慢跑。他的动作是循环的,她的也是。这是流入你眼睛的傅立叶版本的波的第一个证据。假设这个人每秒踩一次脚,或者每两秒踩一次完整的一步。那么在流的波形版本中必须有一个频率为每两秒一个周期(相当于每秒半个周期)的波。假设女人慢跑的速度是男人走路的两倍。那么,在流入你眼睛的波浪版本中,一定有一个频率为每秒一个周期的波浪。
Here are some exercises to help you see them. Watch a man walk by. Or a woman jog by. His motion is cyclic, and so is hers. That’s the first evidence of a wave in the Fourier version of the flow that’s streaming into your eyes. Suppose the man is placing a foot once every second, or one complete step every two seconds. Then there must be a wave with frequency one cycle per two seconds (equivalently, one-half cycle per second) in the wave version of the flow. Suppose that the woman is jogging twice as fast as the man walks. Then there must be a wave of frequency one cycle per second in the wave version of that flow into your eyes.
其他示例包括: 沿街道行驶的汽车流。汽车上的纺车。抽自行车踏板。嘴唇在布朗克斯欢呼。挥手告别。交响乐团指挥的手。一个弹跳球。
Other examples are: A stream of cars moving down a street. Spinning wheels on the cars. Pumping bicycle pedals. Lips in a Bronx cheer. Waving goodbye. The hands of the conductor of a symphony orchestra. A bouncing ball.
从这些到傅立叶的神奇想法是一个巨大的飞跃,但让我们接受它:你在视觉流中看到的一切都是视觉波的总和,并且只是视觉波的总和,而视觉波的东西是摆动的光强度有节奏地在空间和时间上。
It’s a giant leap from these to Fourier’s magical idea, but let’s take it: everything you see in the visual flow into your eyes is the sum of, and only of, visual waves, and the stuff of a visual wave is light intensities that wiggle rhythmically in both space and time.
在傅里叶一章中,我们将构成视觉场景的波浪(静态图片)可视化为波纹,每个波纹都有一个波浪横截面。也就是说,波纹的横截面看起来像时钟秒针描绘的波浪。幸运的是,我们不必为了使用它们而实际看到视觉流的波——运动图像的波。这很好,因为视觉流的傅里叶波是一个四维的东西,很难想象。尽管如此,让我们尝试一下。图 5.7——显示了一个时间周期的一半和四个完整的空间周期——试图显示一个这样的波,但它需要一些想象力。
In the Fourier chapter we visualized the waves that make up a visual scene—a still picture—as corrugations, each with a wave cross section. That is, a cross section of a corrugation looks like the wave traced out by a clock’s second hand. Luckily, we don’t have to actually see waves of a visual flow—of a moving picture—in order to use them. That’s good, because a Fourier wave of visual flow is a four-dimensional thing, quite difficult to picture. Nevertheless, let’s try. Figure 5.7—showing half of one temporal cycle and four full spatial cycles—is an attempt to show one such wave, but it requires some imagination.
考虑图中最顶部的波纹。它像往常一样具有频率和幅度。一个小箭头表示其幅度。请注意,该箭头的副本已被推到最右侧,然后旋转了 90 度。我很快就会回到那个旋转的箭头。
Consider the topmost corrugation in the figure. It has a frequency and an amplitude as usual. A small arrow indicates its amplitude. Notice that a copy of that arrow has been pushed out to the far right, then rotated ninety degrees. I’ll return to that rotated arrow soon.
波纹的幅度随时间变化,沿页面向下移动。此外,振幅随着时钟的秒针波的节奏平滑地变化。但我画不出来。相反,我呼吁你的想象力。
The amplitude of the corrugation changes with time, which advances down the page. Furthermore, the amplitude changes smoothly with the rhythm of a clock’s second-hand wave. But I can’t draw that. Instead, I call for your imagination.
想象一下,你正在看一个单一的波纹,但当你观察时,它的波浪高度随着波浪的节奏而变化。另一种说法是,当你观察时,所有的波谷同时变深,然后同时变浅,然后同时变深,依此类推,那种脉动的节奏就是波浪的节奏。在您的脑海中绘制该动画的单张图片是一项任务。坦率地说,就本书而言,你脑海中的动画已经足够好了。它是表示视觉流所需的各种傅里叶波。
Imagine that you’re looking at a single corrugation, but as you watch, the height of its wave varies, with the rhythm of a wave. Another way to say it is that, as you watch, all the troughs get simultaneously deeper, then simultaneously shallower, then simultaneously deeper, and so on, and the rhythm of that pulsing is the rhythm of a wave. Drawing a single picture of that animation in your mind’s eye is the task. Frankly, for the purposes of this book, the animation in your mind’s eye is good enough. It is one Fourier wave of the variety needed to represent visual flow.
图 5.7
Figure 5.7
然而,图 5.7 试图捕捉该动画。它用九个波纹(如果你愿意的话,动画的九帧)在等间隔的时间代表你脑海中的脉动波纹。我呼吁你的想象力(再次)在描绘的每一对之间的每一刻都放置一个波纹。问题是它们的模拟无穷大是必需的。
Nevertheless figure 5.7 tries to capture that animation. It represents the pulsing corrugation in your mind’s eye with nine corrugations—nine frames of the animation, if you will—at equally spaced moments in time. I call on your imagination (again) to place a corrugation at every moment between each pair depicted. The problem is that an analog infinity of them is required.
一个小箭头显示特定时刻波纹的幅度。这些小箭头的副本被推到最右边并如前所述旋转。连接旋转箭头尖端的曲线是波浪。当您想象在所描绘的任何一对之间插入波纹时,请使用右侧波上的对应点作为其幅度。
A small arrow shows the amplitude of the corrugation at a particular moment. Copies of these small arrows are pushed to the far right and rotated as described earlier. The curve that connects the tips of the rotated arrows is a wave. When you imagine inserting a corrugation between any pair depicted, use as its amplitude the corresponding point on the wave at the right.
总之,视觉流的单个傅立叶波在空间中变化为波(或波纹),并且在时间上也作为波变化。这个脉动波纹上的每个点都是一个光强度。它在所有三个维度以波浪的节奏摆动时空果冻。
In summary, a single Fourier wave for visual flow varies as a wave (or corrugation) in space, and it varies as a wave in time too. Each point on this pulsing corrugation is a light intensity. It’s wiggling spacetime Jell-O with the rhythm of a wave in all three dimensions.
所以这是一波。现在想象一下它们的整个家族,每个都以特定的频率和幅度在空间中荡漾,每个人都以另一种频率和幅度在时间中脉动。这要求很多。您可以理解为什么从业者只是简单地使用简洁地表达同一件事的数学。根据傅里叶的伟大想法,完整的视觉流是这种完美波的总和,具有许多频率和幅度(以及方向和相位)。视觉流是时空音乐。
So that’s one wave. Now imagine a whole family of them, each rippling through space with a particular frequency and amplitude, and each pulsing through time with another frequency and amplitude. That’s asking a lot. You can understand why practitioners simply use the math that succinctly says the same thing. By Fourier’s great idea, a complete visual flow is a sum of such perfect waves, of many frequencies and amplitudes (and directions and phases). A visual flow is spacetime music.
采样定理——Kotelnikov 的好主意——说我们需要以视觉流中最高时间频率的两倍来采样或帧,以便准确地表示流。最高频率可能是多少?在这一点上,早期电影创作者的完全天真变得显而易见。他们只是猜测。他们没有最高频率的概念。他们最关心的是电影的成本,而不是表现的准确性。帧速率越高,他们必须使用的胶卷就越多。因此,使用尽可能低的时间采样率在经济上是明智的。新兴的电影业很快(到 1920 年代)以每秒 24 帧的速度稳定下来,大约一个世纪以来一直如此。18
The Sampling Theorem—Kotelnikov’s great idea—says that we need to take a sample, or frame, at twice the highest temporal frequency in the visual flow in order to represent the flow accurately. What could that highest frequency be? The full naivete of the early creators of cinema becomes obvious at this point. They just guessed. They had no notion of highest frequency. The cost of film concerned them most, not the accuracy of representation. The higher the frame rate, the more film they had to use. So it was economically smart to use as low a temporal sampling rate as they could get away with. The nascent film industry rather rapidly settled (by the 1920s) on 24 frames per second, where it’s been for about a century.18
但在理想世界中,我们应该关心的视觉流的最高频率是多少?回想一下经验法则,在频率方面,视觉场景中非常锐利的边缘具有非常高的频率。在将场景采样为像素之前,我们会通过稍微模糊场景来消除任何过高的频率。否则采样失败,我们会得到令人讨厌的伪影——比如被称为锯齿的阶梯状边缘。
But in an ideal world, what’s the highest frequency in visual flow that we should care about? Recall the rule of thumb, in frequencyspeak, that a very sharp edge in a visual scene has very high frequencies. We remove any too-high frequencies by a slight blurring of the scene before sampling it into pixels. Otherwise sampling fails, and we get annoying artifacts—like the stairstepped edges called jaggies.
视觉流动也是如此——视觉场景随时间变化——同样的技巧也有效。视觉流中的锐利“边缘”是运动方向的突然变化。再想想那个路过的人。假设他正在摆动他的手臂。此时此刻他的手臂一直向后摆动,然后反转方向开始向前摆动,是一瞬间的视觉流动边缘。或者考虑一个弹跳球。反弹的时刻是视觉流中的一个尖锐边缘。在将视觉流采样到帧电影中之前,这些边缘应该被“四舍五入”才能准确工作。换言之,必须去除过高的时间频率。不这样做会产生令人讨厌的伪影——比如看起来向后旋转的轮子。我们很快就会花时间解决这个问题。
The same is true of visual flow—visual scenes changing with time—and the same trick works. A sharp “edge” in visual flow is a sudden change in direction of movement. Think of that man walking by again. Suppose he is swinging his arms. The moment that his arm swings all the way back, then reverses direction to begin the swing forward, is a moment of visual flow edge. Or consider a bouncing ball. The moment of bounce is a sharp edge in visual flow. Those edges should be “rounded off” before the sampling of visual flow into a movie of frames can work accurately. In other words, temporal frequencies that are too high must be removed. Failure to do so creates annoying artifacts—like wheels that appear to spin backward. We’ll spend time on that problem shortly.
理想的电影放映机如何从离散帧重建视觉流?正如已经建议的那样,可以使用与显示设备如何从离散像素重建视觉场景直接类比的采样定理来完成。显示器使用像素散布器(通过空间)散布每个像素,并将结果相加。理想的投影仪会通过帧扩展器扩展每一帧——随着时间的推移——并将结果相加。那么,什么是框架扩展器?
How would an ideal movie projector reconstruct a visual flow from discrete frames? As already suggested, it could be done using the Sampling Theorem in direct analogy with how a display device reconstructs a visual scene from discrete pixels. A display spreads each pixel with a pixel spreader—through space—and adds up the results. An ideal projector would spread each frame with a frame spreader—through time—and add up the results. So, what’s a frame spreader?
图 5.8(上)提醒我们采样定理的理想散布器是什么样的。对于 soxels(音频样本或声音元素),这是及时的扩展器。在像素的情况下,这是理想像素散布器在空间中的横截面。在电影帧的情况下,它是理想帧扩展器的横截面。
Figure 5.8 (top) reminds us of what the ideal spreader of the Sampling Theorem looks like. In the case of soxels (audio samples, or sonic elements), this is the spreader—in time. In the case of pixels, this is a cross section—in space—of the ideal pixel spreader. In the case of movie frames, it’s a cross section—in time—of the ideal frame spreader.
这种理想的吊具在实践中无法实现,因为它的范围是无限的。这些摆动在任何一个方向上都会永远持续下去。图 5.8(中)中的近似值是我们在 Kotelnikov 章节中使用的近似值,用于从像素中很好地重建视觉场景。
This ideal spreader cannot be realized in practice because it’s infinite in extent. Those wiggles go on forever in either direction. The approximation in figure 5.8 (middle) is the one we used in the Kotelnikov chapter for good reconstruction of a visual scene from pixels.
但即使是这种近似的扩展器也不适用于老式的模拟电影世界,因为有两个负波瓣 - 水平线下方的两个倾角。我们不知道如何使投影仪的光变为负值(小于黑色),因此我们无法实现上面的帧扩展器。然而,我们可以使用图 5.8(底部)中的近似值。
But even this approximate spreader doesn’t work for the old-fashioned, analog movie world because of those two negative lobes—the two dips below the horizontal line. We don’t know how to make projector light go negative (less than black) so we can’t realize the frame spreader above. We could, however, use the approximation in figure 5.8 (bottom).
由于扩展框架对大多数人来说是一个新想法,让我们逐步了解这种扩展器形状的含义。时间在下图中向右推进,图 5.9,水平线中心的点表示当前帧时间——投影仪对该帧最大照明的时刻。中心左侧的点代表前一帧时间——当它达到最大照明时。中心右侧的点代表下一帧时间——当它达到最大照明时。等等。详细地说,投影仪光在前一帧时间内逐渐出现(由中心左侧的点表示)。它在当前帧时间的瞬间(中心的点)达到最大强度。然后逐渐消亡在随后的帧时间内(中心右侧的点)。这就是及时传播帧的含义。
Since spreading a frame is a new idea to most, let’s step through what this spreader shape means. Time advances to the right in the next figure, figure 5.9, and the dot at the center of the horizontal line represents the current frame time—the moment of maximum illumination of that frame by the projector. The dot left of center represents the preceding frame time—when it reached its maximum illumination. The dot right of center represents the next frame time—when it will reach its maximum illumination. And so forth. In detail, the projector light comes up gradually during preceding frame times (represented by the dots to the left of center). It reaches full intensity at the instant of the current frame time (the dot at the center). Then it dies off gradually during subsequent frame times (dots to the right of center). That’s what it means to spread a frame in time.
图 5.8
Figure 5.8
您可能还记得,样本的重建是通过将扩展器应用于所有样本并将结果相加来完成的。这是棘手的部分,因为现在我们在时间而不是空间上传播。这意味着在查看当前帧时,我们仍然看到前两帧并开始看到接下来的两帧。由于良好的吊具重叠,理想的投影仪可以同时照亮多个帧。它将投影镜头处的贡献加在一起,从而加到屏幕上。选择的时刻(图 5.9 中的垂直线)恰好发生在当前帧的最大照明之前。在那一刻,前一帧的照明已经下降到大约三分之一的全强度,而前一帧的照明几乎为零。同时,当前帧之后的帧的照明刚刚开始出现。之后的框架还没有点亮。因此,在所选瞬间,四帧对投影图像有贡献——当然是当前帧,还有前两帧和后一帧的添加。
As you might recall, reconstruction from samples is done by applying the spreader to all samples and adding up the results. This is the tricky part because now we’re spreading in time instead of space. This means that while viewing the current frame, we’re still seeing the previous two frames and are starting to see the next two frames. Because good spreaders overlap, the ideal projector illuminates several frames simultaneously. It adds the contributions together at the projection lens and hence onto the screen. The moment chosen (the vertical line in figure 5.9) occurs just before maximum illumination of the current frame. At that moment, illumination of the preceding frame has dropped to about one-third full intensity, and of the frame before that to nearly zero illumination. At the same time, the illumination of the frame following the current one is just starting to come up. The frame after that isn’t lit at all yet. So four frames contribute to the projected image at the chosen instant—the current frame, of course, but also additions from the two before and the one after.
图 5.9
Figure 5.9
令人惊讶的是:实际上从来没有这样的电影放映机存在过。抽样理论告诉我们,本来可以有一个美丽完美的电影系统。这样的投影仪可以重建平滑的视觉流程。我们的眼睛进化到能够感知以这种方式呈现的世界。这不是我们所拥有的,但这个练习告诉我们我们可以拥有什么,以及在数字时代我们应该对电影提出什么要求。没有理由不应该存在这样的系统。19
Here’s the surprise: No such film projector has ever actually existed. Sampling theory informs us that there could have been a beautiful perfect movie system. Such a projector could have reconstructed a smooth visual flow. Our eyes evolved to perceive the world presented just that way. It’s not what we had, but the exercise tells us what we could have had and what we should be asking of cinema in the digital age. There’s no reason such a system should not exist.19
现实世界的电影实际上是那个理想系统的粗略近似——而且它足够接近,可以做得很好。让我们看看它是如何工作的,疣和所有。
Real-world cinema was actually a crude approximation of that ideal system—and it was close enough to do pretty well. Let’s see how it worked, warts and all.
电影的发明者做了什么(或没有做什么)使他们给我们的系统如此不理想?首先,他们没有按照抽样要求给我们瞬时样本。电影框架很胖。他们有持续时间。相机快门打开一小段曝光时间。一个移动的物体在那个短时间间隔内移动,因此在胶片曝光期间会稍微拖过画面。这就像当您尝试拍摄您的孩子扔球的长时间曝光静态照片时会发生什么,而他的手臂只是一片模糊。事实证明,这是电影的一种节省方式,因为它实际上是在实践的。
What did the inventors of cinema do (or not) to make the system they gave us so non-ideal? First, they didn’t give us instantaneous samples as required by sampling. Film frames are fat. They have duration. The camera shutter is open for a short exposure time. A moving object moves during that short interval, and so smears slightly across the frame during the film exposure time. It’s like what happens when you try to take a long-exposure still photo of your child throwing a ball and his arm is just a blur. This turns out to be a saving grace of cinema as it was actually practiced.
其次,他们做到了,每一帧都被投影仪投影两次(至少)。哎哟! 这根本不是抽样。发明者为什么这样做?简单的经济学要求它:每秒 24 帧的胶卷成本是每秒 48 帧的一半。但是眼睛需要每秒刷新大约 50 次,否则视网膜图像会在帧之间褪色。实际上,48 与 50 接近,足以在黑暗的剧院工作。如何从 24 中获得 48?您将每帧显示两次!如果每秒仅显示 24 帧,则屏幕会闪烁。因此,在采用更高帧速率之前,电影早期的“轻弹”。
Second, they made it so each frame is projected twice (at least) by the projector. Ouch! That’s not sampling at all. Why did the inventors do that? Simple economics demanded it: 24 frames per second costs half as much film as 48 frames per second. But the eye needs to be refreshed about 50 times per second, or the retinal image fades between frames. Actually, 48 is close enough to 50 to work in a dark theater. How do you get 48 from 24? You show each frame twice! If you show just 24 frames per second, the screen appears to flicker. Hence the “flicks” from the early days of cinema before higher frame rates were adopted.
最初的发明者做的第三件事是关闭投影帧之间的光。这意味着每秒 48 次,没有任何东西(黑度)投射到眼睛中——瞳孔内,视网膜上。对电影机来说很方便——两者兼而有之相机和投影仪部件——在帧之间像这样“快门”到黑色。它为下一个胶片帧的机械推进到位留出了时间。在相机中,它使胶卷在胶卷的物理推进过程中无法记录真实世界。在投影仪中,它使移动的胶片在物理上处于先进状态时不被看到。
The third thing the original inventors did was to shut off the light between projected frames. This meant that 48 times per second, nothing (blackness) was projected into the eye—inside the pupil, onto the retina. It’s convenient for movie machines—both the camera and projector parts—to “shutter” to blackness like this between frames. It allows time for the mechanical advancement of the next film frame into position. In a camera, it keeps the film from recording the real world during the physical advancement of the film. In a projector, it keeps the moving film out of eyesight as it’s physically advanced.
当你问电影放映机的工作原理时,有人会这样说:有一个上卷轴是胶卷的来源,一个下卷轴。胶片从一个卷轴移动到另一个卷轴,并在投影机的光源和镜头之间通过,从而将帧大小的图像放大到屏幕大小。换言之,胶片连续移动通过光源。但这不起作用。眼睛可以准确地看到那里有什么,通过这种方案,当下一帧从另一侧滑入时,眼睛会看到一帧滑开。它会看到滑动。那是行不通的。
When you ask how a movie projector works, some people say something like this: There’s a top reel of film which is the source of film, and a bottom take-up reel. The film moves from reel to reel and passes between the light source of the projector and its lens, which magnifies the frame-size image up to screen size. In other words, the film moves continuously past the light source. But that doesn’t work. The eye sees exactly what’s there, and with this scheme the eye would see one frame sliding away as the next frame slides in from the opposite side. It would see the sliding. And that won’t work.
投影仪实际上所做的正是这样:它将每一帧都置于固定位置,并遮住光源。这就是快门的作用。然后快门打开,被照亮的框架投射到屏幕上。然后快门关闭。然后它再次打开,被照亮的框架第二次投射到屏幕上。然后快门关闭,下一帧滑入到位,依此类推。
What a projector actually does is exactly this: It brings each frame into fixed position with the light source blocked. That’s the function of the shutter. Then the shutter opens and the illuminated frame projects onto the screen. Then the shutter closes. Then it opens again, and the illuminated frame is projected a second time onto the screen. Then the shutter closes and the next frame slides into position, and so forth.
我们刚刚描述了胶片通过放映机的离散或间歇运动,而不是不可行的连续运动。同样的想法也适用于相机。实现这一动作的物理装置,实际上称为间歇运动。这是电影史上的关键概念,可与计算机历史中的条件分支指令相媲美。对电影机的疯狂追捧取决于谁首先让投影仪正常工作,而这取决于谁让间歇性运动正常工作。这是一个定义性的概念。20
We’ve just described the discrete, or intermittent, movement of film through a projector, as opposed to unworkable continuous movement. The same idea holds for a camera. The physical device that implements this action is called, in fact, an intermittent movement. This is the key notion in cinema history that is comparable to the conditional branch instruction in computer history. The mad rush to the movie machine turned on who first got a projector to work correctly, and that hinged on who got an intermittent movement working properly. It’s a defining notion.20
回顾一下:基于电影的实际电影放映机不会从帧样本中重建连续的视觉流并将其呈现给眼睛。相反,它会将“脂肪样本”——随着时间的推移和运动模糊而变厚——直接发送到眼睛的视网膜。它每帧发送两次,并在两者之间发送黑度。从这些输入中重建运动取决于大脑。这是如何运作的?
To recap: An actual film-based movie projector doesn’t reconstruct a continuous visual flow from the frame samples and present this to the eye. Instead, it sends “fat samples”—thick with time duration and smeared motion—directly to the eye’s retina. It sends each frame twice, and it sends blackness between. It’s up to the brain to reconstruct motion from these inputs. How does that work?
不知何故,眼脑系统“重建了由它接收到的脂肪视觉样本所代表的视觉流”。当然,它真的没有这样的事情。光强度作为输入通过瞳孔进入。但从眼睛到大脑的输出,通过视神经,是一个电化学脉冲序列。神经元脉冲序列不是视觉流。可能是视网膜确实重建了视觉流,然后将其转换为脉冲序列供大脑消耗。眼睛中一些神经元的反应肯定表明了扩张器功能,完成了高正驼峰和负叶。但是大脑活动超出了本书的范围。让我们而是专注于从静止快照序列中对运动感知的习惯解释。
Somehow the eye-brain system “reconstructs the visual flow” that’s represented by the fat visual samples it receives. Of course, it really does no such thing. Light intensities come in through the pupil as input. But the output from the eye to the brain, through the optic nerve, is an electrochemical pulse train. Neuronal pulse trains aren’t visual flows. It could be that the retina actually does reconstruct a visual flow and then converts it to pulse trains for brain consumption. The responses of some of the neurons in the eye certainly suggest the spreader function, complete with a high positive hump and negative lobes. But brain activity is beyond the scope of this book. Let’s concentrate instead on the customary explanations of the perception of motion from sequences of still snapshots.
经典的解释是陈旧的视力持久性. 这是人类视觉的一个真实特征:一旦对视网膜的图像刺激停止,我们会在短时间内继续感知那里的图像。但视觉暂留只能解释为什么在电影电影的情况下看不到帧之间的黑度。如果演员或动画角色在帧之间移动到一个新位置,那么——通过视觉的持久性——你应该在两个位置上看到他:两个汉弗莱·鲍嘉,两个巴斯光年。事实上,你的视网膜确实看到了两者,一个随着另一个进入而淡出——每一帧都被投射足够长的时间来确保这一点。这就是视觉的持久性。但这并不能解释为什么你感知到一个移动的物体,而不是两个不同位置的物体。
The classic explanation is hoary old persistence of vision. It’s a real characteristic of human vision: once an image stimulus to the retina ceases, we continue to perceive the image there for a short while. But persistence of vision explains only why you don’t see the blackness between frames in the case of film-based movies. If an actor or an animated character moves to a new position between frames then—by persistence of vision—you should see him in both positions: two Humphrey Bogarts, two Buzz Lightyears. In fact, your retinas do see both, one fading out as the other comes in—each frame is projected long enough to ensure this. That’s persistence of vision. But it doesn’t explain why you perceive one moving object, not two objects at different positions. What your brain does with the information from the retinas determines whether you perceive two Bogarts in two different positions or one Bogart moving between them.
心理物理学家进行了实验以确定另一种真实大脑现象的特征,称为表观运动。这些实验没有解释大脑如何感知运动,但它们确实描述了这种现象的局限性。黑色背景上的一个小白点呈现给对象的视网膜。然后那个点被移除,另一个点出现在不同的位置。实验者可以改变两件事,两个点的空间分离和位置变化之间的时间延迟。大脑在这里感知一个点,那里感知另一个点,但前提是距离和延迟足够长。如果距离和延迟很短,大脑会感知到点从一个位置移动到另一个位置。很明显运动,因为没有实际运动呈现给眼睛。大脑感知它看不到的东西。
Psychophysicists have performed experiments to determine the characteristics of another real brain phenomenon, called apparent motion. The experiments don’t explain how the brain perceives motion, but they do describe the limitations of the phenomenon. A small white dot on a black background is presented to a subject’s retina. Then that dot is removed, and another dot is presented in a different position. The experimenters can vary two things, the spatial separation of the two dots and the time delay between position change. The brain perceives one dot here and another dot there, but only if the distance and delays are long enough. If the distance and delays are short, the brain perceives that the dot moves from one position to the other. It’s apparent motion because no actual motion is presented to the eye. The brain perceives what it doesn’t see.
视觉的持久性是这样的,当第二个图像到达时,我们仍然能感知到第一个图像。这听起来很像帧扩展。一个持续时间短的帧在时间上展开并添加到下一帧也及时展开。就好像视网膜进行图像扩展和连续扩展帧的添加。这样的事情一定会发生,因为我们感知到一个连续的视野,尽管电影放映机没有呈现。您可以将眼睛的余辉函数的形状想象为内置于我们人类感知器中的帧扩展器的形状。我们可以假设眼-脑系统必须进行重建的另一个原因,即隐含使用采样定理的重建,是因为我们准确地感知到错误如果那是实际的机制,我们会预料到——比如马车车轮向后旋转。21
Persistence of vision is such that we still perceive the first image when the second one arrives. That sounds a lot like frame spreading. A frame of short duration spreads out in time and adds to the next frame also spread out in time. It’s as if the retina does the image spreading and the adding of successive spread frames. Something like this must be going on because we perceive a continuous visual field although the film projector doesn’t present one. You can think of the shape of the persistence function of the eye as the shape of the frame spreader that’s built into us human perceivers. Another reason we can assume that the eye-brain system must be doing a reconstruction, one that implicitly uses the Sampling Theorem, is because we perceive exactly the errors we would expect if that were the actual mechanism—such as wagon wheels spinning backward.21
经典的 cel 动画——旧的赛璐珞墨水品种——依赖于表观运动现象。老动画师凭直觉知道如何将动作的连续帧保持在“不太远,不太慢”的界限内。如果他们需要超过这些限制,他们有技巧来帮助我们感知运动。他们绘制了实际的速度线,向大脑显示了运动的方向,并暗示它很快,就像一个模糊的东西。或者,当 Wile E. Coyote 出人意料地踏下台地,紧追那个真正狡猾的 Road Runner 时,他们提供了一阵灰尘来标记他的快速下降。它们提供了一种大脑可以解释的视觉语言。
Classic cel animation—of the old ink-on-celluloid variety—relies on the apparent-motion phenomenon. The old animators knew intuitively how to keep the successive frames of a movement inside its “not too far, not too slow” boundaries. If they needed to exceed those limits, they had tricks to help us perceive the motion. They drew actual speed lines, which showed the brain the direction of motion and implied that it was fast, like a blur. Or they provided a POOF of dust to mark the rapid descent of Wile E. Coyote as he stepped unexpectedly off a mesa in hot pursuit of that truly wily Road Runner. They provided a visual language that the brain could interpret.
超过明显的运动限制——没有那些动画师的技巧——结果很丑。您可能已经看过老式的定格动画,例如雷·哈里豪森 (Ray Harryhausen) 在Jason and the Argonauts (1963) 中的经典格斗骷髅,这些动画被角色令人不快的抽搐动作所困扰。你至少看到了双重的——同时有几条骨架的边缘——并正确地将其解释为运动,但令人痛苦的是。屏幕上的边缘口吃,或“颤抖”或“频闪”。这些话反映了断奏所带来的痛苦。
Exceed the apparent motion limits—without those animators’ tricks—and the results are ugly. You may have seen old school stop-motion animations—such as Ray Harryhausen’s classic sword-fighting skeletons in Jason and the Argonauts (1963)—that are plagued by an unpleasant jerking motion of the characters. You’re seeing double, at least—several edges of a skeleton at the same time—and correctly interpret it as motion, but painfully so. The edges stutter, or “judder,” or “strobe” across the screen. Those words reflect the pain inflicted by staccato motion.
真人电影是一系列离散帧,就像动画一样。为什么这些电影不卡顿?(想象一下指示 Uma Thurman 保持在“不要太远,不要太慢”的限制内。)有一个普遍的解释是有效的。这叫做运动模糊,而且简单漂亮。由真正的电影摄影机记录的帧很长。它不像 Road Runner 或 Harryhausen 框架那样瞬间成为样本。运动模糊是当主体移动并且快门速度不足以停止运动时您在静止照片中看到的。在静态照片中,这通常是一个意想不到的结果,但事实证明它是电影中的一个特征。如果没有模糊,所有电影都会像哈利豪森的骷髅一样生涩——除非乌玛奇迹般地保持在限制范围内。胖帧中移动物体的运动模糊为大脑提供了关于什么在移动和什么不在移动的线索。模糊的方向表示运动的方向,其长度表示速度。不知何故,神秘地,
Live-action movies are sequences of discrete frames just like animations. Why don’t these movies stutter? (Imagine directing Uma Thurman to stay within “not too far, not too slow” limits.) There’s a general explanation that works. It’s called motion blur, and it’s simple and pretty. A frame that’s recorded by a real movie camera is fat with duration. It’s not a sample at a single instant like a Road Runner or a Harryhausen frame. Motion blur is what you see in a still photograph when the subject moves and the shutter isn’t fast enough to stop the motion. In still photographs, it’s often an unintended result, but it turns out to be a feature in movies. Without the blur all movies would look as jerky as Harryhausen’s skeletons—unless Uma miraculously stayed within limits. The motion blur of moving objects in a fat frame gives clues to the brain about what is moving and what is not. The direction of a blur gives the direction of motion, and its length indicates the speed. Somehow, mysteriously, the brain converts that spatial information—the blurs—into temporal information and then perceives motion with the help of the apparent motion phenomenon.
我们这些在老西部电影中长大的人当时清楚地看到了倒退的车轮。驿马车的轮子占据了大片的银幕空间——以及很长的银幕时间——因为有很多追逐。带头巾的土匪是永远背着一个月的黄金工资单去追逐舞台。令人不安的是,车轮显然以错误的速度旋转,甚至经常向后旋转。
Those of us who grew up on old Western film movies saw backward-moving wheels clearly then. Stagecoach wheels occupied large patches of screen real estate—and long snatches of screen time—because there were lots of chases. Bandana-ed banditos were forever in pursuit of the stage carrying a month’s payroll in gold. Disconcertingly, the wheels clearly rotated at the wrong speed, and often even backward.
电视也是一种采样媒体,所以当电视出现时,我们继续看到车轮倒转,将西部片作为午后节目的重要组成部分。即使在今天,许多汽车广告都展示了车轮以错误的速度甚至向后旋转,但令人惊讶的是,很少有人再看到它们了。现代导演很聪明地将它们隐藏在尘埃云或方便放置的植物和岩石后面。或者,当轮子进入屏幕中心时,它们会进入完全慢动作,因此它们看起来可以正确旋转。或者他们什么都不做。我们都经常看到这个工件,以至于我们现在根本没有“看到”它。
Television is a sampled medium too, so we continued to see the wheels spin backward when television came along, featuring Westerns as a big part of early afternoon programming. Even today many car commercials exhibit wheels spinning at the wrong speed or even backward, but surprisingly few people see them anymore. Modern directors are clever about hiding them behind clouds of dust or conveniently placed plants and rocks. Or they drop into full slow motion as the wheels enter the center of the screen so they appear to rotate correctly. Or they do nothing. We’ve all seen the artifact so often that we simply don’t “see” it now.
但是为什么车轮会向后旋转?采样定理非常清楚。我们必须以所拍摄动作中包含的最高频率的两倍进行采样。回溯一下,在传统的电影采样率下,可以以每秒 24 帧的速度表示的最快运动是多少?每秒变化不超过 12 次的东西。
But why do the wheels spin backward? The Sampling Theorem is very clear. We must sample at twice the highest frequency contained in the motion being filmed. Working backward, what’s the fastest motion that can be represented at 24 frames per second, the traditional sampling rate of movies? Something that changes no faster than 12 times per second.
考虑一下驿马车的前轮——就像曾经在德克萨斯州抛弃 Muygridge 的失控的巴特菲尔德舞台一样。为方便起见,假设它有 12 英尺长,有 12 个辐条。货车每向前移动 1 英尺,车轮就会转一整圈的十二分之一,并且下一个辐条会旋转到与前一个完全相同的位置。因此,在部分旋转之后,车轮看起来完全一样。
Consider the front wheel of a stagecoach—like the runaway Butterfield stage that dumped Muygridge in Texas once upon a time. For convenience, let’s say that it’s 12 feet around and has 12 spokes. Each time the wagon moves forward by 1 foot, the wheel makes one-twelfth of a complete revolution and the next spoke revolves into the exact same place as the previous one. So, the wheel looks exactly the same after that partial revolution.
如果一匹马以每秒 12 英尺的速度移动舞台,则视觉流的傅立叶波版本中的波将以每秒 12 个周期变化。这意味着每秒有 24 个样本(帧)的电影几乎不能代表以每秒 12 英尺的速度移动的驿马车。但这只是每小时大约 8 英里。再快一点,怪事就开始了。由于一匹奔腾的马可以达到每小时 25 到 30 英里的速度,那些土匪肯定会让马车的车轮超过这个采样速度限制。因此,即使是一部每秒 24 帧的理想电影,也无法准确地表示车轮比慢速街道交通中的车轮移动得更快。
If a horse moved the stage at a speed of 12 feet per second, the wave in a Fourier wave version of the visual flow would vary at 12 cycles per second. This means that a movie, with 24 samples (frames) per second, can just barely represent a stagecoach moving at 12 feet per second. But that’s only about 8 miles per hour. Any faster and the weirdness begins. Since a galloping horse can hit 25 to 30 miles per hour, those banditos will surely make the stagecoach wheels exceed this sampling speed limit. So even an ideal movie, working at 24 frames per second, can’t accurately represent wheels moving faster than those in slow street traffic.
但我们知道电影电影以某种方式在大脑中起作用。我们的大脑用来从两个静止图像中推断运动的明显运动现象也可以感知运动方向。在旋转物体的情况下,大脑占据辐条的两个位置并感知它们之间的运动,尤其是在运动模糊的帮助下。它根据两个样本的相对位置决定运动的方向。它以最短路径为假设。
But we know that film movies work inside the brain somehow. That phenomenon of apparent motion our brains use to deduce motion from two still images can also perceive direction of motion. In the case of revolving objects, the brain takes two positions of the spokes and perceives the motion between them, especially if aided by motion blur. It decides the direction of motion from the relative positions of the two samples. It takes the shortest path as its assumption.
如果位置 2 的辐条从位置 1 的辐条顺时针转动并靠近它——只有很小的角度分离——大脑会假设车轮是顺时针旋转的。如果靠近但逆时针方向,大脑假设车轮逆时针旋转。因此,大脑会混淆前向和后向运动,因为它只看到样本,而不是它们之间的平滑视觉流。22
If a spoke in position 2 is clockwise from a spoke in position 1 and near it—only a small angular separation—the brain assumes the wheel is spinning clockwise. If near it but counterclockwise, the brain assumes the wheel is spinning counterclockwise. Hence the brain can confuse forward and backward motion because it sees only samples, not the smooth visual flow between them.22
由于理想电影和电影电影都涉及采样,因此在更高的速度下肯定会出现伪影。如果我们未能以(超过)视觉流中最高频率的两倍进行采样,则需要付出代价。在频率方面,运动混叠成错误的运动——例如向后旋转或向前旋转太慢。它呈现出一种虚假的视觉表现——一个别名。
Since sampling is involved in both ideal and film movies, there must be artifacts at higher speeds. There’s a price to pay if we fail to sample at (more than) twice the highest frequency in a visual flow. In frequencyspeak, the motion aliases into the wrong motion—such as spinning backward or spinning forward too slowly. It takes on a visual representation that’s false—an alias.
不!坚决不!没有,从来没有,活生生的画面的发明者。
No! Emphatically No! There is not, there never was, an inventor of the Living Picture.
——亨利·霍普伍德,《活生生的图画》,1899 23
—Henry Hopwood, Living Pictures, 189923
与计算机一样,需要一个复杂的流程图才能开始代表电影硬件的早期历史。它也让我们看到了人、概念和机器之间的复杂关系。这也是对实际故事的简化。许多名称、设备和国家被省略以减少混淆程度,同时保留足够的细节来表明重要技术开发的实际复杂性。与计算机一样,许多其他播放器和机器出现在注释中。
As with computers, it takes a complicated flow chart to even begin to represent the early history of movie hardware. It too allows us to see the complicated relationships of people, concepts, and machines. It too is a simplification of the actual story. Many names, devices, and countries are omitted to reduce the confusion level, while enough detail remains to signal the actual complexity of the development of an important technology. As with computers, many of the other players and machines appear in the annotations.
上一章中计算机历史的简化流程图仅保留了最终对 Digital Light 重要的人员和发展。这里的等效简化(图 5.10)是只遵循那些类似于前千禧年时期(几乎正是二十世纪(1895-2000))的主导电影系统的系统。我们将那些无胶片或无框架的系统降级为“电影前”——任何基于简单旋转的 Zoëtrope 或 Zoöpraxiscope。
The simplified flow chart of computer history in the previous chapter retained only those people and developments that mattered eventually to Digital Light. The equivalent simplification here (figure 5.10) is to follow only those systems that resemble the dominant movie system of the pre-millennial period—almost exactly the twentieth century (1895–2000). We relegate to “pre-cinema” those systems that were filmless or frameless—anything like the Zoëtrope or Zoöpraxiscope based on simple rotation.
一个主要的简化是从这张图表中完全省略了光化学薄膜本身。提到的每个系统都依赖于它。掌握赛璐珞电影对早期电影系统至关重要。这是一个困难的媒介。它很脆,容易划伤,边缘卷曲,并且具有化学活性。发明者必须制作曝光时间短、分辨率高的胶片。开发和打印它们必须快速且可靠。对于早期的发明者来说,这是一场噩梦,但对于用比特代替胶片的 Digital Light 来说,这并不重要。24
A major simplification is the complete omission of photo-chemical film itself from this chart. Every system mentioned depended on it. Mastery of celluloid film was crucial to early movie systems. It was a difficult medium. It was brittle, scratched easily, rolled at the edges, and was chemically active. Inventors had to create film stocks with short exposure times and high resolution. Developing and printing them had to be rapid and reliable. It was a nightmare for the early inventors, but it matters not a whit for Digital Light, which substitutes bits for film.24
再一次,与计算机一样,我们调用奥林匹克隐喻来跟踪许多球员。这次的主要球队是洋基队和法兰克队。为这张流程图选择的玩家促成了五个强大工作室的崛起,Edison、Biograph、卢米埃尔、高蒙和百代。一张真正显示对早期电影的所有贡献的详细图表必然会显示许多其他早期发明者和设备,并且它将至少包含另外两个国家,一个英国团队和一个德国团队。25
And again, as with computers, we invoke an Olympic metaphor to track the many players. The principal teams this time are the Yanks and the Franks. The players selected for this flow chart contributed to the rise of five powerhouse studios, Edison, Biograph, Lumière, Gaumont, and Pathé. A detailed chart that really showed all contributions to early cinema would necessarily show a host of other early inventors and devices, and it would feature at least two other countries, a Brits team and a German team.25
图 5.10
Figure 5.10
也许最有趣的遗漏是法国、英国和美国的路易·勒王子。1888 年,他在约克郡的利兹制作了短片。它们仍然可以在互联网上以数字重建的形式找到。1890 年,他在法国登上了一列火车,显然是前往巴黎,最终前往纽约展示他的发明。但他从未成功——甚至没有到巴黎。他只是消失了。他的家人认为爱迪生将他视为一个严肃的竞争对手,并将他除名——这不太可能发生,但却表明了爱迪生的暴虐名声。根据一份宣誓书,到 1889 年,勒普林斯拥有了第一个完整的摄影机、胶卷和放映机系统。但这并不重要,因为它显然对电影的发展没有进一步的影响。26
Perhaps the most intriguing omission is Louis Le Prince of France, England, and the United States. He made short movies in Leeds, Yorkshire, in 1888. They can still be found on the internet as digital reconstructions. In 1890 he boarded a train in France, apparently headed for Paris and ultimately New York to demonstrate his invention. But he never made it—not even to Paris. He simply disappeared. His family believed that Edison saw him as a serious competitor and had him removed—an unlikely event but indicative of Edison’s tyrannical reputation. According to an affidavit, Le Prince had the first complete system of camera, film, and projector by 1889. But it doesn’t matter because it apparently had no further effect on the development of cinema.26
下面的文字作为电影流程图的扩展说明——首先是洋基队,然后是法兰克队。但它最重要的信息是明确的:它所代表的历史是复杂的,有着压倒性的细节。推论出来的信息是,如果我们听到有人声称自己是电影之父或发明者,我们应该立即发出危险信号。第二个主要信息是 1895 年是电影年,就像 1948 年是计算机年一样。1895 年是放映机的一年,也是第一次使用赛璐珞胶片实现完整电影机器的一年。
The text that follows serves as an extended caption for the flow chart of cinema—first for the Yanks side and then for the Franks. But its overriding message is clear: the history it represents is complex, with overwhelming details. The corollary message is that we should immediately run up a red flag if we hear one name claimed as father of, or inventor of, cinema. The second principal message is that 1895 was The Year for movies, the way that 1948 was The Year for computers. And 1895 was The Year for the projector, and of the first realizations of full movie machines using strips of celluloid film.
爱迪生的名字和参与保证了媒体的广泛关注。. . . 不仅机器 [Vitascope] 得到了他的完全认可,而且“门洛帕克的向导”也随时准备扮演分配给他的发明者的角色(尽管他不是)。
Edison’s name and involvement guaranteed extensive media attention. . . . Not only did the machine [Vitascope] receive his complete approval, but the “Wizard of Menlo Park” stood ready to play the role of inventor assigned to him [even though he wasn’t].
——查尔斯·马瑟,电影的出现27
—Charles Musser, The Emergence of Cinema27
我是在托马斯爱迪生的美国英雄故事中长大的,所以我很惊讶地发现它没有通过历史的考验。电影历史学家戈登·亨德里克斯 (Gordon Hendricks) 于 1961 年在一本书的书名《爱迪生电影神话》( The Edison Motion Picture Myth ) 中率先开场。在开头的段落中,亨德里克斯陈述了他的第一个目标:开始“清理美国电影开篇就充满了精心编织的传奇的泥潭的任务”。他的第二个目标是“为 WKL Dickson 所做的工作提供一些迟来的功劳”。后来的美国电影史家,在亨德里克斯仔细研究的基础上,稍微缓和了他对爱迪生的攻击,同时保持对迪克森的重视。就在不久前,在国会图书馆工作多年的电影专家保罗·斯佩尔终于写了第一本关于威廉·肯尼迪·劳里·迪克森的学术传记。尽管 Spehr 提到了“爱迪生无情甚至邪恶的一面的问题”,但他认为爱迪生的商业行为与时俱进。然而,爱迪生的遗体与我小时候所认为的英雄形象相去甚远。28
I was raised on the American hero story of Thomas Edison, so I was surprised to learn that it doesn’t pass historical muster. The opening salvo came in 1961 from cinema historian Gordon Hendricks in a book whose title says it all, The Edison Motion Picture Myth. In the opening paragraph Hendricks stated his first goal: to begin “the task of cleaning up the morass of well-embroidered legend with which the beginning of the American film is permeated.” His second goal was “to afford some measure of belated credit to the work done by W.K.L. Dickson.” Subsequent historians of American film, building on Hendricks’s careful research, have softened his attack on Edison somewhat, while maintaining his emphasis on Dickson. And fairly recently, Paul Spehr, a cinema expert for many years at the Library of Congress, finally wrote the first scholarly biography devoted to William Kennedy Laurie Dickson. Although Spehr mentions “the issue of Edison’s ruthless, even villainous side,” he justifies Edison’s business practices as consistent with the times. Nevertheless, what remains of Edison falls far short of the heroic figure I thought him to be when I was a child.28
爱迪生喜欢被称为门洛帕克的巫师,美国公众欣然接受。他为发明和商业创造了良好的环境。新泽西州门洛帕克是爱迪生传说中的实验室之一。渴望的年轻发明家蜂拥而至与他合作。他是他的实验室和他自己的出色营销人员,他很高兴成为那里实际从事这项工作的所有发明家的化身。而且他赚了很多钱。当他的发明者不能胜任这项任务时,他的商业伙伴购买了其他人的专利,用爱迪生的名字代替了他们的名字,并粉碎了专利法庭的竞争。他的一些最初天真的发明家——尤其是迪克森——终于注意到他们在学分中的持续遗漏,并与他们的赞助人分道扬镳,有时并不友好。
Edison loved to be called the Wizard of Menlo Park, and the American public gladly went along with it. He established a wonderful environment for invention and business. Menlo Park, New Jersey, was the location of one of Edison’s fabled labs. Eager young inventors flocked to work with him. He was a superb marketer of his labs and of himself, and he was happy to be the personification of all the inventors there who actually did the work. And he made a lot of money. When his inventors weren’t up to the task, his business partners bought the patents of others, replaced their names with Edison’s, and smashed competition in the patent courts. Some of his initially naive inventors—notably Dickson—finally noticed their continued omission from the credits and parted ways with their patron, sometimes not amicably.
与苹果联合创始人史蒂夫乔布斯的逐句相似之处令人鼓舞。他周围也正在迅速形成一个精心编织的传奇泥潭。在被苹果公司赶下台后,他在加利福尼亚州门洛帕克附近的红木城共同创立了他的第二家公司 Next。他出售 Next to Apple 让他重新获得了 Apple 的认可,他通过出色地推销其热切的年轻创造者的发明和设计(他声称这些发明和设计是他自己的)而著名地扭转了局面。这些声明不一定是直接的,但就像爱迪生一样,当崇拜的公众或他自己的营销部门将功劳分配给他时,他从不否认功劳。他用专利打败了他的竞争对手,赚了很多钱。我们可以很容易地称乔布斯为西门洛帕克的巫师,因为他建立了一个富人,
The sentence-by-sentence parallels with Steve Jobs, the cofounder of Apple, are enlightening. A morass of well-embroidered legend is fast forming around him too. After being ousted from Apple, he cofounded his second company, Next, in Redwood City adjacent to Menlo Park, California. His sale of Next to Apple gained him readmission to Apple, which he famously turned around by superbly marketing the inventions and designs of its eager young creators—which he claimed as his own. The claims weren’t necessarily direct, but just like Edison, he never denied the credit when an adoring public or his own marketing department assigned it to him. He pounded his competitors with patents and made a lot of money. We could easily call Jobs the Wizard of Menlo Park West for establishing a rich, supportive environment for bright inventors and taking credit himself for their inventions.
例如,乔纳森·艾夫(现在的乔纳森·艾夫爵士)设计了 iMac、iPod 和 iPhone。不是乔布斯。但乔布斯确实与艾夫密切互动,并大力支持他。这些设备来自双方以及许多其他人的努力。当然,乔布斯是营销苹果产品的天才——该公司的强尼苹果种子。但是,像爱迪生一样,他推销的主要产品之一是他自己的神话。正如本书所阐明的那样,将一项复杂的技术成就仅仅归功于一个人总是错误的。29
As a case in point, Jonathan Ive—now Sir Jonathan Ive—designed the iMac, iPod, and iPhone. It wasn’t Jobs. But Jobs did interact closely with Ive and strongly supported him. Those devices came about from the efforts of both, and many others. Of course, Jobs was a genius at marketing the Apple products—the company’s Johnny Appleseed. But, like Edison, one of the main products he marketed was the myth of himself. As this book makes clear, it’s always wrong to give just one person all the credit for a complex technological achievement.29
迈布里奇是另一位伟大的营销人员——担任约翰尼·苹果籽的角色。凭借出色的表演技巧,他在全球范围内推销了投影电影的概念,尽管他自己没有一个足够先进的系统来利用这种兴奋他制作了。他的推销给爱迪生留下了特别的力量。这让爱迪生开始思考一种更好的电影制作方式。
Muybridge was another great marketer—in his Johnny Appleseed role. With great showmanship, he sold the notion of projected moving pictures worldwide, although he himself didn’t have a system that was sufficiently advanced to exploit the excitement he produced. His sales pitch struck Edison with particular strength. It set Edison to thinking about a better way to make movies.
两人于 1888 年在迈布里奇的多次巡回演讲中见过几次面。这个想法是将迈布里奇改进的魔术灯,Zoöpraxiscope,与爱迪生流行的留声机产品结合起来——并获得有声照片。迪克森随后的工作表明,这不是一个经过深思熟虑的想法。事实上,成功的有声照片在几十年内都不会出现。但这是个好主意。30
The two men met a couple of times in 1888 on one of Muybridge’s many speaking tours. The idea was to marry Muybridge’s improved magic lantern, the Zoöpraxiscope, to Edison’s popular phonograph product—and get talking pictures. As subsequent work by Dickson showed, this wasn’t a well-thought-out idea. In fact, successful talking pictures wouldn’t appear for decades. But it was a good idea.30
爱迪生很快推断出迈布里奇的方法——即使忽略音频组件——也不可行。迈布里奇没有一台合理的电影机器。一方面,爱迪生很清楚,一旦最初的快感消失,一部只有几秒钟的电影就不会奏效。因此,他立即着手草拟一个更好的主意。字面上地。他向美国专利局提交了一份粗略的草图——当时正式称为警告的一部分——作为一种占位符,打算稍后提交专利申请。尽管这是一个非常有缺陷的想法——例如,百叶窗在哪里?——但它仍然是引发这项发明的火花。31
Edison quickly deduced that Muybridge’s approach—even ignoring the audio component—wasn’t viable. Muybridge didn’t have a reasonable movie machine. For one thing, it was clear to Edison that a movie of only a couple seconds duration wasn’t going to work once the initial thrill wore off. So he immediately set out to sketch a better idea. Literally. He submitted a crude sketch—officially part of what was then called a caveat—to the US Patent Office, as a kind of placeholder, an intention to file a patent application later. Although this was a highly flawed idea—for instance, where’s the shutter?—it was still the spark that set off the invention.31
该草图展示了一种将电影与留声机结合起来的不同方式。当时的爱迪生留声机沿粘土圆柱曲面周围的螺旋轨道录制声音,就像绕在线轴上的线一样。对于电影,爱迪生建议在轨道上录制一系列微小的图片。当圆柱体旋转时,人们可以通过瞄准圆柱体表面的放大镜看到一连串变化的图像。有了这个设备,可以说爱迪生萌生了偷窥秀的想法。声音不在画面中——至少在几十年内。
The sketch showed a different way to marry moving pictures to phonographs. An Edison phonograph at that time recorded sound along a spiral track around the curved surface of a clay cylinder—like thread wound on a spool. For movies Edison proposed recording a succession of tiny pictures along the track instead. As the cylinder spun, one could see a succession of these changing images through a magnifying glass aimed at the cylinder’s surface. With this device one could say the Edison hatched the idea of the peep show. And sound was out of the picture—at least for a couple of decades.
爱迪生(以他的“发明的拿破仑”姿势,图 5.11,左)将完成这幅素描的工作分配给了迪克森(以他的“放肆”姿势,图 5.11,右)并开始了欧洲的盛大之旅。因此,在爱迪生实验室工作的迪克森主要负责创建某种电影系统,与原始草图几乎没有相似之处。它有一个照相机,Kinetograph,它使用长条胶卷——而不是串在圆筒上的小图片。但它没有投影仪。取而代之的是窥视秀,或称nickelodeon——一种名为 Kinetoscope 的单人观看设备。“爱迪生”活动电影放映机系统几乎是电影系统,但比迈布里奇的设备更接近现代电影。它对世界产生了巨大的影响。
Edison (in his “Napoleon of Invention” pose, figure 5.11, left) assigned the job of realizing this sketch to Dickson (in his “giving off airs” pose, figure 5.11, right) and went off on a grand tour of Europe. So Dickson, working at Edison’s lab, was the one principally responsible for creating a movie system of sorts, bearing almost no resemblance to the original sketch. It had a camera, the Kinetograph, and it used film in long strips—not tiny pictures threaded onto a cylinder. But it lacked a projector. In its stead was the peep show, or nickelodeon—a one-person viewing device called the Kinetoscope. The “Edison” Kinetograph-Kinetoscope system was an almost-movie system—but closer to modern cinema than Muybridge’s device. And it had a tremendous effect on the world.
迪克森不得不与爱迪生分离,以创建一个完整的电影系统,并配备一台投影仪。分手并不友好。至少可以说,迪克森和爱迪生的关系是矛盾的。但并非总是如此——即使是在 1895 年,电影真正开始的那一年。32
Dickson had to separate from Edison to create a full movie system, complete with a projector. The split wasn’t amicable. To say the least, the Dickson and Edison relationship was conflicted. But it hadn’t always been so—even on the threshold of 1895, the year movies really began.32
图 5.11
Figure 5.11
我相信,在接下来的几年里,通过我自己和迪克森、迈布里奇、马雷和其他无疑将进入该领域的人的工作,这部大型歌剧可以在纽约大都会歌剧院上演,而不会发生任何实质性的改变。原创,并与早已死去的艺术家和音乐家合作。
——托马斯·爱迪生,约。1894 33
托马斯·阿尔瓦·爱迪生 (Thomas Alva Edison) 的传记是为了响应根深蒂固的公众利益的需求,即爱迪生的辉煌发明所唤起的,为了解这位最伟大的在世发明家的个人和生活而创造的需求。
—WKL 和 [妹妹] Antonia Dickson,托马斯·阿尔瓦·爱迪生的生平和发明,1894 年34
I believe that, in coming years, by my own work and that of Dickson, Muybridge, Marey, and others who will doubtless enter the field, that grand opera can be given at the Metropolitan Opera House at New York without any material change from the original, and with artists and musicians long since dead.
—Thomas Edison, ca. 189433
The biography of Thomas Alva Edison is in response to the demand which the deep-seated public interest, called forth by the brilliant Edison inventions, has created for a knowledge of the person and life of this greatest of living inventors.
—W.K.L. and [sister] Antonia Dickson, The Life and Inventions of Thomas Alva Edison, 189434
他经常只使用他的首字母 WKL,但他的家人称他为 Laurie。他当然从来不是威廉、威尔、比尔或比利。事实上,他有一种让土生土长的美国人反感的形式。四个名字!为什么,那是彻头彻尾的自大。这确实让爱迪生感到困扰,他通过刻意拼错自己的姓氏来刺痛他作为狄克逊。他的一位同事称他为——并不是出于尊重——威廉·肯尼迪·劳里·迪克森的“尊贵的”。35
He often used only his initials W.K.L., but his family called him Laurie. He certainly was never William, Will, Bill, or Billy. In fact, he had a certain formality about him that was off-putting to native-born Americans. Four names! Why, that’s downright uppity. It certainly bothered Edison, who needled him by pointedly misspelling his surname as Dixon. One of his colleagues called him—and not out of respect—the “Right Honorable” William Kennedy Laurie Dickson.35
历史学家——即使是那些赞扬迪克森成就的人——都认为他在装腔作势,自我夸大和夸大事实。甚至他最初的司仪亨德里克斯也列出了迪克森说过的 50 个已知谎言。迪克森通过以下自传加剧了沮丧和不信任,这对美国人或门洛帕克的同事来说听起来不太可能:36
Historians—even those who praise Dickson’s accomplishments—have thought that he put on airs, that he was self-aggrandizing and stretched the truth. Even his original celebrant, Hendricks, listed 50 known lies Dickson told. Dickson fueled the dismay and distrust with autobiographies such as the following, which sounded unlikely to Americans—or colleagues in Menlo Park:36
威廉·肯尼迪-劳里·迪克森出生于法国,在英国接受教育。他的父亲詹姆斯·迪克森(James Dickson)是一位杰出的英国画家和平版画家。许多艺术家在他的祖籍中都有编号,其中包括伟大的霍加斯。他的母亲是苏格兰柯克库布赖特伍德霍尔的伊丽莎白·肯尼迪-劳里小姐,她是一位才华横溢的学者、音乐家,并以她的美貌而闻名。她是麦克斯韦顿劳瑞家族的后裔,在著名的民谣“安妮劳瑞”中永垂不朽,而斯特罗万的罗伯逊家族则与卡西利斯伯爵、阿索尔公爵和皇家斯图亚特家族有联系。37
William Kennedy-Laurie Dickson was born in France and educated in England. His father, James Dickson, was a distinguished English painter and lithographer; many artists are numbered in his ancestral roll, among others the great Hogarth. His mother was Miss Elizabeth Kennedy-Laurie, of Woodhall, Kirkcudbright, Scotland, a brilliant scholar, musician, and renowned for her beauty. She was a descendant of the Lauries of Maxwellton, immortalized in the celebrated ballad, “Annie Laurie,” and the Robertsons, of Strowan, connected with the Earl of Cassilis, the Duke of Athol, and the Royal Stuarts.37
但是,事实上,大部分都是真的——即使是皇家斯图亚特的部分。他的许多祖先家族的数百年血统都记录在英国的经典贵族名录中,伯克的地主贵族和伯克的贵族。他的四个名字继承了他的大部分血统。他的父亲有两个直系祖先威廉·迪克森(William Dickson),还有两个直系祖先叫威廉·贝利·肯尼迪·劳瑞(William Baillie Kennedy Laurie)和威廉·肯尼迪·劳瑞(William Kennedy Laurie)。所以这四个名字对他都很重要。
But, in fact, most of this is true—even the Royal Stuarts part. The centuries-old lineages of many of his ancestral families are recorded in the classic aristocratic registers of the United Kingdom, Burke’s Landed Gentry and Burke’s Peerage. His four names carried much of his lineage. He had two direct ancestors named William Dickson on his father’s side, and two others named William Baillie Kennedy Laurie and William Kennedy Laurie on his mother’s. So all four names were important to him.
然而,他一直在自传中遗漏的内容是有启发性的。像他的远亲伊丽莎白巴雷特布朗宁一样,迪克森来自加勒比奴隶主家庭,他们靠着成千上万的奴隶靠甘蔗发家。因此,1879 年迪克森 18 岁时随母亲移民到美国,这并不奇怪,他们首先居住在美国南部弗吉尼亚州里士满附近,很快他就在那里娶了一个旧邦联家庭的女儿。他在余生中一直对家族过去的广泛奴隶制保持沉默。38
What he consistently omitted from his autobiography, however, is revealing. Like his distant relative Elizabeth Barrett Browning, Dickson descended from Caribbean slaveholder families who made sugarcane fortunes on the backs of thousands of slaves. So it’s not surprising that when Dickson immigrated with his mother to America in 1879, at age 18, they first resided near Richmond, Virginia, in America’s South, where he soon married a daughter of an old Confederate family. He kept quiet the rest of his life about the extensive slavery in his family’s past.38
迪克森是一个贵族,可能是傲慢的法国出生的英国人,有南方倾向和奴隶制的过去,并不是一个真正的美国传奇。然而,爱迪生似乎从霍雷肖·阿尔杰(Horatio Alger)小说的书页中走出来,成为卖报纸谋生的孩子,然后继续发明电灯泡和留声机,最终成为电影背后的美国天才。这是为爱迪生创造的神话,他很高兴地扮演了这个角色。但事实并不支持它。
Dickson, being an aristocratic, probably arrogant French-born Englishman of Southern leanings and a slaveholding past, was not the stuff of a proper American legend. Edison, however, seemed to step from the pages of a Horatio Alger novel as the kid who sold newspapers to make a living, then went on to invent the electric light bulb and the phonograph, only to become the American genius behind movies. That was the myth created for Edison, and he happily played the role. But the facts don’t support it.
迪克森,而不是爱迪生,设计并制造了第一台成功的电影摄影机,Kinetograph,被称为 Edison(当然)Kinetograph。其他人帮助他完成了这项任务,尤其是约翰·奥特。流程图没有传达迪克森整体贡献的深度。例如,他还设计并制作了第一部电影工作室。它被称为黑色玛丽亚(以稻田车命名),位于新泽西州奥兰治的爱迪生公司场地,靠近门洛帕克。而且他制作了许多最早的电影——从 1890 年到 1903 年,其中有 300 多部。他的电影一定很短,一分钟左右,无声,黑白。它们是纪录片——关于一名男运动员、拳击手、一艘进港的船、一场战斗、一位教皇、一位国王、一家理发店。他是一个软件人,也是一个硬件人,尽管没有惊天动地的电影成就。电影的伟大叙事艺术尚未到来。39
Dickson was the man, not Edison, who designed and built the first successful movie camera, the Kinetograph, known as the Edison (of course) Kinetograph. Others helped him in this task, notably John Ott. The depth of Dickson’s overall contribution isn’t conveyed by the flow chart. For example, he also designed and built the first movie studio. It was known as the Black Maria—after the paddy wagon—located on the Edison company grounds in Orange, New Jersey, near Menlo Park. And that he made many of the earliest films—over 300 of them from 1890 to 1903. His movies were necessarily short, a minute or so, silent, and black-and-white. They were documentaries—of a male athlete, boxers, a ship coming into harbor, a battle, a pope, a king, a barbershop. He was a software as well as a hardware man, though not of earthshattering cinematic accomplishment. The great narrative art of cinema was yet to come.39
图 5.12
Figure 5.12
迪克森和奥特提出的另一个爱迪生警告草图成为“爱迪生”活动电影放映机。尽管有范围后缀,但这不是投影仪。这是一种向一个人播放电影的设备——窥视秀。爱迪生的商业伙伴非常成功地将他的设备带入了窥视秀行业。纽约市展览中心的插图(图 5.12)说明了一切——一直到迎接顾客的爱迪生古铜色半身像和两条白炽灯挂在墙上的龙。40
Another Edison caveat sketch that Dickson and Ott brought into existence became the “Edison” Kinetoscope. Despite the scope suffix, this was not a projector. It was a device for displaying a movie to a single person—the peep show. Edison’s business partners took his device into the peep show business quite successfully. The illustration of the New York City showplace (figure 5.12) says it all—down to the bronzed bust of Edison that greeted patrons and the two incandescent wall-mounted dragons.40
事实上,偷窥节目推迟了爱迪生进入电影界的时间。当迪克森建议他们为公开放映制作一台投影仪时,爱迪生拒绝了这个想法。他不想蚕食他在偷窥秀上的成功。他的不情愿有两个主要后果。首先,他的公司迟到了完整的电影系统。到 1895 年,也就是投影机年,其他几个团体拥有了投影仪,其中一个,法国的 Lumière 兄弟,将成为非常重要的竞争对手。其次,他把迪克森丢给了一家对投影仪感兴趣的公司。在爱迪生,迪克森帮助另外两个团队设计投影仪并开展业务。他离开加入其中之一。该集团后来成为了 Biograph 公司,将成为爱迪生在美国电影业最严重的竞争对手。
In fact, the peep shows delayed Edison’s entry into the world of cinema. When Dickson recommended that they build a projector for public showings, Edison rejected the idea. He didn’t want to cannibalize his peep-show success. His reluctance had two major consequences. First, his company came late to the full movie system. Several other groups had projectors by 1895—the Year of the Projector—and one of them, the Lumière brothers in France, would become very serious competitors. Second, he lost Dickson to a company that was interested in projectors. While at Edison, Dickson had helped two other teams design projectors and go into business. He left to join one of them. That group, which became the Biograph company, would be Edison’s most serious American competitor in the movie business.
Edison 的业务合作伙伴很快意识到他们需要一台投影仪来补充 Kinetograph。迪克森退出了爱迪生的圈子,他们需要到别处寻找投影仪。查尔斯·弗朗西斯·詹金斯(Charles Francis Jenkins)和托马斯·阿马特(Thomas Armat)于 1895 年开发了 Phantascope 投影仪,因此爱迪生的商业特许经营者(诺曼·拉夫和弗兰克·金蒙)购买了它的权利,将其更名为 Vitascope,并通过商业合同压制了发明者的名字。最后,还有一个完整的“爱迪生”电影系统,包括主要由 Dickson 和 Ott 开发的 Kinetograph 摄影机,以及主要由 Jenkins 和 Armat 开发的 Vitascope 放映机。爱迪生系统以门洛帕克巫师的名字命名,但这不是巫师所做的——除了他最初为相机部分绘制的不可行的警告草图和对 Jenkins-Armat 机器的一些小修改。爱迪生发明电影的意义就这么大。在实际开发“爱迪生”系统的四个人中,迪克森将在他的有生之年获得更高的声望,但不会声名鹊起。41
Edison’s business partners quickly realized that they needed a projector to complement the Kinetograph. With Dickson out of the Edison picture, they needed to look elsewhere for a projector. Charles Francis Jenkins and Thomas Armat had developed the Phantascope projector in 1895, so Edison’s business concessionaires (Norman Raff and Frank Gammon) bought the rights to it, changed its name to Vitascope, and suppressed the inventors’ names by business contract. Finally, there was a full “Edison” movie system consisting of the Kinetograph camera, developed principally by Dickson and Ott, and the Vitascope projector, developed principally by Jenkins and Armat. The Edison system bore the name of the Wizard of Menlo Park, but it wasn’t the Wizard’s doing—other than his original unworkable caveat sketches for the camera part and some minor modifications of the Jenkins-Armat machine. So much for Edison’s inventing the movies. Of the four people who actually developed the “Edison” system, Dickson would rise to even higher prominence, but not fame—in his lifetime anyway.41
重要的是,流程图中没有,迪克森几乎独自负责爱迪生(品牌)电影系统的电影部分。他是开发类似于最近的胶片系统的人——宽度约为 35 毫米的双孔胶片,每帧有四个矩形穿孔。这是电影史上一个极其困难和根本性的发展,在无胶片数码光中逐渐变得不重要。迪克森是征服卷轴到卷轴赛璐珞电影和创建投影仪的主要参与者。42
Importantly, and missing from the flow chart, Dickson was almost singlehandedly responsible for the film part of the Edison (brand) movie system. He was the one who developed the film system that resembles that of the very recent past—doubly perforated film of about 35 mm width, with four rectangular perforations per frame. This was a tremendously difficult and fundamental development in the history of cinema that fades to unimportance in filmless Digital Light. Dickson was a major player in the conquest of reel-to-reel celluloid film and the creation of the projector.42
有一种信息丰富的方法可以打破流程图所代表的难解之结:连接线表明,除了 Armat-Jenkins Vitascope 之外,Dickson 参与了 Yanks 的每一个开发项目。虽然不那么明显,但他也间接参与了 Franks 的许多开发: Lumières 构建他们的系统是为了直接响应“爱迪生”活动电影放映机。迪克森完善的 35 毫米穿孔胶片格式被 Gaumont 和 Pathé 采用。英国的罗伯特·保罗(Robert Paul)制作了一部活动电影放映机,并将其卖给了百代。我们将在 Franks 部分重温 Lumières、Gaumont、Pathé 和 Paul。
There’s an informative way to cut through the Gordian knot represented by the flow chart: the lines of connection show that Dickson had a hand in every Yanks development except the Armat-Jenkins Vitascope. Although it’s not as obvious, he also was indirectly part of many of the Franks developments: The Lumières built their system in direct response to the “Edison” Kinetoscope. The 35 mm perforated film format that Dickson perfected was adopted by Gaumont and Pathé. And Britain’s Robert Paul built and sold a copy of the Kinetoscope to Pathé. We’ll revisit the Lumières, Gaumont, Pathé, and Paul in the Franks section.
迪克森咨询了两个非爱迪生团体关于投影仪的问题。在他还在爱迪生正式工作的同时,他也在一边做这件事。历史学家无法确定这些是否是道德追求。迪克森显然相信他的行为是光荣的,但爱迪生认为他的行为是背叛。65 岁的迪克森在 1926 年写信给爱迪生,“真相终将浮出水面——这提醒我,关于我对你不忠的旧谣言偶尔会出现,除非你否认,否则永远会阻碍进步。”爱迪生在信上写了一张便条:“他不忠。我认为我们最好不要回答,”并归档。43
Dickson consulted with two non-Edison groups about projectors. He did this on the side while still officially working at Edison. Historians have been unable to establish whether these were ethical pursuits. Dickson apparently believed that he had acted honorably, but Edison considered his actions a betrayal. Dickson, age 65, wrote to Edison in 1926, “Truth will out—which reminds me that that old rumour of my disloyalty to you crops up on occasion, & will ever hamper progress unless denied by you.” Edison wrote a note on the letter, “He was disloyal. I think we better not answer,” and filed it.43
迪克森的第一个课外小组是莱瑟姆一家,他们有一对父亲和两个儿子,还有爱迪生的前雇员尤金·劳斯特。Lauste 为爱迪生实验室的 Kinetoscope 做出了贡献。迪克森在莱瑟姆家族的角色可能只是建议性的。无论如何,他从未接受过公众的信任。Lauste 帮助创建了 Eidoloscope 投影仪,或者一些人认为。这是电影史上有争议的观点之一。无论如何,它在 1895 年 4 月首次公开展出(原名 Panoptikon)。它的首次商业亮相于 5 月开始,使其成为世界上第二台上市的放映机——紧随三月 Lumières 的电影放映机——也是第一台上市的放映机。44
The first extracurricular group for Dickson was the Lathams, a father and two sons, and a former Edison employee, Eugène Lauste. Lauste had made contributions to the Kinetoscope at Edison’s lab. Dickson’s role with the Lathams was probably only advisory. He never took public credit anyway. Lauste helped create the Eidoloscope projector, or so some think. It’s one of the contested points in cinema history. Regardless, it had its first public showing in April 1895 (under its original name, Panoptikon). Its first commercial appearances began in May, making it the second projector in the world to go public—shortly after the Lumières’ Cinématographe in March—and the first to go commercially public.44
那一年,1895年,确实是电影史上奇迹的一年。Lathams 不仅在 5 月展示了 Eidoloscope 商业化,而且 Jenkins 和 Armat 在 10 月展示了 Phantascope,这是有史以来的第二个商业化投影。爱迪生的主要特许经销商 Raff 和 Gammon 将 Phantascope 重新命名为“Edison”Vitagraph。法国的 Lumières 很快在 12 月推出了第四次商业放映,即他们的 Cinématographe。(德国团队的 Max Skladanowsky 在 11 月用他的 Bioskop 拍摄了第三次商业放映。)因此,1895 年确实是突破性的一年——我们所知道的完整电影开始的那一年。比赛开始了。45
That year, 1895, was indeed the miracle year in the history of cinema. Not only did the Lathams show the Eidoloscope commercially in May, but Jenkins and Armat demonstrated the Phantascope in October, as the second commercial projection ever. Raff and Gammon, Edison’s principal concessionaires, would rebrand the Phantascope as the “Edison” Vitagraph. The Lumières in France soon followed up with the fourth commercial projection, of their Cinématographe, in December. (Max Skladanowsky of the German team captured the third commercial projection, with his Bioskop, in November.) So, 1895 was indeed the breakthrough year—the year that full cinema as we know it began. The race was on.45
迪克森与爱迪生的决裂也是如此。从此以后,迪克森因爱迪生否认他的功劳而受到伤害。在 71 岁时,迪克森终于可以写道:“自从爱迪生和伊士曼去世后,我在许多论文和期刊中看到,我在爱迪生制作第一部电影和当今电影的开创性工作受到赞誉。” 46
And so was Dickson’s break with Edison. Forever after, Dickson was hurt that Edison denied him credit. At age 71 Dickson could finally write, “I see in many papers & journals I am, since Edison’s & Eastman’s deaths, given credit for my pioneer work at Edison in producing the 1st film & present day cinema.”46
1895 年,迪克森正式与爱迪生分道扬镳,加入另一个课外团体 KMCD 辛迪加。K 是 Elias Koopman,M 是集团的首席商人 Harry Marvin。C 是 Herman Casler,他成为了 Dickson 的首席设计师和建造者,Dickson 是 D。这群人每年都去纽约北部的一家水疗中心结识,然后一起创造并销售了一个噱头相机——一个侦探相机装在看起来像怀表的东西里。朋友们结成了一家对电影业产生深远影响的公司,但对间谍活动没有令人难忘的影响。47
Dickson formally parted company with Edison in 1895 to join the KMCD Syndicate, the other extracurricular group. K was Elias Koopman, and M was Harry Marvin, the head businessmen of the group. C was Herman Casler, who became the chief designer and builder with Dickson—who was the D. The group had got to know one another in annual visits to an upstate New York spa and then together created and sold a gimmick camera—a detective camera that fit in what looked like a pocket watch. The friends bonded into a company with a profound effect on the cinema industry—but no memorable influence on espionage.47
卡斯勒当然听从了迪克森的建议,设计了该小组的相机 Mutograph。然后,两人将 Mutograph 改装成投影仪。他们称其为 Biograph,该公司以 Biograph 公司而广为人知。迪克森知道如何绕过爱迪生公司的专利,因此 Biograph 成为爱迪生在美国最严肃的竞争对手。48
Casler, with Dickson’s advice surely, designed the group’s camera, the Mutograph. The two then adapted the Mutograph to be a projector. They called it the Biograph, and the company became known popularly as the Biograph company. Dickson knew how to get around the Edison company patents, so Biograph became Edison’s most serious American competitor.48
电影史流程图的右侧是另一个团队——法兰克人。一眼就能看出主要参与者之间的紧密联系网络。他们的故事与 Yanks 的故事一样复杂、强大和令人担忧。我们从 Étienne-Jules Marey 开始。他占据了爱德华·迈布里奇为洋基队担任的弗兰克斯队的鼓舞人心的电影前职位。事实上,马雷和迈布里奇在 1895 年投影仪年之前的几年里相互影响。
The right side of the flow chart of cinema history is devoted to the other team—the Franks. A glance at it reveals a dense web of interconnectedness among the main players. Their story is as complicated, robust, and fraught as the Yanks story. We start at the top with Étienne-Jules Marey. He occupies the inspirational, pre-cinema position for the Franks held by Edward Muybridge for the Yanks. And in fact, Marey and Muybridge influenced one another in the years leading up to 1895, the Year of the Projector.
马雷知道马的四个蹄子可以同时离开地球。在他知道迈布里奇为 Leland Stanford 的赛马拍摄的著名照片之前,以及在他自己成为像迈布里奇一样的时间摄影师或计时摄影师之前,他就知道了这一点。Marey 和 Muybridge 实践的计时摄影术是前电影摄影术——在完整的电影系统存在之前。
Marey knew that all four hooves of a horse can simultaneously leave the earth. He knew it before he knew about Muybridge’s famous photograph of Leland Stanford’s racehorse, and before he himself became, like Muybridge, a photographer of time, or a chronophotographer. Chronophotography as practiced by Marey and Muybridge was pre-cinematography—before complete movie systems existed.
马雷通过非摄影测量了解蹄子。大约在 1873 年,他使用安装在真马蹄上的设备进行了真正的生理测量。他在次年发表的一篇科普文章中对此进行了描述。Marey 一直认为自己是一名科学家,而不是摄影师。这在他的故事中很重要,尤其是关于一位年轻的助手 George Demenÿ——一个真正的门徒——他将把他带到他在巴黎的生理实验室。49
Marey knew about the hooves from non-photographic measurements. He made real physiological measurements with devices mounted on real hooves of live horses about 1873. He wrote about it in a Popular Science article published the following year. Marey always thought of himself as a scientist, not a photographer. This matters in his story, especially as regards a young assistant, George Demenÿ—a disciple really—whom he would bring into his physiology lab in Paris.49
迈布里奇、马雷和斯坦福在早期就相互了解。大约在 1872 年或 1873 年,迈布里奇在加利福尼亚拍摄了第一张四蹄离地照片,但它消失了。这可能不是很好,因为在阅读了 Marey 的科普文章之后,斯坦福聘请了他再次这样做——而且这次可能是正确的。1878 年,马雷直接敦促迈布里奇为他的马静止图像“动画化”。1881 年,马雷在对巴黎的盛大访问中为迈布里奇举办了招待会。50
Muybridge, Marey, and Stanford were aware of one another in the early days. Muybridge made the first four-hooves-off-the-ground photograph in California in about 1872 or 1873, but it disappeared. It probably wasn’t very good because Stanford hired him to do it again—and presumably right this time—after reading Marey’s Popular Science article. In 1878 Marey directly urged Muybridge to “animate” his still images of the horse. And Marey hosted a reception for Muybridge in his grand visit to Paris in 1881.50
但是方法上有很大的不同。迈布里奇在帧中捕获,但马雷在条形中捕获。图 5.13 是 Marey 艺术的一个很好的例子——他认为这是科学。他的设备在本质上是一个单一的、非常宽的胶卷上记录了多次曝光。(我已经修饰了顶部的背景。)
There was a major difference in approach though. Muybridge captured in frames, but Marey captured in strips. Figure 5.13 is a beautiful example of Marey’s art—which he thought of as science. His device recorded a multiple exposure on what was essentially a single, very wide frame of film. (I’ve touched up the background at the top.)
电影的神话之一是,在爱迪生看到马雷使用条带后,他从拧到圆柱体上的帧升级到记录在条带上的帧。但爱迪生在 1889 年前往法国之前就已经知道脱衣舞了。事实上,迪克森可能已经在旅行前向他展示了带有胶片的实验性活动摄影机。然而,在他从凯旋之旅回来之后,爱迪生又画了另一幅粗略的素描,作为另一个专利局的警告,描绘了脱衣舞电影沿两个边缘的穿孔。又是迪克森,他会从这个单纯的想法中煞费苦心地创造出 20 世纪电影的电影格式。51
One of the myths of cinema is that, after Edison saw Marey’s use of strips, he graduated from frames threaded onto a cylinder to frames recorded on a strip. But Edison was already aware of strip film before he left for France in 1889. In fact, Dickson may have already demonstrated an experimental Kinetograph with a film strip to him before he left on the trip. Nevertheless, it was after his return from the triumphal tour that Edison drew another crude sketch, for another Patent Office caveat, depicting strip film with perforations along two edges. It was Dickson, again, who would painstakingly create from this mere idea the film format of twentieth-century cinema.51
图 5.13
Figure 5.13
1890 年,马雷获得了计时胶片相机的专利。这是一台在无孔赛璐珞胶片上间歇记录的相机。那年晚些时候,他在科学院展示了一部来自该设备的电影——当然是一匹小跑的马!据推测,他忠实的助手 Demenÿ 是这一发展的一部分。我们现在见到了法国发明家团队,并发现了这个 Demenÿ 是谁。
In 1890 Marey took a patent for a chronophotographic film camera. It was a camera that recorded intermittently on unperforated celluloid film. He showed a film from the device later that year at the Académie des sciences—of a trotting horse, of course! Presumably his devoted assistant Demenÿ was part of this development. We now meet the team of French inventors and discover who this Demenÿ was.
正如 Demenÿ、Latham 一家、Armat 和 Jenkins 已经意识到的那样,电影业的诞生离不开一系列背叛、可疑的妥协和背后的利刃。
The cinematographic industry, as Demenÿ, the Lathams, and Armat and Jenkins were already aware, did not come into being without a number of acts of betrayal, dubious compromises, and knives in the back.
——劳伦特·曼诺尼, 《光与影的伟大艺术》52
—Laurent Mannoni, The Great Art of Light and Shadow52
Lumières 获得了所有荣誉,其中大部分是应得的。但是还有其他法国发明家和商人,他们中的许多人在职业生涯的不同阶段一起工作并互相“借鉴”。Étienne-Jules Marey 指导 Georges Demenÿ。Demenÿ 与 Leon Gaumont 合作。Henri Joly 借鉴了 Demenÿ 的想法,然后起诉了 Gaumont。Joly 与后来抛弃了他的 Charles Pathé 合作。这是他们的故事。
The Lumières get all the credit, much of it deserved. But there were other French inventors and businessmen, and many worked together and “borrowed” from each other at various stages of their careers. Étienne-Jules Marey mentored Georges Demenÿ. Demenÿ partnered with Leon Gaumont. Henri Joly borrowed ideas from Demenÿ and then sued Gaumont. Joly partnered with Charles Pathé who later dumped him. Here are their stories.
Cinématographe Lumière 的概念存在很大的混乱。两兄弟在后来的生活中讲述了许多不同的版本——在不同的时间混合了不同的说法,每个人都宣扬自己声称将功德归于自己的说法——以至于真相完全被掩盖了。. . . 雪上加霜的是,卢米埃尔的档案已经消失了。永远不会有像戈登·亨德里克斯那样梳理西奥兰治档案馆的机会来重新确定爱迪生电影放映机发明的真相。
There is great confusion over the conception of the Cinématographe Lumière. The two brothers told so many different versions in later life—mixing different accounts at different times, each promoting his own claim to attribute the merit to himself—that the truth became completely obscured. . . . To add to the difficulty, the Lumière archives have disappeared; there will never be an opportunity like the one Gordon Hendricks had in combing the archives of West Orange to re-establish the truth of the invention of the Edison Kinetoscope.
——劳伦特·曼诺尼,光与影的伟大艺术53
—Laurent Mannoni, The Great Art of Light and Shadow53
他们的名字在法语中是光的意思,这真是太棒了——考虑到历史学家 Laurent Mannoni 对他们的信任度的看法,这真是太讽刺了。Lumières 是一个父亲和两个儿子,就像 Yank Lathams 一样。父亲安托万·卢米埃尔有大儿子奥古斯特和小儿子路易斯。收到的故事干净优雅:两兄弟在各方面都互相钦佩和支持。他们设计了一种单一的、优雅的仪器,Cinématographe,它既可以用作摄影机,也可以用作投影仪。他们首次公开放映了电影院,并引发了电影革命。难怪法国人为他们感到骄傲。但正如本书中的许多故事一样,所接受的故事几乎可以肯定是一个精心设计的创世神话。
How pretty it is that their name is French for light—and how ironic given the historian Laurent Mannoni’s take on their trustworthiness. The Lumières were a father and two sons, like the Yank Lathams. Antoine Lumière, the father, had older son Auguste and younger son Louis. The received story is clean and elegant: The two brothers admired and supported one another in all things. They devised a single, elegant instrument, the Cinématographe, that served both as camera and projector. They gave the first public showing of the cinema, and it launched the movie revolution. No wonder the French are so proud of them. But as with so many stories in this book, the received story is almost certainly a manicured creation myth.
曼诺尼的题词对故事中兄弟般的支持部分撒了谎。但毫无疑问,兄弟俩确实展示了一款既是相机又是投影仪的优雅设备。从某种意义上说,它是可逆的,一台设备既可以读取也可以写入胶片,既可以拍摄又可以投影。此外,他们的Cinématographe 也是一台胶片打印机。它真的是一个完整的电影机在一个盒子里。兄弟俩,尤其是 Louis,在与工程师 Jules Carpentier 的密切合作下慢慢完善了它。
Mannoni’s epigraph puts the lie to the mutual brotherly support part of the story. But it’s perfectly true that the brothers did exhibit a single, elegant device that was both a camera and a projector. It was reversible in the sense that one device could both read and write film, both shoot it and project it. Additionally, their Cinématographe was also a film printer. It really was a complete movie machine in a single box. The brothers, particularly Louis, slowly perfected it in tight collaboration with engineer Jules Carpentier.
乍一看,Cinématographe 似乎是一个简单的设备,但当您阅读 Louis 和 Carpentier 之间交换的许多信件时,这种简单的优雅就变得清晰起来。日复一日,路易斯描述了一些小问题和改进,卡彭蒂尔找到了解决方案并提出了其他建议。完美主义令人惊叹。Lumières 不想在他们的设备绝对完美之前出现在付费观众面前。他们等到生产了 200 台机器后,才于 1895 年 12 月 28 日在巴黎正式推出该机器——这是世界上第四个商业投影,也是欧洲第二个商业投影。
The Cinématographe appears to be a simple device at first glance, but the elegance of that simplicity becomes clear when you read the many letters exchanged between Louis and Carpentier. Day after day, Louis described tiny problems and improvements, and Carpentier found solutions and suggested others. The perfectionism is stunning. The Lumières didn’t want to go before a paying audience with their device until it was absolutely perfect. They waited until they had 200 copies of the machine in production before they formally introduced it on December 28, 1895, in Paris—the fourth commercial projection in the world and the second in Europe.
当我们查看竞争者的日期时,首先要求索赔的推动似乎几乎不合时宜。比狡辩的日期更重要的是 1895 年产生的热情,当时大西洋两岸每个月都会宣布和演示新的投影仪。我们可以简单地通过使用或不使用形容词“商业”来改变顺序。第一个和第二个商业预测——即对一个付费公开——发生在美国,Lathams 于 5 月首次发生,Armat 和 Jenkins 第二次发生在 10 月。第三和第四次成功是在欧洲:11 月德国的 Skladanowsky 获得第三,12 月法国的 Lumières 获得第四。
When we look at the dates of the contenders, the push to claim first seems almost unseemly. More important than the quibbled dates was the fervor generated in 1895, when new projectors were being announced and demonstrated every month on both sides of the Atlantic. We can change the order simply by using or not using the adjective “commercial.” The first and second commercial projections—that is, to a paying public—occurred in the United States, the Lathams first in May, Armat and Jenkins second in October. The third and fourth successes were in Europe: Skladanowsky of Germany third in November, and the Lumières of France fourth in December.
但是放弃“商业”这个词,Lumières 成为第一个公开放映电影的人。1895 年 3 月 22 日,他们在巴黎向数百人展示了一台不太完美的机器。凭借这项公开但非商业性的措施,Lathams 排在第二位,仅在一个月后的 4 月 21 日,他们就向媒体公布了他们的 Eidoloscope。Lumières 也位居第三,7 月在巴黎举行了另一场演出,有 150 人参加。从这个角度来看,当他们在 12 月正式上市时——有付费观众——只有 33 人。54
But drop that word “commercial” and the Lumières become the first to project a movie publicly. They exhibited a not-quite-perfect machine in Paris on March 22, 1895, to several hundred people. With this public-but-noncommercial measure, the Lathams become second, unveiling their Eidoloscope to the press only a month later, on April 21. And the Lumières become third as well with another showing in Paris in July, for 150 people. To put this in perspective, when they formally went public in December—with a paying audience—it was to only 33 people.54
毫无疑问,Lumières 将一个盒子设想为一个完整的电影系统。但莱昂-纪尧姆·布利也是如此,早一点。1893 年,他获得了一种相机-投影仪组合系统的专利,也称为 Cinématographe。但他因不支付(或无法支付)年费而让专利失效。这使得 Lumières 可以自由地使用这个名称,也许还可以使用基本设计。目前尚不清楚神秘的 Bouly 在 Lumière Cinématographe 的开发中扮演了什么角色(如果有的话)。他不是收到的故事的一部分。55
There’s no doubt that the Lumières conceived of one box as a complete movie system. But so had Léon-Guillaume Bouly, a bit earlier. He had patented a combined camera-projector system in 1893, also called a Cinématographe. But he let the patent lapse by not paying—or not being able to pay—the annual fee. This allowed the Lumières to use the name freely and perhaps also the basic design. It’s unclear what role, if any, the mysterious Bouly played in the development of the Lumière Cinématographe. He’s not part of the received story.55
不幸的是,Lumières 优雅的盒装电影理念并没有被新兴行业所采用。他们的电影格式也不是。他们自己的同胞 Léon Gaumont 和 Pathé 兄弟 Charles 和 Émile 通过采用 Dickson 的 35 毫米胶片系统,即未获得专利的“爱迪生”系统,帮助终结了他们的厄运。尽管如此,Lumières 在早期的美国市场上竞争激烈。他们当时的规模很大——而且在法国大众的想象中仍然如此。56
Unfortunately, the Lumières’s elegant movie in a box idea wasn’t adopted by the emerging industry anyway. Nor was their film format. Their own countrymen, Léon Gaumont and the Pathé brothers, Charles and Émile, helped seal their doom by adopting Dickson’s 35 mm film system, the unpatented “Edison” system. Nevertheless, the Lumières competed fiercely in the early American market. They figured large then—and still do in the French popular imagination.56
Georges Demenÿ 这个名字出现在电影史流程图中的几个关键位置。然而,像 WKL Dickson 一样,很少有人听说过他。但他在那里,在某种程度上与几乎所有法兰克球员都有联系——马雷、卢米埃尔、高蒙、乔治·德贝茨和亨利·乔利。美国历史学家保罗·斯佩尔为迪克森所做的,法国历史学家洛朗·曼诺尼为德门所做的。Mannoni 是巴黎著名的法国电影资料馆的电影技术策展人,他将 Demenÿ 带回了历史意识。Demenÿ 的故事充满了失望、失败和肮脏的待遇。57
The name Georges Demenÿ pops up in several crucial places in the flow chart of cinema history. Yet, like W.K.L. Dickson, few people have heard of him. But there he is, connected in some way with nearly every Franks player—Marey, the Lumières, Gaumont, George de Bedts, and Henri Joly. What the American historian Paul Spehr has done for Dickson, the French historian Laurent Mannoni has done for Demenÿ. Mannoni, curator of cinema technology at the prestigious Cinémathèque française in Paris, has brought Demenÿ back into historical consciousness. The Demenÿ story is full of disappointment, defeat, and sordid treatment.57
Étienne-Jules Marey 是 Demenÿ 在长达十年的协会中的大师、导师和父亲形象。两人的关系始于 1880 年左右。1882 年,马雷在意大利度假时将他的生理实验室的管理权交给了他信任的弟子。58
Étienne-Jules Marey was master, mentor, and father-figure to Demenÿ in a decade-long association. The relationship between the two began in about 1880. It was so strong by 1882 that Marey left management of his physiology laboratory to his trusted disciple when he vacationed in Italy that year.58
但随着时间的推移,Demenÿ 从事计时摄影业务的商业冲动与 Marey 进一步推动生理学的科学动力发生了冲突——这是计算机中臭气与塔裂的回声。Marey 于 1889 年开始警告 Demenÿ 他对这个方向的不满。但 Demenÿ 坚持了下来,到 1893 年这种关系破裂了。他在一封信中提到了 Marey 的“衰老和不连贯的管理”。在马雷要求他辞职后不久。Demenÿ 基本上被解雇了——“被木星的霹雳击倒”是他自己的措辞。这是Demenÿ的第一次重大失败,他与Marey的关系将进一步失望。
But over time Demenÿ’s commercial urge to make a business of chronophotography collided with Marey’s scientific drive to further physiology—an echo of the stinks versus tower rift in computers. Marey started warning Demenÿ of his displeasure with this direction in 1889. But Demenÿ persisted, and the relationship was in tatters by 1893. He referred to Marey’s “senile and incoherent management” in a letter. And soon after Marey demanded his resignation. Demenÿ was essentially fired—“struck down by a thunderbolt of Jupiter” was his own phrasing. This was Demenÿ’s first major defeat, and further disappointment in his relationship with Marey would follow.
如前所述,Demenÿ 可能帮助 Marey 开发了 Marey 在 1890 年获得专利的计时胶片相机。但这个设备很粗糙。它必须是——没有穿孔以确保恒定的帧速率。Demenÿ 利用这一经验建立了自己的计时摄影机。但他的设备不仅仅是从 Marey 实验室借来的。特别是,Demenÿ 的设备有一个“打手”机制,这是他自己的关键设计。他于 1893 年在英国、1894 年在法国和 1895 年在美国为打浆机机构申请了专利。这是一种凸轮,解决了将胶片的连续运动与间歇使用相匹配的棘手问题。胶片平稳地离开投影机的源卷轴,到达投影镜头和照明。然后收卷轴将投影后的胶片顺利收起。但是电影在放映的那一刻通过间歇性的运动保持静止。如果什么都不做,间歇运动会不断地从源卷轴上猛拉胶卷,或者收卷轴会从间歇运动中拉出胶卷。打手通过有节奏地控制松弛来防止这些压力。59
As mentioned earlier, Demenÿ had presumably helped Marey develop the chronophotographic film camera that Marey patented in 1890. But this device was crude. It had to be—without perforations to ensure a constant frame rate. Demenÿ used this experience to build his own Chronophotographe. But his device was more than just a borrowing from the Marey lab. In particular, Demenÿ’s device had a “beater” mechanism, his own crucial design. He patented the beater mechanism in 1893 in England, 1894 in France, and 1895 in the United States. It was a kind of cam that solved the tricky problem of matching the continuous motion of film to the intermittent use of it. Film leaves a projector’s source reel smoothly, on the way to the projection lens and illumination. Then the take-up reel collects the film smoothly after projection. But the film is held stationary at the moment of projection by an intermittent movement. If nothing were done, the intermittent movement would be constantly jerking the film from the source reel, or the take-up reel would be yanking film from the intermittent movement. The beater guarded against these stresses by taking up slack in a controlled rhythmic way.59
在后来的几年里,马雷指责德门ÿ窃取了他对(德门ÿ)计时码表的功劳。这种指责似乎有些牵强。马雷本人承认,预打浆机的设计是公开的,是科学的一部分。Demenÿ 的过错在于他没有遵守科学信用的标准做法。不邀请 Marey 参与部分建立在共同开发基础上的企业肯定是一个心理错误——尽管 Marey 摆出纯粹的科学家的姿态。Demenÿ 对 Marey 的指控的回应加倍强调:Marey 是,他说,“一个生病的老人,没有思想,充满怨恨。” 60
In later years Marey accused Demenÿ of stealing his credit for the (Demenÿ) Chronophotographe. This accusation seems a bit of a stretch. Marey himself admitted that the pre-beater design was public, a part of science. Demenÿ’s transgression was that he failed to honor standard practices of scientific credit. It was certainly a psychological mistake not to invite Marey to be part of a business built partially on joint developments—despite Marey’s posturing as a pure scientist. And Demenÿ doubled down by his response to Marey’s accusation: Marey was, he said, “a sick old man, unthinking and full of rancor.”60
1895 年,Demenÿ 与 Léon Gaumont 签约,以利用他新改进的 Chronophotographe 相机(不带投影仪)。Gaumont 的第一个动作是将机器的名称改为 Biographe。他们的交易在 1896 年进行了修改,以适应Demenÿ 计划对 Chronophotographe/Biographe 进行改进,使其可翻转——既是相机又是投影仪,是一台成熟的电影机。Demenÿ 最终在 1896 年完成了这项工作。然后他在 1897 年将胶片格式转换为穿孔 35 毫米,即“爱迪生”格式,以使机器具有完全的竞争力。但到那时,Demenÿ 在 Gaumont 手中遭受了他的第二次重大失败。61
In 1895 Demenÿ signed with Léon Gaumont to exploit his newly improved Chronophotographe camera (without projector). Gaumont’s first act was to change the machine’s name to Biographe. Their deal was modified in 1896 to accommodate Demenÿ’s planned improvement of the Chronophotographe/Biographe to make it reversible—both a camera and a projector, a full-fledged movie machine. Demenÿ finally accomplished this in 1896. Then he converted the film format in 1897 to perforated 35 mm, the “Edison” format, to make the machine fully competitive. But by then Demenÿ had suffered his second major defeat, at the hands of Gaumont.61
这是“乔利事件”的结果。Charles Pathé 购买了一部“爱迪生”活动电影放映机,并需要电影胶片。他从盗版了该设计的英国人罗伯特·保罗那里获得了副本。保罗可以自由地做到这一点,因为爱迪生未能在欧洲为电影放映机申请专利。但是百代不能很好地与爱迪生公司联系,为一台本质上是盗版的机器购买胶卷。因此,百代在 1895 年与法兰克人的发明家亨利·乔利达成协议,为盗版的活动电影放映机制造一台照相机。Joly 是一个不错的选择,因为他了解 Marey 和 Demenÿ 以及他们的工作。为了这项任务,Joly 制作了他的 Cinématographe——Cinématographe Joly——并将其制成可翻转的投影仪。他给了它一个直接从 Demenÿ 拿来的打浆机机制,这使得接下来发生的事情特别令人讨厌。
It came as a result of “the Joly affair.” Charles Pathé purchased a copy of the “Edison” Kinetoscope and needed films for it. He obtained the copy from the Englishman Robert Paul, who had pirated the design. Paul could do this freely because Edison had failed to patent the Kinetoscope in Europe. But Pathé couldn’t very well approach the Edison company to purchase films for an essentially pirated machine. So Pathé made a deal in 1895 with the Franks inventor Henri Joly to build a camera for the pirated Kinetoscope. Joly was a good choice because he knew Marey and Demenÿ and their work. For this task Joly built his Cinématographe—the Cinématographe Joly—and made it reversible into a projector. And he gave it a beater mechanism that he took directly from Demenÿ, which makes what happened next especially unsavory.
Joly 有胆量起诉 Demenÿ 的搭档 Gaumont。他的律师明确承认,Joly 改进了 Demenÿ 的机制。然后他开始命令 Gaumont 停止生产 Demenÿ 机器。棘手的论点似乎是 Demenÿ 的机制是 Joly 专利改进的一部分,因此 Joly 的专利也涵盖了 Gaumont 机器。这很荒谬,但 Gaumont 对法律纠纷的回应是抛弃 Demenÿ!毫不奇怪,Demenÿ 永远为自己没有得到应有的荣誉或奖励而苦恼,他就这样死去——名誉扫地。Joly 也同样被 Pathés 甩了,这对他来说并没有什么安慰。62
Joly had the gall to sue Demenÿ’s partner, Gaumont. His lawyer explicitly admitted that Joly had improved on Demenÿ’s mechanism. Then he proceeded to order Gaumont to cease production of the Demenÿ machine. The screwy argument seems to be that Demenÿ’s mechanism was part of Joly’s patented improvement, so the Joly patent covered the Gaumont machine too. It’s absurd, but Gaumont’s response to the legal hassle was to dump Demenÿ! Not surprisingly, Demenÿ was forever bitter that he wasn’t properly credited or rewarded, and he died that way—discredited. It was no consolation to him that Joly was similarly dumped by the Pathés.62
Joly 注意到 Charles Pathé 仅将 Cinématographe Joly 用作摄影机。Pathé 被 Edison 困在了偷窥的心态,并没有利用设备的投影功能。因此,乔利开始四处寻找能够理解投影所提供业务的人。例如,他与乔治·德·贝茨(George de Bedts)讨论了各种可能性——他曾是德梅尼的众多同事之一。Pathé 的紧张是可以理解的,但他的下一个动作是仓促的。他只是将乔利和他的妻子踢出他提供的设施,同时在他们搬出时将乔利的相机藏起来。那是在 1896 年,正值电影业蓬勃发展的时候,使用投影。Pathé 和爱迪生一样,后来才意识到窥视秀是一条死胡同。他很快找到了一台可逆投影仪并开始做生意,最终成为电影界最成功的电影之一。我们不知道 Pathé 实际使用的是什么机器。也许是乔利的。无论如何,Pathé 将 Joly 赶下台,就像投影业务一样Joly 所敦促的实现了盈利——没有补偿,也没有原型机。乔利试图与另一个合伙人一起创业,但失败了。63
Joly noticed that Charles Pathé was using the Cinématographe Joly only as a camera. Pathé was stuck in the peep-show mentality with Edison and wasn’t exploiting the projection capabilities of the device. So, Joly started sniffing around for someone who would understand the business that projection offered. He discussed possibilities, for instance, with George de Bedts—who had been one of Demenÿ’s many associates. Pathé got understandably nervous, but his next act was precipitous. He simply kicked Joly and his wife out of the facilities that he had provided them, while hiding Joly’s camera from him as they were moved out. This was in 1896, just as the cinema business exploded, using projection. Pathé belatedly realized, as had Edison, that the peep show was a dead end. He quickly found a reversible projector and went into business, ultimately one of the most successful in the cinema world. We don’t know what machine Pathé actually used. Perhaps it was Joly’s. Regardless, Pathé ousted Joly just as the projection business that Joly had urged became profitable—without compensation and without the prototype machine. Joly tried to start a business with another partner, but it failed.63
Demenÿ 的第三次失败是由 Lumières 带来的,他们强烈否认他声称他影响了他们的 Cinématographe 设计。这就是可爱的 Lumière 故事开始崩溃的地方。近几十年发现的 Demenÿ 草图显示了一种间歇运动机制,该机制使用由偏心凸轮移动的一对爪子——这是对 1895 年电影摄影机的描述。路易斯·卢米埃在参观时看过这些图纸,尽管承认这些图纸显示了更粗糙的机制Demenÿ 在 1894 年 12 月。64
Demenÿ’s third defeat was delivered by the Lumières who vehemently denied his claim that he had influenced their Cinématographe design. Here’s where the lovely Lumière story starts to crumble a bit. Demenÿ sketches discovered in recent decades show an intermittent movement mechanism that uses a pair of claws moved by an eccentric cam—a description of the Cinématographe of 1895. Louis Lumière had seen these drawings, although admittedly ones showing a much cruder mechanism, when he visited Demenÿ in December 1894.64
Demenÿ 也出现在流程图的 Yanks 一侧,一些历史学家认为他应该在那里得到更多的信任。1895 年,詹金斯和阿马特在后来的“爱迪生”Vitascope 投影仪中使用了打浆机。美国专利局宣布它是从 Demenÿ 借来的。迪克森团队可能也将它借用于传记投影仪,但历史陪审团仍然对此不以为然。当时流行的摄影文献描述了 Demenÿ beater 的专利,所以这已经不是什么秘密了。65
Demenÿ also appears on the Yanks side of the flow chart, and some historians think he should be given even more credit there. Jenkins and Armat employed a beater in 1895 in what became the “Edison” Vitascope projector. The US Patent Office declared that it was borrowed from Demenÿ. The Dickson team might also have borrowed it for the Biograph projector, but the historical jury is still out on that. Popular photographic literature of the time described the Demenÿ beater patent, so it was no secret.65
对 Demenÿ 的描述有足够的柔和和不确定性,表明他可能无法与天才迪克森相提并论。然而,他不应该被遗忘。他参与的太多,认识太多的球员,并且对电影机器的一些根本性改进负责——也许比我们知道的要多。
There is enough softness and uncertainty in this account of Demenÿ to suggest that he probably was no match to the genius Dickson. Nevertheless, he shouldn’t be forgotten. He took part in too much, knew too many of the players, and was responsible for some of the fundamental improvements to the movie machine—perhaps more than we know.
到 1907 年,爱迪生公司拥有美国电影摄影机的一项主要专利,并通过不断的诉讼来行使这项专利。终于筋疲力尽,爱迪生的竞争对手向公司寻求救济。解决方案是 1908 年电影专利公司的诞生,有时也称为爱迪生信托公司。大约 10 家公司将他们的专利集中在一起,并作为一个团队进行竞争。该集团包括法国公司 Pathé 的美国分公司和当时最大的胶卷供应商伊士曼柯达公司。甚至爱迪生最大的竞争对手迪克森的传记也加入了。爱迪生无法抗拒的传记投影仪专利是使信托如此有效的原因。如果这听起来像垄断勾结,那是因为它是。66
By 1907 the Edison company owned one of the major US patents on movie cameras and exercised it with incessant litigation. Finally exhausted, Edison’s competitors approached the company for relief. The solution was the birth in 1908 of the Motion Picture Patents Company, sometimes called the Edison Trust. About 10 companies pooled their patents together and as a group went after competition. Included in the group was the American branch of the French company, Pathé, and the Eastman Kodak company, the largest supplier of film stock at the time. Even Dickson’s Biograph, Edison’s greatest competitor, joined. The Biograph projector patents—which Edison couldn’t combat—were what made the Trust so effective. If this sounds like monopolistic collusion, that’s because it was.66
声称爱迪生信托导致好莱坞诞生的说法过于强烈。这似乎是合理的,因为加利福尼亚距离总部位于新泽西的爱迪生公司还有很长的路要走。毫无疑问,信托基金发现很难在这种情况下追踪和行使专利。但更重要的西海岸福利是充足的阳光、廉价的劳动力和房地产。许多独立电影制片人搬到了那里。例子有环球影城,它在 1912 年成立后不久就搬到了好莱坞,还有派拉蒙影业,于 1912 年在那里成立,它们今天仍然在好莱坞。这两个 Yanks 的制片厂加上 Gaumont 和 Pathé for the Franks 是世界上现存的五个最古老的电影制片厂中的四个。(第五是丹麦的诺德电影。)
A claim that the Edison Trust led to the creation of Hollywood is too strong. It seems plausible because California was a long way from the New Jersey–based Edison company. Surely the Trust found it difficult to track and exercise patents at that remove. But the more important West Coast benefits were plentiful sunshine, and cheap labor and real estate. Many independent film producers moved there. Examples were Universal Studios, which moved soon after forming in 1912 to Hollywood, and Paramount Pictures, founded there in 1912, both still in Hollywood today. These two Yanks’ studios plus Gaumont and Pathé for the Franks are four of the five oldest surviving movie studios in the world. (The fifth is Denmark’s Nordisk Film.)
偏远的好莱坞位置并没有保护环球影城。无论如何,爱迪生信托基金紧随其后。但在 1917 年,美国最高法院以滥用专利为由裁定该信托基金不成立。最后,在 1918 年,爱迪生信托被终止为根据谢尔曼反托拉斯法非法限制贸易。67
The remote Hollywood location didn’t protect Universal Studios. The Edison Trust came after it anyway. But in 1917 the US Supreme Court found against the Trust—citing misused patents. And finally, in 1918, the Edison Trust was terminated as an illegal restraint of trade under the Sherman Antitrust Act.67
这样就完成了电影流程图诞生的扩展标题。现在我们专注于电影的那个特殊分支——动画电影——在我们的讲述中,它导致了数字大融合。通过 Digital Light 有很多途径,但我最了解的一条是通过角色动画。
This completes the extended caption for the birth of cinema flow chart. Now we concentrate on that special branch of cinema—the animated film—that leads, in our telling, to the Great Digital Convergence. There are many paths through Digital Light, but the one I know best is via character animation.
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我们已经区分了数码灯的一半像素和制作像素的一半。到目前为止,从现实世界中提取像素来代表现实世界已经占据了我们的大部分时间。现在让像素代表虚幻世界成为我们的重点。
We have distinguished the taking pixels half of Digital Light from the making pixels half. Taking pixels from the real world to represent the real world has occupied us mostly so far. Making pixels to represent unreal worlds now becomes our focus.
一旦我们了解了计算机内部的几何模型如何成为创建虚幻世界的帧流中的像素帧,那么我们将足够了解游戏的工作原理,以及虚拟现实 (VR)、增强现实 (AR) ),以及所有应用程序和互联网的所有用户界面。我们在 3D 数字角色动画中使用的相同基本原理解释了它们。特别是,它们都共享一个正在显现的计算机内部的不可见模型的概念。在拍摄和制作之间,我们掌握了完整的数码灯。
Once we understand how a geometrical model inside a computer becomes a frame of pixels in a stream of frames that create an unreal world, then we’ll know enough to intuit how games work, and also virtual reality (VR), augmented reality (AR), and, mundanely, all user interfaces with all apps and with the internet. The same basic principles that we use in three-dimensional digital character animation explain them all. In particular, they all share the notion of an invisible model inside a computer that is being made manifest. Between taking and making, we gain a handle on full Digital Light.
现在我们开始着手制作数字光的像素部分——尤其是数字电影。让我们从电影界经典二维角色动画的简史及其工作原理开始。这为我们提供了角色动画所需的语言。然后我们在后面的章节中应用计算机强大的放大功能来达到所有的数字光。
Now we begin our runup to the making pixels part of Digital Light—digital movies in particular. Let’s start with a brief history of classic two-dimensional character animation in the film world and how it worked. This provides the language we need for character animation. Then we apply the computer’s awesome power of Amplification in later chapters to reach all of Digital Light.
动画向我们展示了运动中的一些自然惰性的东西,我们从中得到的本质上是对魔法的满足。
The animated cartoon shows us in movement something that is naturally inert and it is essentially the satisfaction of magic that we get out of it.
——唐纳德·克拉夫顿,在米奇68 岁之前
—Donald Crafton, Before Mickey68
因此,摄影机,乔治·华盛顿的机器,最终被证明是个骗子。
Thus the camera, that George Washington of mechanism, at last is proved a liar.
——Ashton Stephens,一位评论家在看过 Winsor McCay 的Gertie the Dinosaur (1914) 69
—Ashton Stephens, a reviewer upon seeing Winsor McCay’s Gertie the Dinosaur (1914)69
动画电影的存在时间与电影本身一样长,至少从 1895 年的发明热潮开始。但它们是什么?
Animated movies have existed as long as cinema itself, at least since that fervor of invention in 1895. But what are they?
定义它们很棘手。经典电影取材于现实世界。布景和服装可能是虚构的,灯光是人造的,演员扮演的角色可能是虚构的,但它们都是现实世界的一部分。这并不明显,但手绘动画电影的帧也来自现实世界。在卡通动画中,例如迪斯尼的《白雪公主和七个小矮人》(1937 年),每一帧都是一幅图画的照片或一幅虚幻世界的图画。那些图画或绘画是现实世界中的对象。因此,区分动画电影的不是虚幻与真实。
Defining them is tricky. Classic cinema takes its frames from the real world. The sets and costumes may be fictitious, the lighting artificial, and the characters impersonated by actors, but all of them are parts of the real world. It’s not obvious, but a hand-drawn animated movie takes its frames from the real world too. In cartoon animations, such as Disney’s Snow White and the Seven Dwarfs (1937), each frame is a photograph of a drawing or a painting of unreal worlds. Those drawings or paintings are objects in the real world. So it’s not unreal versus real that distinguishes animated movies.
区分他们的不是制造与接受。只有被称为纪录片的小类别声称拍摄现实世界本身。大部分电影都是虚构的。大多数电影的每一帧,无论是否动画,都是在用相机录制之前精心制作的。
It’s not making versus taking that distinguishes them. Only the small category known as documentary films purports to take pictures of the real world itself. Most of cinema is fictitious. Each frame of most movies, animated or not, is crafted—made—before recording with a camera.
正如漫画所暗示的那样,这也不是二维对三个维度。一些所谓的定格动画电影从真实的三维世界中获取每一帧。以雷·哈里豪森 (Ray Harryhausen) 的经典作品Jason and the Argonauts (1963) 中跳舞的骷髅为例。或者任何我喜欢和孙子们一起看的现代小羊肖恩(2007 年至今)剧集。一些最早的动画电影是定格动画,或者至少是间断动画——例如乔治·梅里爱的《闹鬼的城堡》(1896 年)或詹姆斯·斯图尔特·布莱克顿的《闹鬼的酒店》(1907 年)。一些最早的非动画电影是展示一位艺术家绘制二维卡通的电影——例如埃米尔科尔的幻想曲(1908 年)和温莎·麦凯的小尼莫(1911 年)。这些所谓的闪电素描不是动画电影——只要可以看到艺术家的身体——尽管有二维内容。
And it’s not two versus three dimensions either, as cartoons might suggest. Some so-called stop-motion animated movies take each frame from the real three-dimensional world. Take the dancing skeletons of Ray Harryhausen’s classic Jason and the Argonauts (1963), for example. Or any of the modern Shaun the Sheep (2007–present) episodes that I love to watch with my grandkids. Some of the earliest animated movies were stop-motion or, at least, interrupted motion—such as Georges Méliès’s The Haunted Castle (1896) or James Stuart Blackton’s The Haunted Hotel (1907). And some of the earliest non-animated movies were films showing an artist in the act of drawing a two-dimensional cartoon—such as Émile Cohl’s Fantasmagorie (1908) and Winsor McCay’s Little Nemo (1911). These so-called lightning sketches weren’t animated movies—so long as the artist’s body could be seen—despite the two-dimensional content.
这些电影说明动画片段或镜头经常以各种方式与非动画片段混合在一起。动画电影和他们的动画师是延伸的 Yanks vs Franks 电影奥运会的一部分。70
These films illustrate that animated snippets, or shots, were often mixed together in various ways with non-animated ones. And that animated movies and their animators were part of the extended Yanks versus Franks cinema Olympics.70
因此,区别动画电影的不是卡通与摄影现实主义。这在数字光的新世界中变得尤为明显。计算机动画帧现在可以像真实世界的照片一样具有丰富的逼真细节。
So, it’s not cartoons versus photographic realism that distinguishes animated movies. This has become particularly obvious in the new world of Digital Light. Computer-animated frames now can be as rich in photorealistic detail as photos taken of the real world.
如果这些东西都没有将动画与非动画电影区分开来,那又是什么呢?这是时间的利用。虚幻的时间,而不是虚幻的空间,定义了动画电影。动画电影与实时无关。我们称所有其他真人电影为真人电影,因为从根本上说,它们与生物一样受时间的奴役。约翰·韦恩 (John Wayne) 穿着刺耳的牛仔装大步穿过西部片场,占据了一个虚构的精心制作的空间,但他的动作被实时记录下来。
If none of these things sets animated apart from non-animated movies, then what does? It’s the use of time. Unreal time, not unreal space, defines animated movies. Animated movies are unhinged from real time. We call all others live-action movies because they are, at base, as enslaved to time as live beings are. John Wayne striding across a Western set in his jangling cowboy outfit occupies a fictitious crafted space but his movements are recorded in real time.
这可能看起来不对。众所周知,电影是导演或剪辑师及时自由排序或重新排序的一系列镜头。当然,自由地重新安排时间与被时间奴役相反。但请记住,每个镜头都是连续视觉流的时钟采样。它是现场的或实时的动作。
This might not seem right. Famously, a movie is a sequence of shots that a director or editor freely orders, or reorders, in time. Surely being free to reorder time is the opposite of being enslaved by it. But remember that each shot is a clocklike sampling of a continuous visual flow. It’s live, or real-time, action.
早期的电影只是一种奇观——嘿,看看这个,现在看看这个——一个喷嚏,一场拳击比赛,一个诱人的舞者,教皇。迪克森在 1900 年左右的许多电影都是这种类型。在电影开始之后不久,剪辑的力量的发现改变了这一切。编辑打乱了时间。我们可以以任意的时间顺序一起编辑电影片段——每个片段都有自己不可阻挡的内部时间。每个片段或镜头都是实时的奴隶,但镜头的顺序不是。有了这种自由,编辑器会导致感知时间加快或减慢。百年可以在一瞬间过去。
Early cinema was mere spectacle—hey, look at this, now look at this—a sneeze, a boxing match, a seductive dancer, the pope. Dickson’s many films circa 1900 were all of this variety. The discovery of the power of the edit, soon after those beginnings of cinema, changed all that. The edit disrupts time. We can edit together snippets of film—each with its own inexorably advancing internal time—in arbitrary temporal order. Each snippet, or shot, is a slave to real time, but the ordering of the shots isn’t. With this freedom an editor causes perceived time to speed up or slow down. Centuries can pass in an instant.
千年也是如此,如2001 年:太空漫游(1968 年),它著名地从一根骨头棍子跳到了宇宙飞船上(图 5.14)。猿猴向上投掷骨头。随着相机不断地向上和向上,它缓慢地翻滚。. . 它在空间站 V 附近变成了形状大致相同的地球卫星,这是一个雄伟的旋转中转站,供人类前往月球。导演斯坦利库布里克的“比赛剪辑”瞬间跨越了整个人类历史。
So can millennia, as in 2001: A Space Odyssey (1968), which famously jumps from a bone cudgel to a spacecraft (figure 5.14). An ape hurls the bone upward. It tumbles slowly as the camera follows it up and up and . . . it becomes an Earth satellite of roughly the same shape in the vicinity of Space Station V, a majestically rotating waystation for humans bound for the Moon. Director Stanley Kubrick’s “match cut” spans the entire history of mankind in an instant.
剪辑的力量来自于叙事和情感。由此产生的软件就是我们称之为“电影”的艺术形式。比喻说,无数可能的程序在我们的大脑上进行计算。
From the power of the edit comes narrative and emotion. And the resulting software is the artform we call “the cinema.” An infinity of possible programs compute, metaphorically, on our brains.
动画电影将剪辑发挥到了极致——每帧一个。时间不再是限制。没有视觉流程可供采样。下一帧通常是动画师打算在未来 24 秒内拍摄的当前帧,就好像它是从视觉流中实时记录的一样。但不一定是这样。它发生在动画师创建的虚构时间,可能很少或没有与实时的关系——或者是对采样实时的精确模拟。
Animated movies take the edit to the limit—one every frame. Time is no longer a restriction. There is no visual flow to sample. It’s common for the next frame to be what an animator intends to be the current frame taken one twenty-fourth of a second into the future, as if it were recorded in real time from a visual flow. But it doesn’t have to be. It occurs at a fictitious time created by the animator, that might bear little or no relationship to real time—or alternatively be a dead-on accurate simulation of sampled real time.
图 5.14
Figure 5.14
因此,动画电影的世界正在争夺中。它可以像艺术家希望的那样抽象。任何顺序的任何形式都是允许的。到了极限,抽象动画——纯粹来自任意视觉的情感创造,就像音乐来自任意声音一样——是等待莫扎特、肖邦和斯特拉文斯基的伟大艺术形式之一,但一直有一些实践者。著名的例子是 Walter Ruttman 的Lichtspiel: Opus I (1927) 和 Oskar Fischinger 的Motion Paint No. 1 (1947)——纯粹的视觉音乐。71
Hence the world of the animated movie is up for grabs. It can be as abstract as the artist wishes to make it. Any form in any order is permitted. Taken to the limit, abstract animation—the creation of emotion as purely from arbitrary visuals as music is from arbitrary sounds—is one of the great artforms awaiting its Mozart, Chopin, and Stravinsky, but there have been a few practitioners all along. Notable examples are Walter Ruttman’s Lichtspiel: Opus I (1927) and Oskar Fischinger’s Motion Paint No. 1 (1947)—sheer visual music.71
科尔不是外行。相反,他正在成为一个偏执狂,并将他的余生致力于推动动画作为一种艺术和产业。他最有责任将他的前辈们的努力转化为一种独特的 20 世纪艺术。
Cohl was no dilettante; on the contrary, he was on his way to becoming a monomaniac and would dedicate the rest of his life to the promotion of animation as an art and industry. He was the one most responsible for transforming the efforts of his trickfilm predecessors into a unique twentieth-century art.
——唐纳德·克拉夫顿,在米奇72之前
—Donald Crafton, Before Mickey72
与真人电影的奇观时代一样,动画电影也经历了早期的进化阶段。起初有特技电影,比如斩首或魔术。导演使用中断帧之间时间的能力来说服我们一个人失去了他的头,或者茶壶在跳舞。法国的乔治·梅里爱(Georges Méliès)也许是最著名的早期戏法电影大师——例如《月球之旅》( A Trip to the Moon,1902 年)。在普通镜头中使用了剪辑,以使我们相信不可能实时发生的事情。正是在镜头中与时间的混战使特技电影成为动画的一部分。
Like the spectacle era of live-action movies, animated movies went through an early evolutionary phase. At first there were trickfilms, like a beheading or a magic trick. Directors used the ability to interrupt time between frames to convince us that a human had lost his head, or that teapots danced. Georges Méliès in France was perhaps the most famous early trickfilmster—A Trip to the Moon (1902), for example. Editing was used, within a normal shot, to convince us of something impossible happening in real time. It’s the fooling with time in a shot that make trickfilms part of animation.
继特技电影之后的是以主持人本人为主角的闪电小品,他本人就是导演。他会继续在黑板上作画,显然是实时的,然后画出的人物就会“栩栩如生”。就好像导演不愿意承诺制作完整的动画,或者无法相信它会真正起作用——观众会得到它。或者他们不愿意让自己远离聚光灯。闪电素描者会向观众展示他在做什么,或者如何理解正在发生的事情。格蒂恐龙(1914)是一个著名的早期例子。温莎·麦凯出现在屏幕上,指着一张大纸上的风景。他把格蒂从她的洞穴里叫出来。当她出现时,她变成了自己的生命——一个新的意识中心,就像一个新生婴儿。所以格蒂是一部真人电影与动画电影的插曲。73
Succeeding the trickfilms were the lightning sketches that featured a presenter, a human who was the director himself. He would proceed to draw on a board, apparently in real time, and then the character drawn would “come to life.” It was as if directors were unwilling to commit to full animation or couldn’t believe that it would actually work—that an audience would get it. Or they were unwilling to take themselves out of the limelight. The lightning sketcher would show the audience what he was doing, or how to understand what was happening. Gertie the Dinosaur (1914) is a famous early example. Winsor McCay appears onscreen and points to a landscape on a large pad of paper. He calls Gertie forth from her cave there. When she appears, she becomes a life on her own—a new center of consciousness, like a new baby. So Gertie is a live-action movie intercut with an animated one.73
Émile Cohl 对法兰克人来说就像温莎麦凯对洋基队一样,因为他是最早的动画师之一。但两人却截然不同。动画历史学家唐纳德·克拉夫顿(Donald Crafton)将科尔描述为聪明而内向,而麦凯则描述为善于交际的主持人和华丽的表演者。因此,几乎没有人知道科尔也就不足为奇了,尽管与麦凯相比,他制作了数百部电影。此外。Cohl 是一群不连贯的艺术家,他们专注于将精神错乱作为一个美学问题——不完全是一个受欢迎的事业。尽管如此,他的由 Gaumont 发行的Fantasmagorie (1908) 可以说是第一部动画片,克拉夫顿称他为第一位动画师。但他为麦凯保留了最重要的头衔:第一位角色动画师。74
Émile Cohl is to the Franks what Winsor McCay is to the Yanks, so far as being one of the earliest animators. But the two were very different. Animation historian Donald Crafton describes Cohl as cerebral and introverted, and McCay as a gregarious host and a flamboyant showman. So it’s not surprising that hardly anybody knows Cohl, even though he produced hundreds of films compared to McCay’s handful. Furthermore. Cohl was an Incoherent, a group of artists who concentrated on insanity as an aesthetic issue—not exactly a popular cause. Nevertheless, his Fantasmagorie (1908), distributed by Gaumont, was arguably the first animated cartoon, and Crafton calls him the first animator. But he reserves the most important title for McCay: the first character animator.74
几分钟后,麦凯让观众相信他已经复活了一只可爱而有形的动物——这是动画师作为生命给予者的胜利时刻。
In minutes McCay convinces the audience that he has resurrected a lovable and tangible animal—a triumphant moment for animator as life giver.
——唐纳德·克拉夫顿,在米奇75之前
—Donald Crafton, Before Mickey75
动画电影的神奇灵魂在于我们所说的角色动画,这是从迪士尼的《白雪公主》(1937 年)到皮克斯的《玩具总动员 4》(2019 年)等最常见和最受欢迎的动画电影必不可少的现象。手绘角色——如白雪公主中的邪恶女巫——以速度投射时似乎在移动。到这个时候,这应该不足为奇。如果样本制作精良,这正是采样定理所保证的。更重要的是——也是神奇的——动画师的技能使移动的角色变得生动起来!它有良心,做出决定,并感到痛苦——或给予痛苦——或说服我们无论如何它都会这样做。那个狡猾的 Road Runner 又一次比那个笨拙的 Coyote 更聪明。这种魔法并非来自采样定理。这是艺术,我们还无法解释。动画不仅仅意味着移动。它的意思是鼓舞人心。阿尼玛是拉丁文风,空气,呼吸,生命的原则,灵魂。这是自然惰性变得不那么惰性的魔力——不是惰性,但更重要的是,不是死的。
The magical soul of animated movies resides in what we call character animation, a phenomenon essential to the most common and popular animated movies, from Disney’s Snow White (1937) to Pixar’s Toy Story 4 (2019). A hand-drawn character—like the Wicked Witch in Snow White—appears to move when projected at speed. That shouldn’t be a surprise by this time. It’s just what the Sampling Theorem guarantees, if the samples are well made. Much more importantly—and magically—the skill of an animator causes the moving character to come alive! It has a conscience, makes decisions, and feels pain—or gives pain—or convinces us that it does anyway. That crafty Road Runner outsmarts, yet again, that unwily Coyote. This magic doesn’t come from the Sampling Theorem. It’s art, and we can’t explain it yet. To animate means more than to move. It means to inspirit. Anima is Latin for wind, air, breath, the vital principle, soul. It’s the magic of the naturally inert becoming not so—not inert, but more importantly, not dead.
动画电影历史上的一个重要时刻是第一个真正的角色动画的放映——受到启发,而不仅仅是动人。可以肯定地说,它发生在电影早期的某个时候。克拉夫顿在题词中暗示,这件事发生在 1914 年,麦凯和他的恐龙格蒂。在那一刻,角色与屏幕上的创作者断绝了关系。观众可以相信会得到它——意识到动画角色是独立的。不需要笨拙的解释。你可以省略明确的人类教育者。
A momentous moment in the history of the animated movie was the projection of the first true character animation—inspirited, not merely moving. It’s safe to say it occurred sometime in the early years of the cinema. Crafton suggests in the epigraph that it happened in 1914 with McCay and his dinosaur Gertie. At that moment characters were weaned from an onscreen creator. Audiences could be trusted to get it—to realize that animated characters are lives on their own. No clumsy explanations were necessary. You could omit the explicit human pedagogue.
然而,观众是否会明白这一点并不明显——灵感动画应该奏效。我们甚至不知道它是什么。我们也不知道动画师是如何做到的。他们也没有。同样,我们不知道演员是如何让我们相信他们不是他们自己的人。事实上,这两个观察结果是相互关联的。动画师的技能与演员的技能相同。一个演员让我们相信他或她的身心与另一个完全不同的人不同。一位动画师让我们相信,一堆无生命的图画——或者数百万个多边形,就 Digital Light 而言——是有生命的和有意识的。皮克斯根据动画师的表现来雇佣动画师。
It wasn’t obvious, though, that audiences would get it—that inspirited animation should work. We don’t even know what it is. Neither do we have any idea how animators do it. Nor do they. Similarly, we don’t know how actors persuade us that they are somebody other than who they are. In fact, the two observations are linked. The skill of an animator is the same as that of an actor. An actor convinces us that his or her body and mind are those of some other completely different person. An animator convinces us that an inanimate stack of drawings—or millions of polygons in the case of Digital Light—is alive and conscious. Pixar hires animators by how well they act.
作为 1950 年代的孩子,当沃尔特·迪斯尼本人在他的每周迪斯尼乐园电视节目中解释动画制作过程时,我感到非常激动。他描述了一项名为cel动画,下节详述。Cel是赛璐珞的缩写,实际上只有一个“l”。当我在 1970 年代初自学动画时,是 cel 动画。当我在 1970 年代中期从专业人士那里学习动画时,他们教的是 cel 动画。当我和我的同事在 1970 年代后期开始以数字方式实现动画时,我们采用的方法是 cel 动画的数字等价物。而当我们在 1980 年代后期第一次为迪士尼公司实现二维动画时,又是 cel 动画。因此,我认为 cel 动画是唯一的动画技术也就不足为奇了。但是我错了。76
As a child in the 1950s, I thrilled as Walt Disney himself explained the animation process on his weekly Disneyland television show. He described the technology called cel animation, detailed in the following section. Cel is short for celluloid, and it’s really spelled with only one “l.” When I learned animation on my own in the early 1970s, it was cel animation. When I learned animation from professionals in the mid-1970s, it was cel animation that they taught. When I and my colleagues began to implement animation digitally in the late 1970s, the approach we took was the digital equivalent of cel animation. And when we first implemented two-dimensional animation for the Disney company in the late 1980s, it was cel animation again. So it’s no surprise that I thought cel animation was the only animation technology that there was. But I was wrong.76
在 20 世纪之交的早期,埃米尔·科尔(Émile Cohl)采用一种称为剪纸的技术,将他的卡通人物的拼接剪纸放在背景上。一个不透明的切口位于绘制的背景上。例如,科尔可能已经抬起角色的脚准备迈出一步。拍摄了一个框架,然后重新定位切口 - 例如,膝盖略微下降,并且随着步骤的进行,脚趾更直接地对准地板。这本质上是基于定格摄影的二维动画。77
In the early days at the turn of the twentieth century, Émile Cohl placed jointed paper cutouts of his cartoon characters over a background in a technique called decoupage. An opaque cutout was positioned over a drawn background. For example, Cohl might have raised the foot of a character in preparation for a step. A frame was photographed, then the cutout was repositioned—so that, say, the knee descended slightly, and the toes were aimed more directly at the floor as the step proceeded. This was essentially two-dimensional animation based on stop-motion photography.77
在早期的另一种技术中,称为slash and tear,动画师会在背景绘图中切出一个洞,以露出下面一堆绘图的最顶部。然后在拍摄完一帧后,他或她撕下顶部的图画以显示角色的下一个位置,如通过背景中的孔看到的那样。法裔加拿大动画师 Raoul Barré 使用了这种技术。它是 cel 动画技术的唯一重要竞争对手。78
In another technique of the early days, called slash and tear, the animator would cut a hole in a background drawing to reveal the topmost of a stack of drawings underneath. Then after photographing one frame, he or she tore off the top drawing to reveal the next position of the character, as seen through the hole in the background. The French Canadian animator Raoul Barré used this technique. It was the only serious competitor to the cel animation technique.78
竞争技术的一个重要原因是对 cel 动画专利的大力捍卫。负责将动画建立在坚实的商业基础上——准备好维持对真实电影行业产品的永不满足的需求——的人是约翰·伦道夫·布雷。他了解专利的力量,并着手开发我们现在称为 cel 动画的大部分内容,并于 1913 年为其申请了专利。但他未能将透明赛璐珞的关键理念——cels 纳入其中。纸是他的主要材料。79
A strong reason for a competing technology was the vigorous defense of patents on cel animation. The man responsible for putting animation on a firm businesslike foundation—ready to sustain the insatiable demand for product of a real movie industry—was John Randolph Bray. He understood the power of a patent and proceeded to develop most of what we now call cel animation and patent it in 1913. But he failed to include the crucial idea of transparent celluloid—cels. Paper was his main material.79
Earl Hurd 在 1914 年申请了专利,确定了我们所知道的 cel 动画过程。但布雷和赫德并没有在法庭上解决分歧,而是达成协议,共同追求他们的想法,作为布雷-赫德进程。布雷总是把这个过程归功于自己,但很明显赫德的专利才是真正的关键。然后他们追捕那些没有从他们那里购买许可证的动画行业的人。因此,以较小的方式,布雷和赫德将制作爱迪生信托对真人电影的动画。80
Into that patent void leapt Earl Hurd who filed the patent in 1914 that nailed down the cel animation process as we know it. But rather than fight out their differences in the courts, Bray and Hurd reached an agreement to pursue their ideas together, as the Bray-Hurd Process. Bray always took credit for the process, but it’s clear that Hurd’s patent was the real clincher. They then went after those in the animation business who didn’t buy a license from them. So in a smaller way, Bray and Hurd were to animation what the Edison Trust was to live-action movies.80
将苹果浸入啤酒中
Dip the apple in the brew
让沉睡的死神渗透
Let the Sleeping Death seep through
——邪恶的女巫,白雪公主(1937)
—Wicked Witch, Snow White (1937)
由于 cel 动画导致了 Digital Light,我们将详细讨论它。凭借 cel 动画技术,Ub Iwerks 和沃尔特迪斯尼创立了一系列将角色动画带入大时代的公司。这是用于制作迪士尼白雪公主(1937 年)的技术,这是第一部成功的长篇动画电影——这部电影可能暗示艾伦·图灵死于毒苹果。81
Since cel animation led to Digital Light, we’ll discuss it in some detail. With cel animation technology Ub Iwerks and Walt Disney started the chain of companies that would bring character animation into the big time. It was the technology used to make Disney’s Snow White (1937), the first successful feature-length animated movie—the film that might have suggested death with a poisoned apple to Alan Turing.81
一旦你听到它的细节,cel 动画技术似乎很明显。这就是为什么,我怀疑,我们中的许多人对此一无所知。Cel 动画使用摄影来捕捉一系列图像。一位摄影师在一个特殊的“相机架”上放置了一个背景场景,该场景是由背景艺术家在不透明材料上绘制的,作为第一层或最底层。然后他在上面画了一个透明的赛璐珞,上面画了一个角色——一个完整的赛璐珞。这两层通过作为相机支架一部分的金属钉进行严格的注册。沿每层顶部打的孔接收这些钉子。然后他放下另一个 cel,上面有另一个彩绘字符,在第一个之上。等等。将所有前景字符都对准背景上方,并紧紧地靠在背景上,他为堆栈拍了一张照片。相机看到堆栈形成的合成图像。那是电影的一帧。摄影师为电影的每一帧重复这个费力的过程——从下往上——因为每个角色通常在帧之间移动一点。对于一部长片,他这样做了多达 130,000 次。
The cel animation technology seems obvious once you hear its details. That’s why, I suspect, so many of us knew of nothing else. Cel animation uses photography to capture a sequence of images. A cameraman lays down, on a special “camera stand,” a background scene that’s been painted by a background artist on opaque material as the first, or bottommost, layer. Then he layers above that a transparent celluloid with a character painted on it—a completed cel. The two layers are held in strict registration by metal pegs that are part of the camera stand. Holes punched along the top of each layer receive those pegs. Then he lays down another cel, with another painted character on it, above the first. And so on. With all the foreground characters in register above the background, and held tightly against it, he takes a photo of the stack. The camera sees the composite image formed by the stack. That’s one frame of the movie. The cameraman repeats this laborious process—from the bottom up—for each frame of a movie because each character usually moves a little between frames. He does this as many as 130,000 times for a feature-length film.
为了首先创建每个单独的 cel,动画师使用铅笔在纸上绘制分配给他的角色,就位。在随后的每幅画中,他的角色都会轻微移动。每张纸都具有规定尺寸,并在其顶部打有用于登记钉的规定孔。然后一张透明的赛璐珞片,大小相同,打孔方式相同,用钉子牢牢固定在动画师的图纸上方。墨工仔细地在透明的赛璐珞上用黑色墨水在 cel 上描绘铅笔画。
To create each individual cel in the first place, an animator draws the character assigned to him, in position, using pencil on paper. In each subsequent drawing his character moves slightly. Each sheet of paper is of regulation size and punched with regulation holes across its top for the registration pegs. Then a clear sheet of celluloid, of the same size and punched the same way, is registered above the animator’s drawing using the pegs to hold position firmly. An inker carefully traces the pencil drawings, visible through the clear celluloid, with black ink onto the cel.
上墨者将每个上墨的 cel 传递给opaquer,它的工作是用彩绘颜色填充被墨迹线包围的区域 - 就像一个拿着蜡笔和着色书的孩子一样,非常小心不要超出线条。遮光剂将上墨的 cel 翻转过来并在其背面上漆,这样油漆就位于正常通过 cel 观察到的上墨线下方。这保留了墨线的质量——它们的变化例如,相机看到的宽度。不透明是使用的术语,因为油漆必须涂得足够厚以阻止光通过细胞。背景层不能通过一个 cel 的着色不透明部分(通过一个字符)或通过另一个 cel 的任何 cel 看到,除非在未绘制的地方。
The inker passes each inked cel to an opaquer, whose job is to fill the areas surrounded by inked lines with painted color—like a child with crayons and a coloring book, being very careful not to go outside the lines. The opaquer turns the inked cel over and paints on its back side so that the paint lies under the inked lines as viewed normally through the cel. This preserves the quality of the inked lines—their varying widths, for example—as seen by the camera. Opaquing is the term used because the paint has to be applied thickly enough to stop the passage of light through the cel. The background layer can’t be seen through the painted, opaque parts of a cel—through a character—or any cel through another, except in the unpainted places.
实际上,每帧有四个或五个 cel 的限制。没有 cel 是完全透明的。每个额外的 cel 层都会导致轻微的光通过透明部分丢失。事实上,不透明者必须在每一层上稍微改变他们的油漆颜色,以适应通过一堆所谓的透明 cels 缓慢增加的不透明度。
As a practical matter, there’s a limit of four or five cels per frame. No cel is perfectly transparent. Each additional cel layer causes a slight bit of light lost through even the transparent parts. In fact, opaquers have to alter their paint colors slightly on each layer to accommodate the slow buildup of opacity through a stack of supposedly transparent cels.
不难看出,拥有 130,000 帧的 cel 动画是一场后勤噩梦。假设每帧有四层加上背景。这意味着一部 90 分钟长的电影可能需要跟踪 650,000 个对象。并且必须仔细检查它们中的每一个是否完成,没有错误,并且在框架和分层方面都以正确的顺序进行。上个世纪的动画公司使用精细的手写会计流程来跟踪这些物流——诱人迷人的角色动画的丑陋管道。
It’s not hard to see that cel animation, with 130,000 frames, is a logistical nightmare. Suppose there are four layers per frame plus the background. That means that a 90-minute feature-length movie might have 650,000 objects to track. And every single one of them has to be checked carefully for completion, without error, and in correct order both framewise and layerwise. Animation houses of the last century used elaborate handwritten accounting processes to keep track of these logistics—the ugly plumbing of seductively charming character animation.
从角度来看,Digital Light 可以缓解这两个问题,即一堆 cel 中不透明的累积和丑陋的物流任务。在数字动画中,透明度是完美的。细胞数量没有限制。不透明度累积不是动画中的固有问题,仅在基于 cel 的模拟动画中。但物流是内在的。幸运的是,计算机非常适合这项吃力不讨好的但基本的任务。
For perspective, Digital Light eases both problems, the buildup of opacity in a stack of cels and the ugly logistics task. In digital animation, transparency is perfect. There’s no limit to the number of cels. Opacity buildup is not an intrinsic problem in animation, only in cel-based analog animation. But logistics are intrinsic. Fortunately, computers are perfect for that thankless, but fundamental, task.
动画师必须为电影放映的每一秒创建和组合 24 帧,但早期的动画师实际上经常“在 2 秒上拍摄”。也就是说,他们每秒只创建 12 帧,但每帧拍摄两次以获得必要的 24 帧。他们会偏离这种做法,只针对快速移动的序列。“2s 射击”减少了物流,减少了一半的制作工作,但制作的动画更加不稳定。
Animators must create and assemble 24 frames for each second of film projection, but early animators actually often “shot on 2s.” That is, they created only 12 frames per second, but photographed each frame twice to get the necessary 24. They would depart from this practice only for sequences of fast movement. “Shooting on 2s” reduced the logistics and halved the production effort but made for choppier animation.
早期的动画师开发了一系列技巧来弥补由此产生的低时间采样率以及每一帧实际上是静态的这一事实。检查这些非凡的技巧很有启发性和乐趣。主要的是挤压和拉伸,以及预期和夸张。它们是由完全不了解采样定理但深刻理解人类感知和讲故事的动画师创作的。
Early animators developed a bag of tricks to compensate for the resulting low temporal sampling rate and for the fact that each frame is actually static. It’s instructive—and fun—to inspect these remarkable tricks. The principal ones are squash and stretch, and anticipation and exaggeration. They were created by animators who were completely naive of the Sampling Theorem but deeply understood human perception and storytelling.
考虑一下低弹球,通常是初学者的第一个动画。当一个真正的球弹起时,它所遵循的抛物线曲线的高度会降低。在撞击的那一刻,一个真正的球会轻微变形。球越软,变形越大。如图在图 5.15 中,每个帧时间的一个球显示了该时刻样本的样子。请注意,反弹发生在采样时刻,恰好在该帧时间。因为动画师可以选择他们的采样时间——他们不受时间的影响——他们总是选择那个确切的时刻作为帧。
Consider the lowly bouncing ball, often a beginner’s first animation. As a real ball bounces, the parabolic curves it follows decrease in height. At the moment of impact, a real ball deforms slightly. The softer the ball, the greater the deformation. In figure 5.15, a ball at each frame time shows what a sample at that instant would look like. Note that the bounce happens at the moment of sampling, exactly at that frame time. Because animators get to choose their sample times—they’re unhinged from time—they always choose that exact moment as a frame.
图 5.15
Figure 5.15
请记住,任何电影的每一帧都会被投影两次以避免闪烁。这意味着即使在最好的情况下——用 1 秒而不是 2 秒射击——弹跳球的每个位置都会在视网膜上投射两次。但是当动画师在 2s 上拍摄时,每一帧都会重复两次。这意味着在 2s 上拍摄的每一帧都会在视网膜上投影四次!考虑撞击时的框架。视网膜会四次分别看到该帧。然而,大脑设法感知到一个单一的影响时刻。这怎么可能行得通?采样定理中没有任何东西可以处理这种情况。
Remember that each frame of any movie gets projected twice to avoid flickering. This means that even in the best case—shooting on 1s, not 2s—each position of the bouncing ball gets projected on the retina twice. But when animators are shooting on 2s, each frame is repeated twice. That means that each frame shot on 2s gets projected on the retina four times! Consider the frame at the moment of impact. The retina sees that frame four separate times. And yet the brain manages to perceive a single moment of impact. How could this possibly work? There’s nothing in the Sampling Theorem to handle this situation.
此外,反弹的时刻是视觉流中的一个尖锐“边缘”。在频率峰值中,该边缘具有非常高的频率,需要以远高于每秒 24 次的速率进行采样——当然也远高于 2 秒拍摄中隐含的每秒 12 帧。根据采样定理,正确的做法是通过四舍五入方向的急剧变化来消除高频。但这不是动画师所做的。他们想要那种锋利的边缘,所以他们夸大了时刻——最高频率变化的时刻。再说一次,这怎么可能起作用?现在应该清楚的是,动画师也与物理学脱节,但不知何故被他们的经验所引导。
Furthermore, the moment of bounce is a sharp “edge” in visual flow. In frequencyspeak, that edge has very high frequencies and needs to be sampled at a much higher rate than 24 times per second—and certainly much higher than 12 frames per second implicit in shooting on 2s. The right thing to do, according to the Sampling Theorem, is to get rid of the high frequencies by rounding off that sharp change in direction. But that’s not what animators do. They want that sharp edge, so instead they exaggerate the moment—the instant of highest frequency change. Again, how can this possibly work? It should be clear now that animators are unhinged from physics too, but somehow guided by their experience of it.
图 5.16
Figure 5.16
图 5.16 是两位大师弗兰克·托马斯(Frank Thomas)和奥利·约翰斯顿(Ollie Johnston)的弹跳球课程(模型),这两位大师是迪斯尼极具天赋的九个老人——该公司动画电影成功的秘诀。我的电脑效果图很难表现出他们迷人的铅笔素描,尤其是在撞击的那一刻。
Figure 5.16 is (a mockup of) a lesson on the bouncing ball by two masters, Frank Thomas and Ollie Johnston, two of Disney’s extremely talented Nine Old Men—the secret of the company’s animated movie success. My computer renderings poorly represent their charming pencil sketches, particularly at the moment of impact.
众所周知,弗兰克和奥利在他们的标题中表示,顶部更近的间距是实验的结果。实际上,如果路径以相等的时间间隔进行采样,这正是情况的物理要求,如前面精确执行的插图所示(图 5.15)。
Frank and Ollie—as they were known to everyone—state in their caption that the closer spacing at the top was a result of experiment. Actually, it’s exactly what the physics of the situation demands if the path is sampled at equal time intervals, as shown in the preceding, precisely executed illustration (figure 5.15).
他们歪曲现实以“给人一种弹跳的感觉”。请注意图 5.16 的下半部分,球是如何向接触点伸长(伸展),在接触时变平(压扁),并在接触后在框架中缓慢放松的伸展。这说明了壁球和伸展,但也说明了对事件的预期(在反弹发生之前伸展),以及对反弹和后续的夸大。用弗兰克和奥利的话说,这些技巧“让行动更加迅速”。这些技巧改善了观众的主观、感知“现实”。82
They distorted reality to “give the appearance of bouncing.” Notice in the bottom half of figure 5.16 how the ball elongates (stretches) toward the point of contact, flattens (squashes) at the moment of contact, and slowly relaxes its stretch in the frames after contact. This illustrates squash and stretch, but also anticipation of an event (stretching toward the bounce before it happens), and exaggeration of the bounce and of the follow-through. In Frank and Ollie’s words, these tricks “gave more snap to the action.” The tricks improved the viewer’s subjective, perceived “reality.”82
事实上,弗兰克和奥利在每一步都改进了它。将图 5.16 中的上图(没有挤压和拉伸的弹跳)与图 5.15 进行比较。两张图片都是为了展示同样的东西,一个真实发生的弹跳球。但是弗兰克和奥利,摆脱了现实世界的物理联系,摆脱了重力及其抛物线——也摆脱了采样定理——画出了一个已经比物理上正确的反弹更丰富和更充分的反弹。然后他们改进了壁球和拉伸的改进。请注意,他们的样本并不完全位于正确的位置,并且球并不完全遵循真正的抛物线。而且撞击瞬间的变形(在他们的实际图纸中更加古怪)与实际变形几乎没有关系。它更像是一个装满水的弹性袋,而不是一个橡皮球。
In fact, Frank and Ollie improved it at every step. Compare the top drawing in figure 5.16—of the bounce without squash and stretch—to figure 5.15. Both pictures are meant to exhibit the same thing, a bouncing ball as it actually occurs. But Frank and Ollie, free of the physical bonds of the real world, free of gravity and its parabolas—and free of the Sampling Theorem—drew a bounce that is already somehow richer and fuller than the physically correct one. Then they improved on the improvement with squash and stretch. Notice that their samples aren’t exactly at the right locations, and the ball doesn’t quite follow true parabolas. And the deformation at the moment of impact (even more outlandish in their actual drawing) has little to do with real deformation. It’s more like an elastic bag full of water than a rubber ball.
他们声称,弗兰克和奥利凭直觉发现了如何克服弹跳球采样中的缺陷。为什么这些非凡的技巧会如此有效?有人怀疑它一定与采样过程有关。由于我们并不真正知道大脑如何从呈现给视网膜的样本(尤其是四倍样本)中重建动画,因此我们必须猜测它们为什么起作用。动画师似乎在他们的样本和帧中打包了人类大脑的丰富提示。弹跳前后的细长球在运动方向上拉长。这对大脑来说是一个很大的暗示,就像标准电影帧中的运动模糊一样。
Frank and Ollie discovered with raw intuition, they claimed, how to overcome the flaws in the sampling of a bouncing ball. Why should these remarkable tricks work so well? One suspects it must have something to do with the sampling process. Since we don’t really know how the brain reconstructs an animation from samples presented to the retina—especially quadrupled samples—we have to guess why they work. It appears that animators pack their samples, their frames, with rich hints for the human brain. The elongated balls, before and after the bounce, elongate in the direction of motion. That’s a big hint to the brain, like motion blur in a standard film frame.
击球时球的夸张变形一定会让大脑充满戏剧性的信息。动画师保持了球的感知体积——保留了一些工作中的物理概念。但他们夸张地垂直压扁球并水平拉伸——有时几乎变成了煎饼。当这样的序列快速回放时,弹跳的球是流动的、有趣的、松软的——动作很快。球具有您可以感觉到的重量和可变形性。动画师通过夸大挤压和拉伸来控制我们的情绪。明显运动的现象并不能完全捕捉到发生的事情。表观变形更像它。
And that exaggerated deformation of the ball at the moment of impact must flood the brain with dramatic information. The animators maintain the perceived volume of the ball—preserving some notion of a physics at work. But they exaggeratedly squash the ball vertically and stretch it horizontally—sometimes almost into a pancake. When such a sequence plays back at speed, the bouncing ball is liquid, fun, and floppy—with snap to the action. The ball has weight and deformability you can feel. The animators control our emotions by how much they exaggerate the squash and stretch. The phenomenon of apparent motion doesn’t quite capture what happens. Apparent deformation is more like it.
我最难忘的与期待、夸张、挤压和拉伸的相遇发生在我用电脑掌握 3D 动画的时候。这个1970 年代中期在长岛,当时计算机还很简陋。我将左手建模为一个简化的骨架,由用于骨骼的小圆柱体和用于关节的小球体组成。我什至手腕有 8 个腕骨(如腕管综合症)——8 个小球体。如果你不仔细看,它的效果出奇的好。
My most memorable encounter with anticipation, exaggeration, squash, and stretch happened just as I was mastering three-dimensional animation with computers. This was on Long Island in the mid-1970s when computers were still very crude. I modeled my left hand as a simplified skeleton composed of little cylinders for bones and little spheres for joints. I even had 8 carpals (as in carpal tunnel syndrome) for the wrist—8 little spheres. It worked surprisingly well if you didn’t look too closely.
我复制了左手并将其镜像,给了我右手。复制和镜像对于计算机来说非常容易。两只手,现在我该怎么办?我可以制作什么动画?当我拍手时,我仔细观察了我的两只手。自己做这个,你会注意到你的手掌之间的距离只有几英寸左右。当手掌合在一起时,一只手的手指在另一只手的食指或小指周围略微弯曲。一只手的拇指在拇指或另一只手的手掌周围略微弯曲。动作是僵硬的——手掌分开,手掌合拢。即使使用当时粗糙的工具,它也很容易实现。
I made a copy of the left hand and mirrored it, giving me a right hand. Copying and mirroring are very easy for a computer. With two hands, now what should I do? What animation could I make? I observed my two hands closely as I clapped them. Do this yourself, and you’ll notice that the distance separating your palms is only a couple of inches or so. The fingers of one hand curve slightly around the index finger or little finger of the other hand as the palms come together. The thumb of one hand curves slightly around the thumb or the palm of the other hand. The motion is rigid—palms apart, palms together. It was an easy animation to implement, even with the crude tools of the day.
但是很无聊!它是无菌的。我突然想到,这正是壁球和伸展、预期和夸张的目的,旨在缓解。它们旨在改善感知的“现实”。他们应该为这个新的 3D 动画工作,就像他们为旧的二维 cel 动画所做的那样。在这两种情况下,结果都是人类查看的二维帧。
But it was boring! It was sterile. It occurred to me that this was exactly what squash and stretch, anticipation and exaggeration, were designed to alleviate. They were meant to improve perceived “reality.” And they should work for this new three-dimensional animation just like they did for old two-dimensional cel animation. In both cases, the results are two-dimensional frames viewed by humans.
因此,我将手向后弯曲到手腕处——不可能向后弯曲,如图 5.17 所示。我夸大了那个动作。我通过先将它们分开来预测双手合拢的动作——向后移动以强调向前移动。那是期待。然后我双手合十。我夸大了速度。当双掌合十,突然停住的时候,手指却没有。他们伸出了刚刚经过的手掌——难以置信的远,夸张的远。然后他们缩回到一个自然的位置。当它们伸展时,它们的尖端也会膨胀,然后它们会在它们缩回到自然位置时塌陷到自然形状。我对两组手指和两个拇指都这样做了。有很多伸展,但没有太多的壁球。
So I bent the hands back at the wrist—impossibly far back, as shown in figure 5.17. I exaggerated that motion. I anticipated the motion of the hands going together by separating them first—going backward to emphasize going forward. That’s anticipation. Then I slung the hands together. I exaggerated the speed. When the palms slammed together and stopped suddenly, the fingers did not. They stretched out beyond the palm they had just passed—impossibly far, exaggeratedly far. And then they retracted to a natural position. They also swelled at the tips as they stretched, and then they collapsed to their natural shape just as they retracted to their natural position. I did this for both sets of fingers and both thumbs. Lots of stretch, but not much squash.
当我快速播放这个动画时,结果很好吃!一双又大又肥又邋遢的拍手,看起来还活着,让我感觉很好。让我对大师们充满感激。
When I played this animation back at speed, the result was delicious! A big, fat, sloppy pair of clapping hands that seemed alive and made me feel good. And filled me with appreciation for the masters.
手工绘制动画电影的每一帧都是一项艰巨的苦差事。为什么不拍摄真人演员,然后勾勒出他们以获得动画卡通片?这种被称为转描法的捷径概念被多次改造。爱德华·迈布里奇(Edward Muybridge)让一位艺术家将那匹著名的小跑马的每一帧复制为墨迹、绘画或剪影。因此,我们建议我们应该将他视为转描法之父,而不是(真人)电影之父。
Drawing every frame of an animated film by hand is high drudgery. Why not film live actors and then outline them to get animated cartoons? This short-cut notion—called rotoscoping—was reinvented several times. Edward Muybridge had an artist replicate each frame of that famous trotting horse as an inked tracing, painting, or silhouette. Hence our suggestion that we should consider him the father of rotoscoping, rather than of (live action) movies.
图 5.17
Figure 5.17
Cinémathèque française 的 Laurent Mannoni 向我展示了两个从电影开端开始的短片循环。其中一个由显然是乔治·梅里爱表演技巧的相框组成。另一个循环来自 1897 年的德国,使用了从第一个循环衍生的手绘框架,每个循环都是相应相框的彩色卡通画。83
Laurent Mannoni, of the Cinémathèque française, showed me two short film loops from the beginnings of cinema. One consisted of photographic frames apparently of Georges Méliès performing a trick. The other loop, from Germany in 1897, used hand-painted frames derived from the first loop, each a colorful painted cartoon of the corresponding photographic frame.83
但该工艺的美国专利于 1917 年授予 Max Fleischer。他开始使用该工艺制作他著名的 Ko-Ko the Clown in the Out of the Inkwell动画1915 年的系列。他的兄弟戴夫为相机表演了 Ko-Ko 精心编排的动作。然后马克斯用他的旋转镜架从每一帧中提取出一幅卡通画。一台投影仪从后面将戴夫的每个真人画面放大到一个透明的画架上。Max 在画架上安装了一个 cel,位于投影图像上。然后,他在 cel 上描绘了 Dave 的卡通轮廓,制作了动画电影的框架。Max 和 Dave 都声称是这个想法的始作俑者,但他们的说法相互矛盾。正如我们所见,这可能无关紧要,因为无论如何他们肯定不是第一个提出这个想法的人。但他们确实有效地利用了它。Dave 曾在 Pathé 工作,但最终还是 Bray 发布了Out of the 1919 年的Inkwell,无疑很高兴将转描过程置于专利控制之下——就像 cel 动画一样。84
But the US patent for the process went to Max Fleischer in 1917. He began using the process to animate his famous Ko-Ko the Clown in the Out of the Inkwell series in 1915. His brother Dave performed the choreographed movements of Ko-Ko for the camera. Then Max used his rotoscope stand to derive a cartoon from each frame. A projector enlarged each live-action frame of Dave onto a transparent easel, from behind. Max mounted a cel on the easel, over the projected image. Then he traced a cartoon outline of Dave onto the cel to make a frame of the animated film. Both Max and Dave claimed to have originated the idea, but their claims conflict. As we’ve seen, it probably doesn’t matter, as they surely weren’t the first with the idea anyway. But they did exploit it effectively. Dave had worked at Pathé, but it was Bray who finally released Out of the Inkwell in 1919, undoubtedly delighted to have the rotoscoping process under patent control—like cel animation.84
Dave Fleischer 在 Digital Light 中扮演了一个角色,但他从来不知道。Dave 和 Max 成立了 Fleischer Studios,以许多动画电影而闻名,包括大力水手电影。一位年轻的动画师约翰·真蒂莱拉(John Gentilella )参与了由戴夫在麦克斯去世很久之后制作的菠菜包装大力水手( Spinach Packin' Popeye ,1944)。然后,化名 Johnny Gent,他领导了Tubby the Tuba (1975) 的动画,该动画是在 Alexander Schure 拥有的纽约理工学院校园内使用老式 cel 动画制作的。85
Dave Fleischer played a role in Digital Light, but he never knew it. Dave and Max formed Fleischer Studios, famous for many animated films, including the Popeye films. A young animator, John Gentilella, worked on Spinach Packin’ Popeye (1944), produced by Dave long after Max died. Then, under the alias Johnny Gent, he headed up the animation for Tubby the Tuba (1975), produced with old-fashioned cel animation on the campus of the New York Institute of Technology, owned by Alexander Schure.85
Schure 聘请 Ed Catmull 和我(以及其他人)将一台数字计算机整合到 Johnny 的动画制作过程中。Ed 负责前景轮廓动画,我负责动画轮廓的颜色填充和背景绘制。我们前进的速度不够快,无法帮助Tubby,但我们和纽约理工学院计算机图形实验室的其他成员确实开发了最初的想法,这些想法后来成为 - 经过多年和大量改进 - 数字 cel 动画系统 CAPS(计算机动画制作系统)在迪士尼。
Schure hired Ed Catmull and me (and others) to incorporate a digital computer into Johnny’s animation process. Ed worked on foreground outline animation and I on color fills of the animated outlines and on painting the backgrounds. We didn’t advance fast enough to help with Tubby, but we and the rest of the Computer Graphics Lab at NYIT did develop the original ideas that later became—after many years and much refinement—the digital cel animation system CAPS (Computer Animation Production System) at Disney.
Ed 和我(以及其他人)于 1980 年左右加入 Lucasfilm。在那里,迪士尼与我们接洽,希望我们将他们的 cel 动画流程数字化。我与迪士尼就 CAPS 合同进行了一年多的谈判。此后不久,我和 Ed 于 1986 年共同创立了 Pixar,我们将 CAPS 带到了一起,并在两家公司的共同满意和钦佩下完成了。CAPS 一直使用到 2006 年沃尔特迪斯尼公司收购皮克斯。约翰尼·根特和他在纽约理工学院的团队在 1970 年代教会了我们全尺寸 cel 动画的复杂性,这构成了我们与迪斯尼的关系的基础,达到了大约 30多年后,迪士尼收购了皮克斯。
Ed and I (and others) joined Lucasfilm in about 1980. While there, Disney approached us to digitize their cel animation process. I negotiated the CAPS contract for over a year with Disney. When Ed and I shortly thereafter cofounded Pixar, in 1986, we took CAPS with us, where it was completed to the mutual satisfaction and admiration of both companies. CAPS was used until the Walt Disney Company bought Pixar in 2006. It was Johnny Gent and his team at NYIT who had taught us the intricacies of full-scale cel animation in the 1970s that formed the basis of our relationship with Disney, culminating about 30 years later in the purchase of Pixar by Disney.
你会注意到,当 Ub 和 Walt 在动画行业摸索他们的路时,他们只能通过对获得发行和寻找资金的前景极其天真地生存下去。他们一直在被剥削,一直被欺骗,没有什么能阻止他们。
You’ll notice as Ub and Walt feel their way through the animation business, they can only survive by being supremely naïve about the prospects of getting distribution and finding money. They are consistently being fleeced, consistently being bamboozled, and nothing stops them.
——Russell Merritt,引自The Hand behind the Mouse 86
—Russell Merritt, quoted in The Hand behind the Mouse86
沃尔特·迪斯尼正在成长为一个有魅力的领导者和有远见的人,他的说服力并没有在乌贝身上消失。
Walt Disney was maturing into a charismatic leader and visionary whose powers of persuasion were not lost on Ubbe.
— Leslie Iwerks 和 John Kenworthy,鼠标背后的手87
—Leslie Iwerks and John Kenworthy, The Hand behind the Mouse87
是时候讲述非常有影响力的迪斯尼公司的故事了——即使是不漂亮的部分。沃尔特·迪斯尼 (Walt Disney) 于 1901 年 12 月 5 日出生于芝加哥,原名沃尔特·埃利亚斯·迪斯尼 (Walter Elias Disney),在服役一段时间后,他搬到了密苏里州堪萨斯城。Ub Iwerks 出生于Ubbe Eert Iwwerks 于 1901 年 3 月 24 日在堪萨斯城,1924 年他将自己名字的拼写改为 Ub Iwerks。我为他使用这个别名,就像我为其他人所做的那样,因为这是他在完成他最伟大的工作时使用的别名。两人受雇于堪萨斯城的同一家商业艺术公司,很快成为了好朋友。88
It’s time to tell the story of the very influential Disney company—even the unpretty parts. Walt Disney was born Walter Elias Disney on December 5, 1901, in Chicago, and after his stint as a soldier, he moved to Kansas City, Missouri. Ub Iwerks was born as Ubbe Eert Iwwerks on March 24, 1901, in Kansas City, and in 1924 he adapted the spelling of his name to Ub Iwerks. I use that alias for him, as I’ve done similarly for others, because it’s the one he used when he did his greatest work. The two men were hired by the same commercial art company in Kansas City and soon became fast friends.88
大约一年后,两人都被解雇了,所以他们成立了一家公司,Iwwerks-Disney Commercial Artists。他们考虑将其命名为 Disney-Iwwerks,但一致认为这听起来像是一家眼镜公司。没关系,因为公司很快就倒闭了,于 1920 年破产。这两个朋友随后受雇于堪萨斯城电影广告公司。就在那时,他们发现了动画世界——并疯狂地爱上了它。
After about a year both were fired, so they formed a company, Iwwerks-Disney Commercial Artists. They thought about calling it Disney-Iwwerks but agreed that it sounded like an eyeglass company. It didn’t matter because the company soon failed, entering bankruptcy in 1920. The two friends then hired on with Kansas City Film Ad Company. This was when they discovered the world of animation—and fell madly in love with it.
他们吞噬了迈布里奇著名的定格动画人和动物光栅阵列,并从各个帧中制作了活页簿。他们从 Edwin G. Lutz 的有影响力的书Animated Cartoons (1920) 中学习了动画制作工艺。他们学会了刀耕火种、墨水和油漆。他们学会了转描。他们研究了赫德、麦凯和弗莱舍一家。而且,当然,他们还得亲自动手制作一部动画电影。Ub 天生的机械天赋帮助他们实施了先驱者的系统并做得很好。他们没有受到专利问题的困扰,因为他们远离了堪萨斯城的聚光灯。89
They devoured Muybridge’s famous raster arrays of stop-motion humans and animals and made flipbooks from the individual frames. And they learned the animation craft from the influential book Animated Cartoons (1920) by Edwin G. Lutz. They learned slash and tear, and ink and paint. They learned rotoscoping. They studied Hurd, McCay, and the Fleischers. And, of course, they had to try their own hand at an animated movie. Ub’s natural mechanical bent helped them implement the systems of the pioneers and do it well. They weren’t hounded by patent issues because they were out of the limelight, in far off Kansas City.89
沃尔特很快就将自己定位为这对搭档的谈话者、营销者和组织者。例如,他说服堪萨斯城电影广告公司的老板借给他们一台定格相机供课外使用。沃尔特把它安装在他家的车库里。然后,他、兄弟罗伊和朋友乌布开始下班后制作动画短片。
Walt quickly distinguished himself as the talker, marketer, and organizer of the duo. For example, he talked their boss at Kansas City Film Ad into loaning them a stop-motion camera for extracurricular use. Walt set it up in his family’s garage. He, brother Roy, and friend Ub then set to work after hours to make short animated movies.
闪电草图的想法启发了他们的早期作品之一。他们拍摄了沃尔特的手,然后迅速将那只手移到一幅画上方。那只手似乎在画画。他们很快就从这些作品中组装了一个演示或演示。其目的是支持沃尔特销售一系列短片的营销工作。堪萨斯城弗兰克纽曼剧院连锁店的经理买下了这个系列的想法,所以他们把这部短片命名为 Newman Laugh-O-grams。其中一个卖女士长筒袜,这部电影主要是因为他们使用的一位名叫 Lucille Fay LeSueur 的漂亮模特,别名 Billie Cassin,别名——在她的职业生涯后期——琼·克劳馥。另一个取笑当地街道的坑洼。
The idea of lightning sketches inspired one of their early works. They photographed Walt’s hand, then moved that hand rapidly above a drawing. The hand appeared to do the drawing. They soon assembled a demonstration—or demo—reel from such pieces. Its purpose was to support Walt’s marketing efforts to sell a series of short films. The manager of the Frank Newman Theatre chain in Kansas City bought the series idea, so they called the shorts Newman Laugh-O-grams. One of them sold ladies’ stockings, a film remembered mainly for a beautiful model they used named Lucille Fay LeSueur, alias Billie Cassin, alias—much later in her career—Joan Crawford. Another poked fun at potholes in local streets.
正如这些作品所暗示的那样——以及 Newman Laugh-O-grams 这个名字强烈暗示——沃尔特、乌布和罗伊的目标是娱乐,而不是广告。但他们在堪萨斯城电影广告公司的老板不支持朝这个方向扩张。如果你想娱乐,那就创办自己的公司,他告诉他们。沃尔特正是这样做的。
As these pieces suggest—and the name Newman Laugh-O-grams strongly implies—Walt, Ub, and Roy were headed for entertainment, not ads. But their boss at Kansas City Film Ad wouldn’t support an expansion in that direction. If you want to entertain, then start your own company, he told them. Walt did exactly that.
他对这个想法深信不疑,于 1922 年离开堪萨斯城电影广告公司,创办了 Laugh-O-gram Films。乌布留在后面。他需要稳定的收入来支持他的母亲。沃尔特通过为新公司达成分销协议迅速解决了这个问题。这似乎为 Ub 提供了他需要的安全保障,因此他做出了飞跃并重新加入了 Walt。但他犯了一个错误。第二家公司也破产了。Ub 重新加入堪萨斯城电影广告公司。沃尔特搬到了罗伊兄弟现在居住的加利福尼亚。90
He was so convinced of the idea that he left Kansas City Film Ad in 1922 and started Laugh-O-gram Films. Ub stayed behind. He required a steady income that would support his mother. Walt quickly solved that problem by swinging a distribution deal for the new company. It seemed to provide Ub with the security he needed, so he made the leap and rejoined Walt. But he’d made a mistake. The second company went bankrupt too. Ub rejoined Kansas City Film Ad. Walt moved to California where brother Roy now lived.90
沃尔特和罗伊在那里创办了一家名为迪斯尼兄弟卡通工作室的公司,这是沃尔特的第三家公司。在 Laugh-O-gram Films 倒闭之前,他和 Ub 已经成功制作了电影《爱丽丝的仙境》。沃尔特用它来宣传——并成功地达成了另一笔分销交易。但在爱丽丝系列中的七条短裤交付后,经销商查尔斯·明茨给沃尔特发了一封带有明确信息的起泡信。他们必须立即提高质量。因此,沃尔特在 1924 年写信给 Ub,恳求他在加利福尼亚加入他们。而乌布做到了。爱丽丝的品质电影明显改善。沃尔特停止了动画。制作将是他永远的强项。Ub 成为该工作室收入最高的动画师,并于 1924 年正式化名为 Ub Iwerks。迪士尼兄弟工作室继续制作了数十部爱丽丝电影。
There Walt and Roy started a company called Disney Brothers Cartoon Studio, Walt’s third. Before Laugh-O-gram Films collapsed, he and Ub had managed to make the film Alice’s Wonderland. Walt used it to make pitches—and succeeded in landing another distribution deal. But after delivery of seven shorts in the Alice series, the distributor Charles Mintz sent Walt a blistering letter with a clear message. They had to improve the quality immediately. So Walt wrote Ub in 1924 pleading with him to join them in California. And Ub did. The quality of the Alice films improved markedly. Walt ceased animating. Producing would be his forte forever after. Ub became the highest paid animator at the studio, and in 1924 officially took the alias Ub Iwerks. And Disney Brothers studio went on to make dozens of Alice films.
迪士尼兄弟的下一个系列以兔子奥斯瓦尔德为基础,像往常一样由 Ub 创建和动画。但随后发生了一件令人讨厌的事情。他们的发行商 Mintz 暗中雇佣了迪士尼兄弟的所有动画工作人员——除了忠实的 Ub Iwerks——还剥夺了 Oswald the Rabbit 的版权。
Disney Brothers based their next series on Oswald the Rabbit, as usual created and animated by Ub. But then something nasty happened. Their distributor Mintz underhandedly hired away all the Disney Brothers animation staff—except loyal Ub Iwerks—and also took away the rights to Oswald the Rabbit.
米老鼠就是在这个可怕的时刻诞生的。沃尔特要求乌布换一个新的主角来代替奥斯瓦尔德,乌布设计的这个角色将成为全世界迪斯尼的象征。91
It was in this dire moment that Mickey Mouse was born. Walt asked Ub for a new main character to replace Oswald, and Ub designed the character that would come to symbolize Disney throughout the world.91
他们秘密制作了后来成为疯狂飞机(1928)的电影,这是第一部由米老鼠主演的电影,Ub 担任联合导演(与沃尔特一起)和动画师。然后他们创作了他们的第一部有声电影《汽船威利号》( Steamboat Willie,1928 年),由 Ub 担任导演和动画师(图 5.18 是标题卡文本的模型)。这两部电影都取得了成功,并继续成为经典。接下来是The Skeleton Dance (1929),Ub 担任动画师,Walt 担任导演。这是该公司 75 首愚蠢交响曲中的第一首。乌布导演了本系列前七部中的四部,沃尔特导演了另外三部。作为工作室的负责人,沃尔特是所有这些电影的制片人。92
They worked in secret on what would become Plane Crazy (1928), the first film to star Mickey Mouse, with Ub as codirector (with Walt) and animator. Then they created Steamboat Willie (1928), their first sound film, with Ub as both director and animator (figure 5.18 is a mockup of the text of the title card). Both films were successes and went on to become classics. Next was The Skeleton Dance (1929), with Ub as animator and Walt as director. It was the first of the company’s 75 Silly Symphonies. Ub directed four of the first seven of this series, and Walt the other three. Walt was, as head of the studio, the producer of all these films.92
一切似乎都很好,但事实并非如此。
All seemed well, but it wasn’t.
Walt 开始摆弄 Ub 的动画时间——他对采样时刻的选择——动画感觉的秘密。沃尔特会不经询问就改变它们。沃尔特开始用力骑乌布,同时从他身上夺走功劳。很明显,迪斯尼公司已经成为沃尔特迪斯尼的全部——事实上,这最终将成为它的名字。
Walt began to fiddle with Ub’s animation timings—his choice of the sampling moments—the secret to the feel of animation. Walt would change them without asking. Walt began riding Ub hard, while taking credit away from him. It became clear that the Disney company had become all about Walt Disney—and that would, in fact, eventually become its name.
众所周知,压垮 Ub 的最后一根稻草或许就是这件事:一个派对上的一个男孩让沃尔特为“他的”著名的米老鼠画画并签名。沃尔特转向乌布并说,“你为什么不画米奇,我会签的。” Ub 回击道:“画你自己的——米奇!” 那是 1929 年。他们一直在一起,就像他们认为的朋友一样,已经有 10 年的大部分时间了。乌布决定他必须去。沃尔特从朋友变成了暴君。营销变得比发明更重要。93
Perhaps the proverbial straw that broke Ub’s back was this incident: A boy at a party asked Walt to draw and autograph “his” famous Mickey Mouse. Walt turned to Ub and said, “Why don’t you draw Mickey and I’ll sign it.” Ub snapped back, “Draw your own—Mickey!” It was 1929. They had been together, as friends they’d thought, for most of 10 years. Ub decided that he had to go. Walt had moved from friend to tyrant. Marketing had become more important than invention.93
图 5.18
Figure 5.18
重新开始的最佳时机可能不是在 1929 年的崩盘之后,但那年晚些时候,Ub 被联系到这样做。一位名叫帕特鲍尔斯(Pat Powers)的商人是迪斯尼的竞争对手,他资助他成立了一家新公司。鲍尔斯将乌布的决定告知沃尔特,并向震惊的沃尔特暗示他并没有失去乌布——如果他愿意与鲍尔斯达成协议的话。“我不要他,”沃尔特苦涩地回答。“如果他有这种感觉,我永远无法和他一起工作。”
The best time to start afresh might not have been after the crash of 1929, but late that year Ub was approached to do so. A businessman named Pat Powers, a Disney competitor, financed him in a new company. Powers informed Walt of Ub’s decision, suggesting to the shocked Walt that he hadn’t lost Ub—if he would do a deal with Powers. “I wouldn’t want him,” responded Walt bitterly. “If he feels that way, I could never work with him.”
1930 年 2 月,Ub 成立了 Ub Iwerks Studio。在接下来的十年里,这是 Ub 的生活。一系列基于他最新角色 Flip the Frog 的电影是新工作室的主菜。但是,尽管制作了数十部电影,Iwerks 工作室却从未蓬勃发展。到 1936 年,它不得不关门大吉。在那之后出现了溅射和开始,但到了 1940 年Ub 厌倦了制作,而是想为这种艺术形式做出贡献。只有一个工作室能让他做到这一点。他重新加入了沃尔特——但条件完全不同。94
In February 1930 Ub formed Ub Iwerks Studio. For the next decade, it was Ub’s life. A series of films based on his newest character, Flip the Frog, was the new studio’s entrée. But the Iwerks studio never thrived, despite producing dozens of films. By 1936 it had to close its doors. There were sputters and starts after that, but by 1940 Ub was sick of production and wanted to contribute to the artform instead. There was only one studio where he could do that. He rejoined Walt—but on completely different terms.94
图 5.19
Figure 5.19
(左)© Sharon Green/Ultimate Sailing。(右)© Doug Gifford。
(Left) © Sharon Green/Ultimate Sailing. (Right) © Doug Gifford.
可悲的是,华特迪士尼公司的故事不再包括 Ub 的基础角色。他被写出来了,显然是沃尔特和罗伊相信他们的朋友乌布在他们与白雪公主创造动画历史的那些年里抛弃了他们的代价。但一旦他回到迪斯尼,乌布就重新确立了自己的地位,尤其是在技术问题上,如果不是在沃尔特和罗伊的心中的话。95
Sadly, the Walt Disney Company’s story of itself no longer includes Ub’s foundational role. He’s been written out, apparently the price of Walt and Roy’s belief that their friend Ub had abandoned them during the years when they made animation history with Snow White. But once he was back at Disney, Ub strongly reestablished himself, especially on technical matters if not in the hearts of Walt and Roy.95
当 Ed Catmull 和我在 1970 年代中期开始每年秘密前往迪斯尼朝圣,为电脑动画寻找资金时,沃尔特和乌布都已经去世(1966 年和 1971 年)。但 Ub 的良好声誉仍然完好无损。他的儿子 Don Iwerks 在那里继承了他父亲的传统。那里的技术人员向我们保证,“Ub 会”支持我们提出的想法——将迪士尼 cel 动画流程数字化。沃尔特的侄子(和长得相像)罗伊·爱德华·迪斯尼(图 5.19),沃尔特的兄弟罗伊·奥利弗·迪斯尼的儿子,Pyewacket的船长,最终将在大约十年后实现这一目标,成为 CAPS 项目的冠军。再过两年,他将为迪士尼收购皮克斯扫清道路。96
By the time Ed Catmull and I started making our annual surreptitious pilgrimages to Disney in the mid-1970s, looking for funding of computer animation, both Walt and Ub had died (in 1966 and 1971). But Ub’s sterling reputation was still intact. And his son, Don Iwerks, was there to carry on his father’s tradition. People at the technical level there assured us that “Ub would have” backed the idea that we proposed—digitizing the Disney cel animation process. Walt’s nephew (and lookalike) Roy Edward Disney (figure 5.19), son of Walt’s brother Roy Oliver Disney, and skipper of the Pyewacket, would finally make that happen about a decade later, as champion of the CAPS project. And another two decades after that, he would help clear the way for the purchase of Pixar by Disney.96
我给了菲利克斯一个个性,使用了许多面部表情。. . . 他会是一只宠物。. . . 他会影响年幼的孩子。. . . 他会满足很多愿望。. . . 回首过去,我们看到一扇门在通往视觉艺术新领域的道路上微微打开。
I gave Felix a personality, using many facial expressions. . . . He would be a pet. . . . He would influence young children. . . . He would fulfill many wishes. . . . Looking back, we see a door opening slightly on a road that led to a new field of visual arts.
——Otto Messmer,唐纳德·克拉夫顿在米奇97之前的前言
—Otto Messmer, foreword to Donald Crafton’s Before Mickey97
对我来说,老鼠是一件令人厌恶的事情。
To me a mouse is a repulsive thing.
——Otto Messmer,在米奇98之前的题词
—Otto Messmer, epigraph in Before Mickey98
在 Pat Sullivan 和 Otto Messmer 中有 Walt 和 Ub 的回声。他们的产品是Felix the Cat,一个仍然深受动画爱好者喜爱的角色和系列。Messmer 做了动画(图 5.20)。沙利文是推动者和震动者,变得富有,并获得了荣誉。
There’s an echo of Walt and Ub in Pat Sullivan and Otto Messmer. Their product was Felix the Cat, a character and series still beloved of animation aficionados. Messmer did the animation (figure 5.20). Sullivan was the mover and shaker, became rich, and took the credit.
图 5.20
Figure 5.20
菲利克斯在抽象动画和卡通人物动画之间占据了一个特殊的领域——比如带有大量现实主义的超现实主义。在适当的时候,他的尾巴可能会变成问号或感叹号。他的耳朵会像剪刀一样咔哒一声。菲利克斯可以用最荒谬的方式解决问题。例如,为了到达没有梯子的高处,他会拆下自己的尾巴,将其变形为阶梯线,然后爬上“楼梯”。
Felix occupies a special territory between abstract animation and cartoon character animation—surrealism with a large dose of realism, say. His tail could become a question mark or an exclamation point at appropriate times. His ears would click together like scissors. Felix could solve problems in the most absurd ways. For example, to get to an elevated place with no ladder, he would detach his own tail, deform it into a stairstepped line, and climb up the “stairs.”
唐纳德·克拉夫顿 (Donald Crafton) 在其权威动画史的封面上庆祝菲利克斯,在米奇之前,并将整个最后一章献给他:“这是 1920 年代的典型动画片。” 它是黑白的,无声的,但它工作并继续工作。99
Donald Crafton celebrates Felix on the cover of his definitive animation history, Before Mickey, and devotes the entire last chapter to him: “It was the quintessential cartoon of the 1920s.” It was black-and-white and soundless, but it worked and keeps on working.99
到 1926 年——在米奇之前——菲利克斯几乎和查理卓别林一样受欢迎。菲利克斯娃娃卖得很好——这是电影推销的早期练习。但声音的缺失最终注定了沙利文的事业。多年来他一直拒绝使用它,直到迪斯尼和艾沃克斯的威利汽船(1928 年)中音频的巨大成功迫使他改变了主意。但后来他选择了劣质的音响系统,到 1930 年,工作室基本上已经死了。
By 1926—before Mickey—Felix was almost as popular a screen star as Charlie Chaplin. Felix dolls sold very well—an early exercise in merchandising the movies. But the lack of sound eventually doomed the Sullivan enterprise. He refused to use it for years, until the resounding success of audio in Disney and Iwerks’s Steamboat Willie (1928) forced him to change his mind. But then he chose an inferior audio system, and the studio was essentially dead by 1930.
尽管如此,费利克斯还是让沙利文成为了百万富翁——在 1920 年代。他和他的妻子 Marjorie 在爵士时代的神话般的纽约市非常富有。当 Messmer 经营他们的赚钱工作室时,他们酗酒和狂欢。但在 1932 年,玛乔丽从他们公寓的五楼窗户坠落身亡,帕特再也没有恢复完全的情绪稳定。
Nevertheless, Felix made Sullivan a millionaire—in the 1920s. He and his wife Marjorie were incredibly wealthy in the fabulous New York City of the jazz age. They drank hard and partied hard while Messmer ran their money-making studio. But in 1932 Marjorie fell to her death from the fifth-story window of their apartment, and Pat never regained full emotional stability.
沙利文的名字是菲利克斯猫系列的名字,而不是梅斯梅尔的名字。但沃尔特当然知道是谁在做这项工作。1928 年,随着Steamboat Willie的成功,他在纽约市期间多次访问了 Sullivan 工作室的 Messmer 。沃尔特开始有远大的想法——一部长篇电影——他需要人才。“他恳求并恳求,”梅斯默说,他对离开纽约市不感兴趣。“而且,看起来菲利克斯可以永远继续下去。他正处于成功的顶峰。” 然而,沙利文很快就失败了,沃尔特独占了整个领域,但他从未签下梅斯梅尔。
Sullivan’s name was the one attached to the Felix the Cat series, not Messmer’s. But Walt certainly knew who was doing the work. He visited Messmer at the Sullivan studio several times in 1928 while in New York City following the success of Steamboat Willie. Walt was starting to think big—a feature-length film—and he needed talent. “He begged and pleaded,” said Messmer, who wasn’t interested in leaving New York City. “And besides, it looked like Felix could go on forever. He was at the height of his success.” Sullivan soon failed, however, and Walt had the whole field to himself, but he never signed Messmer.
我还没有真正解释过电影是如何运作的——尤其是动画电影。就像我们对演员和动画师如何做他们所做的事情一无所知一样,这是因为大脑几乎肯定会参与其中。在动画的一般情况和特殊情况下,这种未知领域是电影技术的极限。一旦技术通过学生,我们就不得不举手——或者做出有根据的猜测。换句话说,到依靠视觉持久性和明显运动的心理物理现象只是另一种说法,“大脑做到了”。
I haven’t really explained how films work—especially animated films. As with our ignorance of how actors and animators do what they do, it’s because the brain is almost certainly involved. That terra incognita is the limit on film technology in both the general case and the special case of animation. Once the technology passes through the pupil, we have to throw up our hands—or make educated guesses. In other words, to rely on the psychophysical phenomena of persistence of vision and apparent motion is just another way of saying, “The brain does it.”
这本书的一个主要主题是采样定理,科捷尔尼科夫的伟大想法,是理解数字光的关键。由于电影似乎以每秒 24 帧的速度对视觉流进行采样,因此采样定理肯定应该解释为什么电影有效。但我们发现它们并非完全那样工作。从抽样理论得出的可爱的理想电影系统并不是实际使用的系统。
A major theme of this book is that the Sampling Theorem, Kotelnikov’s great idea, is key to understanding Digital Light. Since films appear to sample visual flow at 24 frames per second, surely the Sampling Theorem should explain why films work. But we discovered instead that they don’t work exactly that way. The lovely ideal movie system that follows from sampling theory was not the one that was actually used.
实际的系统绝对是某种采样过程,但它每帧投影两次,而且帧很胖,充满了诸如运动模糊之类的线索,供大脑享用。在理想的系统中,框架很薄——瞬时的。因此,它们不能包含运动模糊线索。但它们可以表示任何不超过两倍最高频率限制的运动。采样定理保证了这一点。当我们接近 Digital Light 时,我们将寻找对理想系统的遵守。现代现实世界是否在瞳孔之外传播和添加样本?还是继续依靠“大脑做它”的手波?
The actual system was definitely a sampling process of some sort, but it projected each frame twice, and the frames were fat and filled with clues such as motion blur for the brain to feast on. In an ideal system the frames are thin—instantaneous. They therefore cannot contain motion blur clues. But they can represent any motion that doesn’t exceed the twice-the-highest-frequency restriction. The Sampling Theorem guarantees it. As we approach Digital Light, we’ll look for adherence to the ideal system. Does the modern real world spread and add the samples outside the pupil? Or continue to rely on “the brain does it” handwave?
动画电影甚至超出了采样定理的范围——尤其是那些用 2 秒拍摄的。在这种情况下,每一帧都被投射到视网膜上四次!考虑弹跳球。它与地面接触的那一刻一次又一次地发生。然而,我们的大脑会弄清楚。它没有看到四重打击,而是感受到了一种持久的美味冲击——毫无疑问,这得益于动画大师的技巧,如挤压和拉伸、预期和夸张。
Animated films fall even farther outside the bounds of the Sampling Theorem—especially those shot on 2s. In that case, every frame is projected onto the retina four times! Consider the bouncing ball. The moment of its contact with the ground happens again and again and again and again. Yet our brain figures it out. It doesn’t see the quadruple whammy, but rather perceives one long delicious impact—aided undoubtedly by the tricks of the animation masters, like squash and stretch, anticipation and exaggeration.
理想与现实暗示了塔与臭,这是本书的另一个主题。它们从根本上都很重要。事实上,这正是塔与臭的对比,以及为什么将一个人的创造力评价为另一个人的创造力是错误的。真正的电影机器是在臭气熏天的环境中创造出来的。我们可以稍后在象牙塔中出现,并提出一个美丽的数学想法来“解释”电影机器工作的原因。但很明显,电影发明者并不是从理论开始的。采样定理不能解释他们的机器。但它确实告诉我们下一步该走哪条路。这种行为和思考的相互作用比理论家或工程师通常愿意承认的更接近世界的运作方式。
Ideal versus actual is suggestive of tower versus stinks, another theme of this book. They both fundamentally matter. Indeed, it’s exactly the tower versus the stinks, and why it’s wrong to rate the creativity of one over that of the other. Actual movie machines were created in the stinks. We can come along later in the ivory tower and propose a beautiful mathematical idea to “explain” why movie machines work. But it’s clear that the movie inventors didn’t start from theory. The Sampling Theorem doesn’t work as an explanation of their machines. But it does show us which way to go next. This interplay of doing and thinking is closer to the way the world works than either theoreticians or engineers commonly like to admit.
电影和动画的故事也生动地让我们想起了电影技术的另一部分秘密,一个我们更不了解的秘密。沙利文和迪斯尼业务的关键在于他们聘请了具有稀有艺术天赋的人来使照片栩栩如生。这也是在数字世界中有效的方法。我一生中最好的雇佣是迪斯尼训练有素的动画师约翰拉塞特,他莫名其妙的天赋是皮克斯无与伦比的早期成功的无可置疑的关键。
The story of film and animation also vividly reminds us of another part of the secret of movie technology, one we understand even less. The key to both the Sullivan and Disney businesses was the fact that they hired people with the rare artistic talent to make pictures come alive. That’s the method that works in the digital world too. The best hire of my life was the Disney-trained animator John Lasseter, whose inexplicable talent was the unquestioned key to Pixar’s unmatched early success.
摩尔定律因子现在(2020 年)为 1000 亿X,并迅速接近 1 万亿X。尽管所有关于人工智能和深度学习的主张都受到了计算能力的超新星爆发的启发,但我们现在几乎没有比 1920 年代和 1930 年代更接近于理解动画师或演员是如何创造个性的。根据电视广告,现在所有的汽车都是智能的,但没有一辆汽车能激发一个人物的灵感。
The Moore’s Law factor is now (2020) 100 billion X and rapidly approaching 1 trillion X. Despite all the claims about artificial intelligence and deep learning inspired by that awesome, supernova surge in computational power, we are hardly any closer now to understanding how an animator or actor creates a personality than we were in the 1920s and 1930s. According to television commercials, all automobiles are now intelligent, but none of them can inspirit a character.
我并不是说技术存在硬性限制——机器不能具有创造力。我个人的信念是,我们总有一天会了解创造者是如何创造甚至是机器的。但那是信仰,而不是科学。如果有足够的理由,我可以选择相信相反的观点——许多人也这样做。声称或暗示我们几乎就在那里,现在任何一天都是“基于信仰的科学”。与此同时,在可预见的未来,我们将继续聘请最优秀的人类艺术人才来制作动画和表演——他们是唯一已知的解决方案。我们仍然在寻找世界上为数不多的 Ubs、Ottos 和 Lasseters。
I am not saying that there exists a hard limit to technology—that machines cannot be creative. My personal faith is that we will someday understand how creators create and perhaps even machines. But that’s faith, not science. I could, with as much justification, elect to believe just the opposite—and many humans do. It’s “faith-based science” to claim or imply that we are almost there, any day now. Meanwhile, into the foreseeable future, we continue to hire the best human artistic talent we can to animate and act—they’re the only known solution. We still seek out the few Ubs, Ottos, and Lasseters of the world.
样条近似包含了普罗科菲耶夫 [原文如此] 古典交响曲的美妙悖论:似乎它可能是几个世纪前写的,但当然不可能。
Spline approximation contains the delicious paradox of Prokofieff’s [sic] Classical Symphony: it seems as though it might have been written several centuries ago, but of course it could not have been.
——菲利普·J·戴维斯,数学家,1964 1
—Philip J. Davis, mathematician, 19641
旧金山地区的一大乐趣是轻松享受美妙的音乐。即便如此,当伟大的印度西塔琴演奏家 Ravi Shankar 在 1982 年的一个凌晨时分走进卢卡斯影业的计算机图形实验室时,我还是感到震惊。我独自一人在我们的一位常驻天才编写的绘画程序上工作,汤姆波特。那天晚上我一直致力于了解 Tom 的最新功能——样条曲线。Ravi 的主持人是 Clark Higgins,他是 Grateful Dead 摇滚乐队和我们的视频向导。2
A pleasure of the San Francisco area is easy access to fine music. Even so, I was astounded when Ravi Shankar, the great Indian sitar player, walked into the computer graphics lab at Lucasfilm in the wee hours of a night in 1982. I was working alone on the paint program written by one of our resident geniuses, Tom Porter. I had devoted that evening to learning about Tom’s latest feature—splines. Ravi’s host was Clark Higgins, the video wizard for both the Grateful Dead rock band and us.2
“你认识拉维·香卡,不是吗,阿尔维?”
“You know Ravi Shankar, don’t you, Alvy?”
我融化了。“我当然是了。” 我第一次见到他是在 60 年代的一部决定性电影《蒙特雷流行》(1968 年)中。我知道他曾于 1969 年在伍德斯托克演出,这是那个时代的另一个决定性事件。我不认识他,但我肯定认识他。
I melted. “Of course I do.” I had seen him first in Monterey Pop (1968), a defining movie of the Sixties. I knew he’d performed at Woodstock in 1969, another defining event of the era. I didn’t know him, but I certainly knew him.
拉维是一个漂亮的男人,身材娇小,面带微笑,穿着(大部分)白色印度服装无可挑剔。最重要的是,他身上散发着一种微妙而令人惊讶的香味——一种感性的光环,既增强了他的存在感,又在他站在我的肩膀上凝视时将我吞没。
Ravi was a beautiful man, small, smiling, and impeccably dressed in (mostly) white Indian apparel. Best of all, he wore a subtle and surprising fragrance that surrounded him—a sensual aura that both enhanced his presence and engulfed me as he stood peering over my shoulder.
碰巧在靠近顶部的电脑屏幕上显示了一朵花。前一天一位来访的艺术家在那里画了一朵红色和蓝色花瓣的小花,中心有一个白点。当拉维加入我时,它照亮了房间,就像一朵真正的花一样。
By happenstance there was a flower displayed on the computer screen, near the top. A visiting artist the previous day had painted a small blossom there of red and blue petals and a white-dotted center. It brightened the room when Ravi joined me, like a cutting of a real flower.
“样条曲线,”我解释说,“是通过几个点的优美曲线。我们的计算机只能记录这条路径上的几个点。” 我做了一个盛大的手势,用手写笔在一个大平板电脑上划过。那天晚上我没说什么。我只是向拉维展示了它是如何工作的。
“A spline,” I explained, “is a graceful curve through a few points. Our computer can register only a few points along this path.” With a grand gesture, I stroked a stylus across a large tablet. I said little else that night. I simply showed Ravi how it worked.
手势是任意的,从低处开始向上移动。手腕一甩,我在中风时短暂地向下扫过,然后再次向上扫过,最终结束。
The gesture was an arbitrary one, starting low and moving upward. With a wrist flick, I swept briefly downward in midstroke, then upward again, ending high.
然后汤姆的绘画程序立即接管了。首先,它通过平板电脑的稀疏点创建了一条样条曲线。请注意,我们看不到样条曲线。它是纯几何图形,宽度为零,存储在计算机的某个地方。但随后,在稍作停顿之后,程序将其渲染为我们面前彩色显示屏上的一笔画。不可见的样条线成为可见笔画的支柱。我的手势和程序的笔划之间的延迟是如此短暂,以至于似乎——带着一点想象力——我,而不是电脑,直接在屏幕上画了它。颜色是随机选择的——棕色,幸运的是。
Then Tom’s paint program instantly took over. First, it created a spline through the sparse points from the tablet. We couldn’t see the spline, mind you. It was pure geometry, with zero width, stored inside the computer somewhere. But then, after a hint of a pause, the program rendered it into what looked like a stroke of paint on the color display before us. The invisible spline became the backbone of a visible paint stroke. The lag between my gesture and the program’s stroke was so brief that it seemed—with a pinch of imagination—that I, not the computer, had painted it directly on the screen. The color had been a random choice—a brown, as luck would have it.
该程序模拟了具有柔软边缘和不同宽度的笔触。笔画在显示屏底部附近开始时没有宽度,然后随着向上扫过并进入曲线逐渐变宽,最后在向上结束时再次变窄。. . 只是在花!一个完美的茎。好像我是这样计划的。但我没有。我们三个人都知道我没有。它让我们大吃一惊。在那个漫长的时刻,我的音乐英雄拉维·香卡(Ravi Shankar)和我一起沉浸在他自己的天堂般的气味中,和我一样震惊,他摸了摸我的肩膀,低声说:“Allllllllvyyyyy!”
The program simulated a brushstroke with soft edges and varying width. The stroke began with no width near the bottom of the display, then widened gradually as it swept upward and into the curves, and finally narrowed to nothing again as it ended upward . . . just at the flower! A perfect stem for it. As if I had planned it that way. But I hadn’t. All three of us knew I hadn’t. It took our breaths away. In that extended moment Ravi Shankar, my musical hero, swimming with me in his own heavenly scent and as startled as I, touched my shoulder and whispered, “Alllllllvyyyyy!”
一群“肥嘟嘟”的鸭子同时站起身来,在它们吵闹的表亲之后向北走。
A “plump” of ducks rose at the same time and took the route to the north in the wake of their noisier cousins.
——亨利·大卫·梭罗,瓦尔登湖,1864 年3
–Henry David Thoreau, Walden, 18643
Ravi Shankar 演示的样条曲线是源自同名绘图员工具的几何图形。早在个人电脑出现之前,我父亲就教我机械绘图。这些工具是用于画圆的精密德国罗盘、用于直角和直线的 T 形方尺以及印度墨水笔和笔尖。他有另一个相当神秘的工具,叫做法式曲线(图 6.1),如果你把图片倒过来,它就类似于圣诞老人的雪橇。它的目的是在我们试图绘制一条不寻常的平滑曲线时稳定我们颤抖的手。在插图中,绘图员将法式曲线放置在三个连续的位置,以帮助他分段绘制曲线。这些部分是曲线部分 A、B 和 C,每个部分都位于法国曲线的许多边缘的不同位置。这位绘图员很幸运。他找到了所有需要的曲线沿着圣诞老人的雪橇滑道,彼此靠近。但有时你找不到你所寻找的曲线。
The spline of the Ravi Shankar demo is a piece of geometry that derives from a draftsman’s tool of the same name. My father taught me mechanical drawing as a child, long before the personal computer. The tools were a precision German compass for drawing circles, a T-square for right angles and straight lines, and India ink pens and nibs. He had another rather mysterious tool called a French curve (figure 6.1) that resembled Santa’s sleigh if you turn the picture upside down. Its purpose was to steady our shaky hands as we tried to draw a smooth curve of unusual shape. In the illustration a draftsman has placed a French curve in three successive positions to help him draw a curve piecewise. The pieces are curve parts A, B, and C, each found in various places along the French curve’s many edges. This draftsman was lucky. He found all needed curve parts near one another along the runner of Santa’s sleigh. But sometimes you can’t find the curve you seek.
图 6.1
Figure 6.1
图 6.2
Figure 6.2
认真的绘图员需要更值得信赖的东西。豪华游艇的设计师不会忍受可能缺少所需曲线部件的法国曲线。例如,为了绘制赛车船体的曲线,他们使用一个用重物固定在适当位置的薄柔性条带,如图 6.2(右)所示。条带通过重物固定的点并通过它们松弛成平滑的曲线,因此条带的边缘可以追踪到船计划中。那个绘图工具——条带和砝码——被称为样条线。4
Serious draftsmen need something more trustworthy. Designers of luxury yachts won’t put up with a French curve that might lack the curve parts needed. To draft curves for a racing hull, say, they use a thin flexible strip held in place with heavy weights, as shown in figure 6.2 (right). The strip passes through points fixed by the weights and relaxes into a smooth curve through them so the edge of the strip can be traced into the boat plans. That drafting tool—the strip and the weights—is called a spline.4
Ravi Shankar 演示中的几何样条直接受到船设计师的物理启发。出于显而易见的原因,物理版本中的重量被称为鸭子(或鲸鱼)。如图所示,您甚至可以购买画成绿头鸭、秋沙鸭、丑角等的丰满鸭子。从物理鸭子突出的钩尖是物理样条必须通过的点。几何样条只有虚拟鸭子,没有实体或钩子。在这种情况下,鸭子只是样条必须通过的点。在 Ravi Shankar 演示中,鸭子是我做出手势时从平板电脑获得的分离点。
The geometrical spline in the Ravi Shankar demo was directly inspired by the boat designer’s physical one. The weights in the physical version are known as ducks (or whales), for obvious reasons. You can even buy a plump of ducks painted as mallards, mergansers, harlequins, and so forth, as shown. The hook tips protruding from physical ducks are the points that the physical spline must pass through. A geometrical spline has only virtual ducks, without bodies or hooks. The ducks in this case are simply the points that the spline must pass through. In the Ravi Shankar demo, the ducks were the separated points obtained from the tablet as I made my gesture.
观点值 80 IQ 点。
Point of view is worth 80 IQ points.
——艾伦·凯,施乐 PARC,ca。1980 5
—Alan Kay, Xerox PARC, ca. 19805
样条曲线提供了连接分离点的答案,例如 Ravi Shankar 演示中来自平板电脑的点。它是一条平滑、优美起伏的几何曲线,穿过这些点。这是对它们之间的猜测,附带条件是那里的东西应该很有趣,甚至很漂亮。否则连接点是微不足道的:只需用直线段将每个点连接到下一个点。曲折的结果并不讨大多数人的喜欢。
A spline provides an answer to what joins separated points—such as those from a tablet in the Ravi Shankar demonstration. It’s a smooth, gracefully undulating geometric curve that passes through the points. It’s a guess at what lies between them, with the proviso that the something there should be interesting, even pretty. Connecting the dots is trivial otherwise: just join each to the next with a straight line segment. The zigzag result doesn’t please most eyes.
为了理解样条曲线,我们再次调用,不管你信不信,采样定理。但我们必须采取稍微不同的观点。
To understand splines we invoke, believe it or not, the Sampling Theorem yet again. But we have to take a slightly different point of view.
我们在关于采样定理的章节中遇到了埃德蒙·泰勒·惠特克爵士,他的名字可能不会响起。他是 1915 年英国采样定理发现者的候选人,比 Vladimir Kotelnikov 早 18 年。他是英格兰最伟大的数学家之一。他曾就读于艾萨克牛顿学院的剑桥三一学院,并于 1896 年成为那里的研究员。1905 年,他被选为皇家学会会员。为了结束他辉煌的职业生涯,惠特克领导了爱丁堡大学的数学系。
We met Sir Edmund Taylor Whittaker so briefly in the chapter on the Sampling Theorem that his name might not ring a bell. He was England’s candidate for Sampling Theorem discoverer in 1915, 18 years before Vladimir Kotelnikov. He was one of England’s great mathematicians. He studied at Trinity College, Cambridge, Isaac Newton’s college, and became a Fellow there in 1896. He was elected a Fellow of the Royal Society in 1905. To cap his illustrious career, Whittaker headed the mathematics department at the University of Edinburgh.
然而,我把采样定理的王冠给了科捷尔尼科夫。为什么不是惠特克?有两个原因。首先,他没有从我们在数码光中用于像素显示的角度证明这个定理。其次,即使你接受他的观点,他也没有完全证明目前使用的定理。
Yet I gave the crown for the Sampling Theorem to Kotelnikov. Why not Whittaker? There are two reasons. First, he didn’t prove the theorem from the point of view we use in Digital Light for the display of pixels. Second, even if you accept his point of view, he didn’t completely prove the theorem as it’s currently used.
Whittaker 的专长是插值。他的观点体现在他与人合着的一本书中:
Whittaker’s expertise was interpolation. His point of view is captured in a book he coauthored:
插值理论。. . 从最基本的方面来看,它可以被描述为“在数学表的行间阅读”的科学。6
The Theory of Interpolation . . . in its most elementary aspect may be described as the science of “reading between the lines of a mathematical table.”6
数据表对大多数人来说并不是什么漂亮的东西,但它们很方便。假设我们在加州大学伯克利分校的某个特定位置每小时测量一次温度。那么,在任何给定时间后 15 分钟,我们对同一天下午 3 点的温度的最佳猜测是什么?Whittaker 的插值理论产生了一个很好的估计,一个有用的数字。
Data tables aren’t things of beauty to most people, but they are handy. Suppose we’ve taken the temperature at every hour on the hour at a particular location on the University of California at Berkeley campus. Then what’s our best guess at the temperature there at 15 minutes after any given hour, let’s say 3 p.m., on the same day? Whittaker’s theory of interpolation yields a good estimate, a useful number.
插值意味着在 之间放置一些东西。定义中隐含的是,它们之间的东西被创建在那里。如果幸运的话,创建的数据可能实际上代表了现实世界——例如,伯克利校园下午 3:15 的温度。它本来是有意义的,就好像它被测量了一样,但事实并非如此。Whittaker 是一位插值大师,或者说是数据之间的创建大师。
To interpolate means to put something between. It’s implicit in the definition that the something between is created to be there. If we’re lucky, the created data might actually represent the real world—the temperature at 3:15 p.m. on the Berkeley campus, say. It’s meant to make sense as if it were measured, but it wasn’t. Whittaker was a master of interpolation, or the creation of data between.
Kotelnikov 的对比观点从未包括平滑曲线的创建。他的观点是平滑的重建,而不是构建。他从平滑的曲线开始——比如亮度或响度。他找到了一种方法来丢弃大部分数据以获取一组离散样本(例如像素或索素),然后他可以从中重建原始平滑度。他的采样定理教我们如何做到这一点。
Kotelnikov’s contrasting point of view never encompassed the creation of smooth curves. His point of view was the reconstruction, not the construction, of smoothness. He started with smooth curves—of brightnesses or loudnesses, say. He found a way to throw away most of that data to get a set of discrete samples—pixels or soxels, for example—from which he could later reconstruct the original smoothness. His Sampling Theorem teaches us exactly how to do that.
惠特克的观点正好相反。离散数据点是他开始的。他试图找到一个连接它们的平滑事物,这就是为什么他没有证明 Kotelnikov 证明的更强大的采样定理版本(以及 Claude Shannon 重新证明的)。7
Whittaker’s point of view was the opposite. Discrete data points were what he started with. He sought to find a smooth thing that connected them, and that’s why he didn’t prove the more powerful version of the Sampling Theorem that Kotelnikov proved (and Claude Shannon re-proved).7
正如我们所描述的,Kotelnikov 的最简单形式的采样定理有两个部分。第一部分告诉我们如何对可以描述为傅里叶波之和的平滑事物进行采样——结果证明这是自然界中最平滑的事物。特别是,它告诉我们在该总和中以(超过)两倍的波最高频率进行采样。第二部分告诉我们使用理想的散布器来散布样本并将它们相加以重建原始平滑的东西。换句话说,第二部分告诉我们如何对样本进行插值,通过它们得到一条平滑的曲线,即原始曲线。Kotelnikov 从平滑开始,取离散样本,然后重建原始平滑:从平滑到离散再到平滑。
Kotelnikov’s Sampling Theorem in its simplest form has two parts, as we’ve described. The first part tells us how to sample a smooth something that can be described as a sum of Fourier waves—which turns out to be most smooth things in the natural world. In particular, it tells us to sample at (more than) twice the highest frequency of a wave in that sum. The second part tells us to use the ideal spreader to spread the samples and add them up to reconstruct the original smooth something. In other words, the second part tells us how to interpolate the samples to get a smooth curve, the original curve, through them. Kotelnikov starts with smoothness, takes discrete samples, then reconstructs the original smoothness: smooth to discrete to smooth.
Whittaker 的插值定理告诉我们用散布器(与 Kotelnikov 指定的理想散布器相同)散布每个给定的数据点。然后将结果相加以获得数据点之间的平滑插值,平滑曲线。该曲线是傅立叶波的总和,最高频率与使用的扩频器一致。回想一下,理想的扩频器与最高频率的波一样频繁地摆动。Whittaker 从离散数据开始,在它们之间插入平滑度,然后沿着原始数据点之间的新曲线发现所需数据:离散到平滑到离散。
Whittaker’s Interpolation Theorem tells us to spread each given data point with the spreader—the same ideal spreader as Kotelnikov specified. Then add up the results to get a smooth interpolation, a smooth curve, between the data points. That curve is a sum of Fourier waves up to a highest frequency consistent with the spreader used. Recall that the ideal spreader wiggles as often as does the wave of highest frequency. Whittaker starts with discrete data, interpolates a smoothness between them, then discovers the desired data along the new curve between the original data points: discrete to smooth to discrete.
尽管有两种观点,但结果在数学上是等效的。一个只是另一个相反。那么为什么不把采样定理归功于惠特克呢?推迟的原因是他没有证明科捷尔尼科夫采样定理的更复杂形式,即现代世界经常使用的所谓带通变体。我们在关于图灵的章节中使用了它,用于他的声码器工作,他打破了包含每秒 0 到 3,000 个周期的音频信号,分为 10 个波段,每个波段的带宽为每秒 300 个周期(0 到 300、300 到 600,...)。
Despite the two points of view, the results are mathematically equivalent. One is just the other in reverse. So why not give Whittaker credit for the Sampling Theorem? The reason to hold back is that he didn’t prove the more complex form of Kotelnikov’s Sampling Theorem, the so-called bandpass variation that’s used so often in the modern world. We used it in the chapter about Turing, for his vocoder work, where he broke an audio signal containing 0 to 3,000 cycles per second into 10 bands each with bandwidth 300 cycles per second (0 to 300, 300 to 600, . . .).
图 6.3
Figure 6.3
尽管如此,我们在本章中将 Whittaker 冠以插值之王是恰当的。在为计算机图形创建平滑对象时采用 Whittaker 的插值观点和在离散显示中采用 Kotelnikov 的采样观点,这是一个很好的平衡。从两个不同的角度来看,一个基本的想法在两个数字光领域都存在,这一点一点也不明显——惠特克在制作,科捷尔尼科夫在接受。
Nevertheless, it’s fitting that we crown Whittaker the king of interpolation in this chapter. It’s a beautiful balance to feature Whittaker’s interpolation point of view in the creation of smooth objects for computer graphics and Kotelnikov’s sampling point of view in the discrete display of them. It’s not at all obvious that one basic idea, from two different points of view, figures in both Digital Light domains—Whittaker in making, Kotelnikov in taking.
图 6.3(左)是 Ravi Shankar 演示中来自平板电脑的点的图片。小箭头显示了我手势的方向。平板电脑以相同的时间步长记录了手势,所以你可以看到我一开始画得很快,转弯时放慢了速度,然后很快完成了。右图是我们不要的,用直的点之间的线。这是相同数据的插值,但并不令人愉悦。这是一条僵硬的锯齿形“曲线”。在过去糟糕的日子里,人们认为这就是计算机所能做的一切。在摩尔定律证明它们是错误的之前,他们认为计算机是僵硬的、棱角分明的——简单地说是机械的。在计算机图形学中,线性插值(点之间的直线)几乎是不可取的。8
Figure 6.3 (left) is a picture of the points from the tablet in the Ravi Shankar demonstration. The tiny arrow shows the direction of my gesture. The tablet recorded the gesture in equal time steps, so you can see that I drew fast at first, slowed down for the turns, and finished rapidly. The picture at the right is what we do not want, with straight lines between the points. It’s an interpolation of the same data, but not a pleasing one. It’s a stiff zigzag “curve.” Back in the bad old days people thought that this was all that a computer could do. They imagined that computers were rigid and angular—mechanical, in a word—before Moore’s Law proved them wrong. In computer graphics, linear interpolation—straight lines between points—is hardly ever desirable.8
图 6.4
Figure 6.4
我们可以做得更好。可以从平板电脑的下边缘垂直测量每个点的位置。图 6.4(右)是每个点的垂直位置图。它只是左侧的点以相等的时间步长水平分布。
We can do much better. The location of each point can be measured vertically from the lower edge of the tablet. Figure 6.4 (right) is a plot of the vertical positions of each point. It’s just the points at the left spread out horizontally in equal time steps.
我们已经使垂直位置看起来像前面章节中描述的示例。它们不是已知现实的样本,但我们没有理由不能像它们那样行事。让我们用采样定理构建那个虚构的“现实”。请注意,我们说的是构造而不是重构。又是那个观点。我们知道如何进行这种构造:用一个好的撒布器传播每个样本,然后将结果相加。图 6.5 就是你得到的。平滑曲线通过(插值)“采样”垂直位置,位于图片中的扩展器峰值处。该曲线上的点是所需的垂直位置,因为它们会随着时间平滑地变化。
We’ve made the vertical positions look like samples as depicted in an earlier chapter. They aren’t samples of a known reality, but there’s no reason we can’t act like they are. Let’s construct that fictitious “reality” with the Sampling Theorem. Notice that we say construct rather than reconstruct. It’s that point-of-view thing again. We know how to do this construction: spread each sample with a good spreader, and add up the results. Figure 6.5 is what you get. The smooth curve passes through—interpolates—the “sampled” vertical positions, located at the spreader peaks in the picture. The points on this curve are the desired vertical positions as they change smoothly in time.
接下来,我们对水平位置重复相同的技巧。结果是一条平滑的曲线,它通过(插值)“采样”的水平位置。该曲线上的点是所需的水平位置,因为它们随时间平滑变化。(本段见在线注释中的实际构造。)
Next we repeat the same trick for the horizontal positions. The result is a smooth curve that passes through—interpolates—the “sampled” horizontal positions. The points on that curve are the desired horizontal positions as they change smoothly in time. (See the actual construction in the online annotation for this paragraph.)
使用这两条曲线,我们可以在任何特定时刻绘制所需的二维空间曲线,即样条曲线:我们从第一条曲线及其与第二条曲线在同一时刻的水平位置。如果我们随着时间的增加有条不紊地执行此操作,那么我们会以与手写笔在平板电脑上的原始手势相同的方向和顺序绘制所需的曲线。也就是说,我们为垂直和水平位置构建了一对平滑曲线,它们穿过或插入 Ravi Shankar 演示的数位板点。这是一种复杂的方式来说明我们已经通过这些点创建了一条平滑曲线。
With these two curves we can plot the desired two-dimensional spatial curve, the spline, at any particular instant: we take its vertical position at that very instant from the first curve and its horizontal position at that same instant from the second curve. If we do this methodically as time increases, then we trace out the desired curve in the same direction and order as the original gesture of the stylus over the tablet. That is, we’ve constructed a pair of smooth curves, for vertical and horizontal positions, that pass through, or interpolate, the tablet points of the Ravi Shankar demonstration. Which is a complicated way to say that we’ve created a smooth curve through the points.
图 6.5
Figure 6.5
让我们再过一遍。我们假设通过给定的数位板点有一条平滑的曲线,并且它是原始手势的路径。如果您考虑一下,要实现这一点,沿路径的垂直变化必须平滑变化,水平变化也必须变化。所以我们使用采样定理的重建技术来构造一条垂直位置的平滑变化曲线,以及另一个平滑变化的水平位置曲线。两者都必须经过二维空间中样本点的垂直和水平位置。在笔划期间的任何其他时间,我们都可以简单地从两条构造曲线中读取当时必须位于该路径上的点的垂直和水平位置。图 6.6(右)显示生成的样条曲线与确定它的点(鸭子,左)相比的样子。通过平板电脑的人工输入在左侧,计算机的输出在右侧。它是平滑的,而不是曲折的。这是一条样条线,是 Digital Light 中最可爱的想法之一。样条是一个很好的词。
Let’s go through that again. We assume there is a smooth curve through the given tablet points and that it’s the path of the original gesture. If you think about it, to make that possible, the vertical changes along the path must vary smoothly, and so must the horizontal changes. So we use the Sampling Theorem’s reconstruction technique to construct a smoothly varying curve of vertical positions, and another of smoothly varying horizontal positions. Both have to pass through the vertical and horizontal positions of the sample points in two-dimensional space. At any other time during the stroke, we can simply read off the vertical and horizontal positions—from the two constructed curves—of the point that must lie on that path at that time. Figure 6.6 (right) shows what the resulting spline looks like, compared to the points (ducks, left) that determined it. The human input via the tablet is on the left and the computer’s output on the right. It’s smooth, not zigzag. It’s a spline, one of the loveliest ideas in Digital Light. And spline is such a nice word.
图 6.6
Figure 6.6
再看一张 Kotelnikov 和 Whittaker 指定的吊具的图片(图 6.7,顶部)。这是理论上正确的吊具。
Look again at a picture (figure 6.7, top) of the spreader specified by both Kotelnikov and Whittaker. It’s the theoretically correct spreader.
但是我们不能将那个理想的扩展器用于我们的样条构造,因为它是无限的。这些涟漪逐渐减弱,但它们会永远持续下去。我们之前在图 6.7(底部)中使用了实用的有限扩展器,并声称它是理想扩展器的“良好近似”。但那是在重建的背景下——Kotelnikov 的领域。在这里,上下文是构造,而不是重构,我们不需要使用理想的、无限的扩展器。我们非常乐意使用更简单、更有限的,吊具。并且近似的概念是无关紧要的。我们准确地构造了一条新曲线,而不是近似地重构了一条已知曲线。
But we can’t use that ideal spreader for our spline constructions because it’s infinite. Those ripples diminish, but they go on forever. We previously used instead the practical, finite spreader in figure 6.7 (bottom) and claimed that it was a “good approximation” to the ideal spreader. But that was in the context of reconstruction—Kotelnikov’s domain. Here, where the context is construction, not reconstruction, we don’t need to use the ideal, and infinite, spreader. We’re perfectly happy using the simpler, and finite, spreader. And the notion of approximation is irrelevant. We exactly construct a new curve, not approximately reconstruct a known one.
图 6.7
Figure 6.7
您使用这种更简单的吊具获得的样条曲线已被多次重新发现。在计算机图形学中,它被称为 Catmull-Rom 样条曲线,以纪念重新发现它的两位计算机图形学学生:与我共同创立皮克斯的 Ed Catmull 和 Raphael Rom。9
The spline that you get using this simpler spreader has been rediscovered several times. In computer graphics, it’s called the Catmull-Rom spline in honor of two computer graphics students who rediscovered it: Ed Catmull, who cofounded Pixar with me, and Raphael Rom.9
由于 Catmull 和 Rom 都是从 Whittaker 的插值角度得出他们的样条曲线来构建平滑曲线,他们不会想到它是从 Kotelnikov 样本的重建,也不会认为他们的扩展器是近似于理想的吊具。他们不会想到他们生成的样条曲线的傅立叶频率内容。
Since both Catmull and Rom came to their spline from the Whittaker point of view of interpolation to construct smooth curves, it wouldn’t have occurred to them to think of it as a reconstruction from Kotelnikov samples, nor that their spreader was an approximation to the ideal spreader. And they wouldn’t have thought of the Fourier frequency content of the splines they generated.
这两种不同的用途——创作和展示——来自不同的观点,这就是为什么我把建筑归功于惠特克,把重建归功于科捷尔尼科夫。实际结果是一个吊具可以在两种情况下使用。一个计算机程序足以满足两者。同样的想法在创意空间和展示空间中都很有用,这是一种令人惊讶和美丽的联系。
The two different uses—in creation and display—come from different points of view, and that’s why I give construction credit to Whittaker and reconstruction credit to Kotelnikov. The practical consequence is that the one spreader can be used in both contexts. One computer program suffices for both. That the same idea is useful in both Creative Space and Display Space is a surprising and beautiful connection.
Ravi Shankar 样条演示是计算机图形学的一个示例,它是 Digital Light 的一个主要分支——一个合成分支,可以制作图片而不是拍摄它们。计算机图形学总是需要两个步骤:我们通过在 Creative Space 中使用不可见的几何图形建模来创建对象,这一过程我将在本章中详细描述下一个。然后我们通过将基于几何的模型渲染到显示空间的散布像素中来查看它们,例如打印页面、手机显示器或虚拟现实 (VR) 护目镜。这就是我们对计算机图形的定义。
The Ravi Shankar spline demonstration is an example of computer graphics, a major branch of Digital Light—a synthetic branch, making pictures not taking them. Computer graphics always requires two steps: We create objects by modeling them with invisible geometry in Creative Space, a process I’ll describe at length in this chapter and the next. Then we view them by rendering the geometry-based models into the spread pixels of a Display Space, such as a printed page, a cellphone display, or virtual reality (VR) goggles. That’s our definition of computer graphics.
在与 Ravi Shankar 合作的那个晚上,Tom Porter 的程序创建了一个不可见的样条线作为笔画的主干。那是笔画背后的几何形状。尽管几何是计算机图形定义的基础,但模型不仅仅是几何。笔画模型还具有颜色、柔和的半透明边缘和随时间变化的宽度。该程序将笔画模型渲染为像素,然后通过卢卡斯影业图形实验室的全彩显示器传播到可见性。这是二维计算机图形的一个例子,因为该模型是基于二维几何的。
On that night with Ravi Shankar, Tom Porter’s program created an invisible spline as the backbone of a paint stroke. That was the geometry underlying the stroke. Although geometry is fundamental to the definition of computer graphics, a model isn’t only geometry. The stroke model also had color, soft semi-transparent edges, and a width that varied in time. The program rendered the model of the stroke into pixels which were then spread into visibility by the full-color display in the Lucasfilm graphics lab. It was an example of two-dimensional computer graphics, because the model was based on two-dimensional geometry.
本章中同一样条曲线的图片是一个更简单的渲染。它的模型与我向 Ravi Shankar 展示的笔画具有完全相同的几何路径。但是该模型的其他组件是不同的。它是白色背景上等宽的黑线。两张图片都是计算机图形的示例。创意空间中的单个几何对象可以在显示空间中以多种方式呈现,具体取决于那些非几何模型组件。10
The picture in this chapter of that same spline is a much simpler rendering. Its model has exactly the same geometrical path as the paint stroke I showed to Ravi Shankar. But the other components of the model are different. It’s a black line of constant width on a white background. Both pictures are examples of computer graphics. A single geometric object in Creative Space can be rendered a great many ways in Display Space, depending on those non-geometrical model components.10
另一方面,如果没有几何图形,那么它就不是计算机图形学。Adobe Illustrator 将二维几何模型渲染为像素。这是一个计算机图形程序。Adobe Photoshop 从头开始创建像素或修改从现实世界中获取的像素。它不是计算机图形程序。这是一个图像处理程序,来自 Digital Light 的另一个主要分支。同样,早期的 Apple 提供了 MacDraw(一种计算机图形程序)和 MacPaint(一种像素打包或图像处理程序)。(有关“几何”的广义概念的讨论,请参见注释。)
On the other hand, if there’s no geometry, then it’s not computer graphics. Adobe Illustrator renders two-dimensional geometric models into pixels. It’s a computer graphics program. Adobe Photoshop creates pixels from scratch or modifies pixels taken from the real world. It’s not a computer graphics program. It’s an image processing program, from another major branch of Digital Light. Similarly, early Apple offered MacDraw, a computer graphics program, and MacPaint, a pixel-packing, or image processing, program. (See the annotation for discussion of a generalized notion of “geometry.”)
计算机图形是几何输入,像素输出。图像处理是像素输入,像素输出。两者都用于创建图片。在内存非常昂贵的早期,图像处理只是为了拍照,但摩尔定律使得在新千年的现在,直接从像素制作照片成为可能。
Computer graphics is geometry in, pixels out. Image processing is pixels in, pixels out. Both are used for creating pictures. In the early days of very expensive memory, image processing was about taking pictures only, but Moore’s Law has made it possible now, in the new millennium, to make pictures directly from pixels.
Adobe 和 Apple 产品对反映了我在第 4 章中提到的书法“绕道”造成的旧数字光划分。早期,基于几何的程序设计用于书法显示,而基于像素的程序用于光栅显示。现在使区分变得棘手的是,自从大数字融合以来,这两个品种都以像素显示。计算机图形与图像处理的区别在于其独特的基于几何的创意空间的内容。但是两个分支现在共享相同的显示空间。
The Adobe and Apple product pairs reflect the old division of Digital Light caused by the calligraphic “detour” I mentioned in chapter 4. In the early days, geometry-based programs were designed for calligraphic displays, and pixel-based programs for raster displays. What makes the distinction tricky now is that, since the Great Digital Convergence, both varieties display in pixels. What separates computer graphics from image processing is the contents of its distinctive geometry-based Creative Space. But both branches now share the same Display Space.
有很多二维计算机图形的例子。甚至我现在使用的 Microsoft Windows 界面也是计算机图形。窗户开着显示空间中的屏幕是程序创意空间中桌面上一堆文件的矩形模型。与 Microsoft Word 的界面类似。它的模型是代表文档页面的一系列矩形,页面上的每个字母最终都由一个几何模型定义。网页设计和使用结果页面的浏览器是进一步的例子。几何输入,像素输出。
There are many examples of two-dimensional computer graphics. Even the interface to Microsoft Windows that I’m using right now is computer graphics. The windows on the screen in Display Space are rectangular models of a stack of papers on a desktop in the program’s Creative Space. And the interface to Microsoft Word is similar. Its model is a sequence of rectangles representing the document pages, and each letter on the pages is defined ultimately by a geometric model. Webpage design and the browsers that use the resulting pages are further examples. Geometry in, pixels out.
本书的一个主要目标是展示一部类似皮克斯的电影是如何从计算机中出现的。这种电影的每一帧都用计算机内部的三维几何建模,然后渲染成二维扩展像素以进行全彩显示。这就是我们所说的三维计算机图形学,这本书的主要焦点。电子游戏的创建方式相同。VR 也是如此——每帧有两个显示器,每只眼睛一个,以产生立体效果。
A major goal of this book is to show how a Pixar-like movie emerges from a computer. Each frame of such a movie is modeled with three-dimensional geometry internal to the computer, then rendered into two-dimensional spread pixels for full-color display. That’s what we mean by three-dimensional computer graphics, the main focus of this book. Videogames are created the same way. And VR too—with two displays of each frame, one for each eye, to produce a stereo effect.
样条曲线是曲线,而不是曲面,我们现在要将注意力集中在曲面建模上。我们考虑的下一个形状用于此目的。其中第一个简单而熟悉。
A spline is a curve, not a surface, and we want to focus attention now on modeling surfaces. The next shapes we consider serve that purpose. The first of them is simple and familiar.
究竟什么是三角形?我查阅了我在新墨西哥州克洛维斯高中时精心保存的平面几何教科书,这本书塑造了我的整个未来。本书从第 7 页开始,以点和直线开头。这两个概念无法真正定义——我们只是“知道”它们是什么——但我们可以通过它们缺少什么或不具备什么来开始“理解”它们:一个点没有宽度、没有高度和没有厚度。这是纯粹的位置。一条直线没有宽度,没有厚度,并且在一维的两个方向上都趋于无穷大。可以通过命名其上的任意两个点来指定。线段是由直线上的两个点(线段的端点)定义的有限段直线。折线由线段组成,除了最后一条线段外,每条线段都以头尾相连。11
What exactly is a triangle? I consulted the carefully preserved plane geometry textbook from my Clovis, New Mexico, high school, a book that shaped my entire future. The book begins on page 7 with points and straight lines. The two ideas can’t really be defined—we just “know” what they are—but we can start to “understand” them by what they lack, or what they are not: A point has no width, no height, and no thickness. It’s pure location. A straight line has no width, no thickness, and goes to infinity in both directions of its one dimension. It can be specified by naming any two points on it. A line segment is a finite piece of a straight line defined by two points on the line, the line segment’s endpoints. A broken line is composed of line segments, each connected nose-to-tail with one other, except the last one. So a broken line has two dangling endpoints.11
令我惊讶的是,教科书直到第 57 页才到达低三角形。它说,多边形是一条闭合的折线。最后一条线段的最后一个端点连接到第一条线段的第一个端点——没有悬垂端点。最后,三角形是只有三个边的多边形。这些都不是可见的,但教科书确实说一个点由图片中的一个点表示。图 6.8 在一张图中显示了几何课。这些是我刚才提到的五个不可见几何对象的可视化。它们是简单抽象几何模型的具体渲染。
To my surprise, the textbook doesn’t arrive at the lowly triangle until page 57. A polygon is a closed broken line, it says. The last endpoint of the last line segment is connected to the first endpoint of the first line segment—no dangling endpoints. Finally, a triangle is a polygon with just three sides. None of these is visible, but the textbook does say that a point is represented by a dot in a picture. Figure 6.8 shows that geometry lesson in one figure. These are visualizations of the five invisible geometrical objects I just mentioned. They are concrete renderings of the simple abstract geometric models.
图 6.8
Figure 6.8
图 6.9
Figure 6.9
教科书对三角形的冗长方法确实具有引入一个重要术语的优点。它是多边形,计算机图形学中一个非常受欢迎的词。计算机图形学的一般方法是用多边形描述一个虚构的世界。
The textbook’s longwinded approach to the triangle does have the advantage that it introduces an important term. It’s polygon, a much beloved word in computer graphics. A general approach in computer graphics is to describe a fictitious world with polygons.
但是我们将立即摆脱对多边形一词的需求,因为这个关键事实:任何多边形都可以细分为三角形:选择多边形的任何角或顶点,并用线将其连接到所有其他角(顶点)段。所以,我们只需要谈论三角形。图 6.9 显示了将四边形多边形转换为两个三角形的两种不同方法,并带有一条额外的线段(虚线)。五边形多边形需要两条额外的线,依此类推。(注意事项见注释。)12
But we’ll immediately rid ourselves of the need for the word polygon with this key fact: Any polygon can be subdivided into triangles: choose any corner, or vertex, of a polygon and connect it to all the other corners (vertices) with line segments. So, we only ever have to talk about triangles. Figure 6.9 shows two different ways to convert a four-sided polygon into two triangles with one additional line segment (dotted). It would take two additional lines for a five-sided polygon, and so forth. (See the annotation for caveats.)12
由于这个技巧,我们只需要专注于由三角形组成的模型。不过,并不是每个模型都可以用三角形制作。Ravi Shankar 曲线的几何模型只是样条曲线,而不是多边形。第一张数码图片“First Light”中的文字,以及“数码之光的黎明”一章中早期电子游戏的游戏板也有简单的模型,并未简化为三角形。除了少数例外,这些模型只是直线段。
Because of this trick, we only need to concentrate on models made of triangles. Not every model can be made with triangles, though. The geometric model for the Ravi Shankar curve is just a spline, not a polygon. The text in the first digital picture, First Light, and the game boards of the early videogames in the Dawn of Digital Light chapter also had simple models that didn’t reduce to triangles. The models were, with few exceptions, just straight line segments.
但是考虑一下皮克斯的动画电影,从玩具总动员到超人总动员 2、Illumination 的卑鄙的我,以及所有其他具有 3D 角色的动画电影——“皮克斯式”电影。它们的特征是由曲面组成的,曲面可以只用三角形来建模。
But consider Pixar’s animated films from Toy Story to Incredibles 2, Illumination’s Despicable Me, and all other animated films with three-dimensional characters—“Pixar-like” movies. Their characters are composed of surfaces, and surfaces can be modeled just with triangles.
如果我们学会了如何处理一个三角形,那么我们就可以让 Amplification(计算机的伟大荣耀)来处理所有其余部分,通常是数百万个。本章(和下一章)的中心思想是,如果你能理解一个三角形是如何从计算机内存到显示屏的,那么通过调用 Amplification您可以直观地了解完整图片是如何进入屏幕的。正是计算机不知疲倦地一遍又一遍地计算同一件事,数百万甚至数十亿次,速度非常快,这使得计算机图形成为可能。这很难做到——对于一个没有帮助的人来说是不可能的——但很容易理解。
If we learn how to deal with a single triangle, then we can let Amplification—that great glory of computers—take care of all the rest, often many millions of them. The central idea of this chapter (and the next) is that if you can understand how one triangle gets from computer memory to display screen, then by invoking Amplification you can intuit how a full picture gets to the screen. It’s the computer tirelessly computing the same thing over and over, millions even billions of times, very fast, that makes computer graphics possible. It’s hard to do—impossible for an unaided human—but easy to understand.
图 6.10
Figure 6.10
几十年来,计算机图形学家通过制作单个物体的图片来展示他们的最新进展。. . 一个茶壶。事实上,正是这个真正的茶壶——图 6.10 是它的照片,而不是计算机渲染图——在计算机历史博物馆中占有一席之地。茶壶属于 Martin Newell,自然是英国人,他是 1970 年代犹他大学的计算机图形学教授。鲜为人知的是,纽厄尔用茶杯和茶托、茶匙和奶精模拟了整个茶具来搭配茶壶。13
For decades computer graphicists showed off their latest advances by making pictures of a single object . . . a teapot. In fact, it’s this actual teapot—figure 6.10 is a photograph of it, not a computer rendering—that holds a place of honor in the Computer History Museum. The teapot belonged to Martin Newell, an Englishman naturally, who was a computer graphics professor at the University of Utah in the 1970s. It’s less well known that Newell modeled an entire tea set with teacups and saucers, teaspoons, and a creamer to accompany the teapot.13
图 6.11 展示了如何在计算机中使用几何模型来模拟一个复杂的对象,一个茶壶。同样的想法被用于模拟皮克斯风格中每个角色的形状电影。这是 Newell 茶壶的两种不同表示形式——出于显而易见的原因,它们被称为线框表示形式。左边的模型是三角形的网格。右边的一个是四边多边形的网格。在每个四边多边形上绘制的对角线也会将其转换为三角形网格。三角形是平的,但我们用许多小三角形来表示曲面,以至于在适当的观察距离上,集体表面看起来是弯曲的。很快,我们将描述如何创建这样的网格,但只是假设它们现在存在。
Figure 6.11 shows how you can use geometry to model a complex object, a teapot, in a computer. The same idea is used to model the shape of each character in a Pixar-like movie. These are two different representations of Newell’s teapot—called wireframe representations for obvious reasons. The model on the left is a mesh of triangles. The one on the right is a mesh of four-sided polygons. Diagonals drawn on each of the four-sided polygons would convert it to a mesh of triangles too. Triangles are flat, but we represent curved surfaces with so many small triangles that the collective surface appears curved at an appropriate viewing distance. Soon, we’ll describe how to create such meshes, but just assume they exist for now.
图 6.11
Figure 6.11
需要明确的是,这些图片不是计算机内部的内容。电脑里没有图片,即使是看起来像几何图形的图片。这些图片是计算机内几何模型的散布像素的渲染,然后呈现在显示器上——即您现在正在阅读的打印页面。
To be clear, these pictures are not what’s inside the computer. There are no pictures inside a computer, even ones that look like geometry. The pictures are renderings into spread pixels of the geometric models inside the computer that are then presented on a display—namely the printed page you are reading now.
什么是“计算机内部的几何模型”?让我们回想一下,计算机内部只有信息模式。尽管计算不需要位,但如今信息模式总是以这种方式存储。因此,该模型是位于计算机内部某处的集成电路芯片中的高压和低压模式。
What is a “geometric model inside a computer”? Let’s recall that there are only patterns of information inside a computer. Although bits aren’t required for computation, nowadays patterns of information are always stored that way. So the model is a pattern of high and low voltages in an integrated circuit chip located somewhere in the bowels of a computer.
我还在前面的章节中指出,位不一定代表数字,但它们经常代表数字,而且在计算机图形的几何模型中也是如此。形成三角形的每条线段(即它的每条边)都由标识其两个端点位置的数字表示。换句话说,计算机内存保存着每个顶点的坐标(边相交的点)、它的水平、垂直和深度位置。因此,计算机内部由三角形组成的模型只是表示数字的位模式,这些数字是三角形顶点在三维空间中的位置。该模型本质上是一个数字列表——通常是一个很长的列表。茶壶列表将使用大约 26,000 个数字——仅用于茶壶。巴斯光年将需要数百万。放大是我们可能处理这些数字的唯一方法。
I also noted in earlier chapters that bits don’t necessarily represent numbers, but they often do, and they do in geometric models for computer graphics. Each line segment forming a triangle—that is, each of its sides—is represented by numbers that identify the positions of its two endpoints. In other words, a computer memory holds the coordinates of each vertex (the point where the sides meet), its horizontal, vertical, and depth locations. So, a model made of triangles inside a computer is simply patterns of bits representing numbers that are the locations of triangle vertices in three-dimensional space. The model is essentially a list of numbers—generally a very long list. The teapot list would use about 26,000 numbers—just for a teapot. Buzz Lightyear would require millions. Amplification is the only way we can possibly deal with such numbers.
另一种信息通常存储在几何模型中。你可以把它想象成模型的结构:这个点连接那个点,这个三角形和那个点共享一条边,这个茶壶把手在这里连接到茶壶主体,或者髋骨连接到一个人的大腿骨特点。这些信息也是数字。它们是计算机内存地址。例如,一个点的三个坐标后面可能跟第四个数字。它告诉程序在内存中的哪个位置找到与该点相连的另一个点。
Another kind of information is usually stored in a geometric model. You can think of it as the model’s structure: this point is connected to that one, this triangle shares an edge with that one, this teapot handle is connected here to the teapot body, or the hip bone is connected to the thigh bone of a character. These pieces of information are numbers too. They are computer memory addresses. For example, the three coordinates of a point might be followed with a fourth number. It tells the program where to go in memory to find another point that is connected to this one.
计算机根本不知道这些数据的含义。计算机本身不知道这些高低电压模式是几何模型。需要一个程序来理解这些模式。它是一个“知道”位代表数字并且存储的数字代表三角形的程序。或者数字是可以找到连接组件的地址。一长串无意义的步骤,一个程序,为存储在计算机中的模型赋予意义,该模型将成为计算机显示器上的图片。事实上,是编写程序的人知道程序的含义和它操作的数据。
The computer doesn’t in any way know what any of this data means. The computer itself has no notion that those patterns of high and low voltages are a geometric model. It takes a program to make sense of the patterns. It’s a program that “knows” that the bits represent numbers and that the stored numbers represent triangles. Or that a number is an address where a connected component can be found. A long list of meaningless steps, a program, gives meaning to a model stored inside a computer that is to become a picture on the computer’s display. In fact, it’s the human who wrote the program who knows the meaning of the program and the data it manipulates.
您不必在创建模型时查看它。在早期,没有人看到他们制作的模型。马丁纽厄尔在电脑中制作茶壶时看不到它的模型。但是现代计算机图形程序确实让我们在设计模型时看到它。我们在构建模型时第一次看到模型的那一刻,在计算机图形学中是一个非常荣幸的时刻,我们很快就会发现。
You don’t have to see a model as it’s created. In the early days nobody saw the models they made. Martin Newell couldn’t see the model of his teapot as he built it in a computer. But a modern computer graphics program does let us see a model while we design it. That moment when we first could see a model while we built it is a highly honored one in computer graphics, as we will soon discover.
数字列表如何变成茶壶或巴斯光年?如果您知道一个三角形如何完成从比特到散布像素的旅程,那么剩下的就是计算机的放大荣耀——繁重的工作,无论多么熟练、聪明或精通计算机,人类都无法做到这一点做。计算机做得这么好是愚蠢的。所以,我们的目标归结为让一个三角形出现在屏幕上。如果你明白这一点,你就会明白这一切。
How does a list of numbers become a teapot or Buzz Lightyear? If you know how one triangle makes the journey from bits to spread pixels, then it’s the Amplification glory of computers that does the rest—the heavy lifting, the part that no human being, no matter how skilled, smart, or computer savvy, could do. It’s the dumb thing that computers do so well. So, our goal boils down to getting one triangle onto a screen. If you understand that, you understand it all.
由三角形组成的模型是三维的,但它的图片(即渲染到显示空间的散布像素中的几何模型)只有二维。图 6.11 中描绘的两个线框茶壶看起来是 3D 的,因为它们是透视渲染的,这压扁了三角形。但它们仍然是三角形。这是我们在这里学习如何绘制的那些二维三角形。
A model made of triangles is three-dimensional, but a picture of it—that is, the geometry model rendered into the spread pixels of a Display Space—has only two dimensions. The two wireframe teapots depicted in figure 6.11 appear three-dimensional because they were rendered in perspective, which squashed the triangles. But they’re still triangles. It’s those two-dimensional triangles we learn how to draw here.
在老式的书法展示上很容易。一个程序简单地指示显示器从它的一个端点扫出一条线段——三角形的一侧给对方。然后程序对另外两侧重复该指令。而已。现在可以看到一个三角形的图片。以位形式存储在内存中的简短数字列表现在是显示器上的三角形图片。使用放大的奇迹,我们让我们的计算机非常快速地重复这个简单的过程数万次,以在书法显示器上将完整茶壶的几何模型视为线框图片。
It’s easy on an old-fashioned calligraphic display. A program simply instructs the display to sweep out a line segment—one side of a triangle—from one of its endpoints to the other. And then the program repeats the instruction for the other two sides. That’s it. A picture of one triangle is now visible. A short list of numbers stored as bits in a memory is now a picture of a triangle on a display. Using the miracle of Amplification, we then have our computer repeat this simple process tens of thousands of times very rapidly to view the geometric model of a full teapot as a wireframe picture on a calligraphic display.
尽管以这种方式显示三角形在概念上很简单,但计算机图形学家花了数年时间来提高这个过程的效率。例如,如果三角形边被另一个三角形共享,则多次绘制它是浪费宝贵的时间。我们已经掩盖了对计算机图形学家很重要的其他几个问题,但它们是管道(参见注释)。您无需了解它们即可直观地理解将作为数值存储在计算机内存位置中的三角形转换为显示屏上的三角形图片最终是多么简单。或者将三角形网格变成茶壶的图片。14
Although displaying triangles in this way is conceptually simple, computer graphicists spent years making the process efficient. It’s a waste of precious time, for instance, to draw a triangle side more than once if it’s shared by another triangle. We’ve glossed over several other matters important to computer graphicists, but they are the plumbing (see the annotation). You needn’t know about them to understand intuitively how ultimately simple it is to convert a triangle stored as numeric values in computer memory locations into a picture of the triangle on a display screen. Or of a mesh of triangles into a picture of a teapot.14
在书法显示器上很容易画出一条线段,也就是一个三角形。但现代显示器不是书法。它们是散布像素的光栅显示。如何在严格按行和列排列的显示器上表示任意角度的直线段?问这个问题的另一种方法是:如何将线段渲染到光栅显示?
It’s easy to draw a line segment, hence a triangle, on a calligraphic display. But modern displays aren’t calligraphic. They’re raster displays of spread pixels. How do you represent a straight line segment at any angle on a display that is arranged in strict rows and columns? Another way to ask the question is this: How do you render a line segment to a raster display?
计算机图形学中第一个以人名命名的渲染算法是Bresenham 算法。这是已知最早的用像素逼近直线段的程序之一。Jack Bresenham 在 1962 年不得不使用开启或关闭的像素来(粗略地)表示线段。这就是他当时所拥有的一切。15
The first rendering algorithm in computer graphics to bear a person’s name was Bresenham’s algorithm. It was one of the earliest known procedures for approximating a straight line segment with pixels. Jack Bresenham in 1962 had to use pixels that were either on or off to (crudely) represent line segments. That’s all he had then.15
这是一条线段(图 6.12,对角线),使用 Bresenham 算法渲染为白色背景上的黑色扩展像素。精确点是像素位置。散布像素(大点)放置在最近的位置或给定的线段。Bresenham 的算法是最有效的一种,可用于仅显示黑色或白色的简单光栅显示器。
Here’s a line segment (figure 6.12, the diagonal) rendered with Bresenham’s algorithm as black spread pixels on an otherwise white background. The pinpoint dots are pixel locations. Spread pixels (the big dots) are placed at the locations nearest or on the given line segment. Bresenham’s algorithm is the most efficient one possible for use on simple raster displays that can display only black or white.
图 6.12
Figure 6.12
当然,您在此处看到的对角线段实际上是对其他不可见线段的现代显示器(或打印页面)的扩展像素的渲染。Bresenham 近似线段的“扩展像素”(大点)并不是画得很大的实际像素。像素不是完美的小圆盘,也不是完美的小方块。
Of course, the diagonal line segment that you see here is actually a rendering into the spread pixels of a modern display (or printed page) of the otherwise invisible line segment. And the “spread pixels” (the large dots) of Bresenham’s approximation of the line segment aren’t actual pixels drawn large. Pixels are no more perfect little disks than they are perfect little squares.
Bresenham 的算法和其他类似的算法给了我们早期计算机图形学的“锯齿”。如果你眯着眼睛看图 6.12,你可以看到明显的阶梯(忽略对角线段)。当时许多人认为这是一种丑陋的外观,这是计算机图像必须看起来的样子——再次错误地认为计算机必须是死板的和“机械的”。正如我们在“数字光的黎明”一章中看到的那样,Dick Shoup 花了 10 多年的时间才向我们展示锯齿并不是计算机固有的。1973 年,他展示了用散布像素渲染的精美直线(图 4.26)。但这些像素的值远不止两个——多了两个数量级。
Bresenham’s algorithm and others like it gave us the “jaggies” of early computer graphics. You can see the telltale stairsteps if you squint your eyes at figure 6.12 (and ignore the diagonal line segment). It’s an ugly look that many people thought at the time was what computer pictures had to look like—that misperception again that computers had to be rigid and “mechanical.” As we saw in the Dawn of Digital Light chapter, it took 10 more years before Dick Shoup showed us that jaggies weren’t intrinsic to computers. In 1973 he demonstrated straight lines that were rendered beautifully with spread pixels (figure 4.26). But those pixels had far more than two values—two orders of magnitude more.
Bresenham 的算法首先吸引我的不是它的效率。布雷森汉姆就是这个名字。它的拼写与来自新墨西哥州克洛维斯的高中同学 Dick Bresenham 的拼写完全一样。当然,该算法的 Jack Bresenham 也不可能来自 Clovis。我查了一下,发现他其实是在英国的IBM工作的,这件事就解决了。或者我是这么想的。但是当一本重要的计算机图形学教科书的第一版出版时,克洛维斯的布雷森汉姆夫人打电话给克洛维斯的史密斯夫人说:“我儿子有一个章节,你的也有。” 她像妈妈们一样夸大了我们的重要性,但重点是:杰克是迪克的兄弟,他确实来自我的家乡。当我终于见到杰克时,我得知他在我认识他之前就离开了克洛维斯。16
What first attracted me to Bresenham’s algorithm wasn’t its efficiency. It was that name Bresenham. It’s spelled exactly the way Dick Bresenham, a high-school classmate from Clovis, New Mexico, spelled it. Surely Jack Bresenham of the algorithm couldn’t have come from Clovis too. I checked and found that in fact he worked for IBM in England, which settled the matter. Or so I thought. But when the first edition of an important computer graphics textbook was published, Mrs. Bresenham in Clovis called Mrs. Smith in Clovis and said, “My son has a chapter, and so does yours.” She exaggerated our importance, as moms do, but the point was made: Jack was Dick’s brother, and he did come from my hometown. When I finally met Jack, I learned that he’d left Clovis just before I was old enough to know him.16
现在让我们将这些发展置于历史背景中。我在这里使用了一个流程图,就像我在前两章中使用的那样,来引导我们了解涉及许多参与者的复杂历史。我在“数字光的黎明”一章中介绍的计算机历史流程图涵盖了 1940 年代末和 1950 年代初。我们可以将那个时期视为摩尔定律之前时期的第一阶段——即第一纪元的第一阶段。图 6.13 是该图表(图 4.6)到 1950 年代后期和 1960 年代大部分时间的延续, Epoch 1 的第二阶段。此处重复标有“Whirlwind”的框以显示两个图表的连接位置。
Let’s now turn to placing these developments in historical context. I use a flow chart here, like those I used in the preceding two chapters, to guide us through a complex history involving many players. The flow chart of the history of computers I presented in the Dawn of Digital Light chapter covered the late 1940s and the early 1950s. We can think of that period as the first stage of the period before Moore’s Law—that is, the first stage of Epoch 1. Figure 6.13 is the continuation of that chart (figure 4.6) into the late 1950s and through much of the 1960s, the second stage of Epoch 1. The box labeled “Whirlwind” is repeated here to show where the two charts join.
“Moore's Law 1965” 项出现在流程图的中下部,表示启动 Epoch 2 的重大事件。我们将在下一章中保留对 Epoch 2 的探索,除了为了方便起见,此处包含一个经过仔细标记的事件. (发生在 1965 年之后的事件并不意味着它利用了摩尔定律。)个人被包围在圆圈中,而群体被包围在椭圆中。计算机和专用硬件设备位于矩形中。程序、书籍和概念——所有软想法——都是平行四边形。
The item “Moore’s Law 1965” appears in the lower middle of the flow chart, indicating the fateful event that kicked off Epoch 2. We’ll save exploration of Epoch 2 for the next chapter, except for one carefully labeled event included here for convenience. (That an event occurred after 1965 doesn’t imply that it utilized Moore’s Law.) Individuals are enclosed in circles, and a group in an ellipse. Computers and a special-purpose hardware device are in rectangles. Programs, books, and concepts—all soft ideas—are in parallelograms.
我在前几章中所说的关于流程图的所有内容也仍然适用于这一章:这不是对该领域的详尽介绍。此处省略的许多球员和事件在文本的其他地方或注释中提供 - 但肯定不是全部。本章的散文可以被认为是图表的冗长标题。和以前一样,图表的复杂性表明,高科技的故事很少,如果有的话,是一个单一领导者的简单叙述。17
Everything I said about flow charts in earlier chapters continues to hold for this one too: It’s not an exhaustive presentation of the field. Many players and events that are omitted here are supplied elsewhere in the text or in the annotations—but certainly not all of them. And the chapter’s prose can be thought of as a lengthy caption for the chart. As before, the chart’s complexity demonstrates that the story of a high technology is seldom, if ever, a simple narrative of a single leader.17
根据定义,计算机图形是从计算机内存中保存的不可见几何模型创建可见图片。使用这些模型有两种主要方法,这种区别导致计算机图形的主要划分。
Computer graphics by definition is the creation of visible pictures from invisible geometric models held in computer memory. There are two major ways to use those models, and that distinction leads to a major partitioning of computer graphics.
在一种情况下,模型表示旨在存在于现实世界中的对象。计算机辅助设计(CAD) 从业者使用计算机图形来设计对象。归根结底,对象在 CAD 中很重要,而不是图片。CAD是面向对象的计算机图形学。
In one case, the models represent objects intended to exist in the real world. A computer-aided design (CAD) practitioner uses computer graphics to design objects. Ultimately, objects matter in CAD—not pictures of them. CAD is object-oriented computer graphics.
相反的情况是面向图片的计算机图形学。数字电影是一个很好的例子,说明只有图片才是重要的——而不是所描绘的物体。
The opposite case is picture-oriented computer graphics. A digital movie is an excellent example of how only pictures matter—not the objects pictured.
一个主要的附带条件是将 CAD 与面向图片的计算机图形学分开。一句话,就是准确。CAD 中对象的计算机模型是旨在存在于现实世界中的对象的准确表示,例如汽车、建筑物和机器零件。早期,CAD 生成的是对象,而不是图片。例如,计算机模型可用于驱动铣床,从金属、泡沫或木块上切割出相应的物体。
A major proviso separates CAD from picture-oriented computer graphics. In a word, it’s accuracy. The computer models of objects in CAD are accurate representations of objects intended to exist in the real world, such as cars, buildings, and machine parts. In the early days, CAD produced objects, not pictures. For example, a computer model might be used to drive a milling machine that cut the corresponding object from blocks of metal, or foam, or wood.
由于计算机辅助设计对象必须承受现实世界的磨损,因此它们通常在仍处于计算机模型形式时接受严格的测试。因此,在锻造和组装实际的桁架之前,可能首先在应力的计算机模拟中测试由钢桁架制成的桥梁。桥梁的精确计算机模型用作模拟交通或风对桥梁的预期载荷的输入。或者在计算机中检查打算刚性连接的航天器的两个部分模型形式,以确保它们在金属中实际实现时能够可靠地组合在一起。
Since computer-aided design objects must sustain real-world wear and tear, they are often subjected to serious testing while still in computer model form. So a bridge made of steel trusses might first be tested, in a computer simulation of stresses, before the actual trusses are forged and assembled. The accurate computer model of the bridge serves as input to the simulation of expected loading of the bridge by traffic or wind. Or two parts of a spacecraft intended to attach rigidly are checked, while still in computer model form, to ensure that they will reliably fit together when actually realized in metals.
图 6.13
Figure 6.13
但在其他计算机图形学中,图片即输出就是一切——因此是面向图片的计算机图形学。准确的测量和测试是无关紧要的。图片只需要看起来令人信服。皮克斯可能会将伍迪的《玩具总动员》模型发送给某人,后者将其转化为准确的、可构建的 CAD 模型并制作玩具,但原始模型的主要目的是电影《玩具总动员》。
But in the rest of computer graphics, pictures-as-output are everything—hence picture-oriented computer graphics. Accurate measurements and testing are irrelevant. The pictures only have to look convincing. Pixar might send Woody’s Toy Story model to someone who turns it into an accurate, buildable CAD model and makes a toy, but the principal purpose of the original model was Toy Story the movie.
好莱坞以其虚假的战线而闻名。想想牛仔射击游戏中的主要街道。计算机生成的电影都是虚假的前线。伍迪的表面里面什么都没有。他只是肤浅。里面没有什么可测试或压力的。谁在乎他是否可以建造?字符只需要看起来正确。
Hollywood is famous for its false fronts. Think of the main street in a cowboy shoot-’em-up. Computer-generated movies are all false fronts. There’s nothing inside Woody’s surfaces. He’s only skin deep. There’s nothing to test or stress inside. Who cares if he’s buildable? Characters only have to look right.
C.R.T. STORE考虑一下第一光的文本和HELLO MR. MURROW数字光的黎明一章中呈现的早期动画。现实世界中没有任何对象与这些显示相对应。或者回想一下同一章节中的两个早期游戏,跳棋和井字游戏。同样,现实世界中不存在与这些相对应的实际游戏板或棋子。Whirlwind 上显示的数学曲线并不是现实世界中的物体。除了在计算机显示器上散布像素和它们的(简单)不可见模型之外,这些早期示例从未有任何形式。因此,来自数字光黎明的所有图片都是面向图片的计算机图形实例,而不是计算机辅助设计。然而我们会发现,计算机图形学的最早领导者通常来自 CAD。
Consider the texts C.R.T. STORE of First Light and HELLO MR. MURROW of the early animation presented in the Dawn of Digital Light chapter. No objects in the real world corresponded to those displays. Or recall the two early games from that same chapter, checkers and tic-tac-toe. Again, no actual game board or pieces corresponding to these ever existed in the real world. And the mathematical curves displayed on Whirlwind weren’t objects in the real world. There was never any form to these early examples other than spread pixels on a computer display and (simple) nonvisible models of them. Thus all the pictures from the Dawn of Digital Light were instances of picture-oriented computer graphics, not computer-aided design. Yet we’ll find that the earliest leaders of computer graphics generally came from CAD.
计算机辅助设计和面向图片的计算机图形学密切相关,并且有着相互交织的历史。他们经常混为一谈也就不足为奇了。在本书中,计算机图形学通常意味着“图片为王”,并缩写为面向图片的计算机图形学。我小心地将“物为王”模式指定为计算机辅助设计。需要重复一遍:虽然 CAD 是计算机图形学的一部分,但我在本书中通常指的计算机图形学是非 CAD 部分。
Computer-aided design and picture-oriented computer graphics are closely related and have intertwined histories. It’s no surprise that they are often conflated. From here on in this book, computer graphics will usually mean “pictures are king” and abbreviate picture-oriented computer graphics. I carefully designate the “objects are king” mode as computer-aided design. That bears repeating: although CAD is part of computer graphics, I’ll usually mean by computer graphics in this book the non-CAD part.
我限制了前几章中的图表来绘制通向数字光的路径。该图表(图 6.13)仅进一步关注那些导致 Digital Light 的计算机图形部分的内容。它强调了对制作数字电影特别重要的计算机图形部分,这是下一章的重点。幸运的是,它仍然捕捉到了早期计算机图形学的许多重大事件。
I constrained the charts in previous chapters to map the pathways leading to Digital Light. This chart (figure 6.13) concentrates further only on those that led to the computer graphics part of Digital Light. It emphasizes those parts of computer graphics that are especially important for making digital movies, the focus of the next chapter. Fortunately, it nevertheless captures many major events of early computer graphics.
计算机图形学出现在特定环境中。它与个人计算机和互联网的发明共享。这是一个国家技术蓬勃发展的故事。
Computer graphics emerged in a particular milieu. It shares it with the inventions of the personal computer and the internet. It’s quite a story—of a national technological blossoming.
美国政府对纳粹德国的威胁作出反应,向少数几个研发中心投入大量资金,这在资本主义社会中通常是不做的。战争迫在眉睫。速度是必不可少的。这些基金没有市场竞争——没有概述细节的征求建议书文件,没有投标。他们刚刚被分发出去。麻省理工学院是这笔捐款的主要受益者,这份礼物巩固了麻省理工学院作为世界顶尖科技大学的地位。
The US government responded to the threat of Nazi Germany by pouring massive amounts of money into a few centers of research and development, not something that’s normally done in a capitalist society. War was imminent. Speed was essential. There was no market competition for these funds—no Request For Proposal documents outlining the details, no bidding. They were just handed out. The Massachusetts Institute of Technology was a major beneficiary of the largesse, a gift that solidified MIT’s position as a top technological university in the world.
麻省理工学院于 1940 年获得巨额资助,设立了两个实验室。辐射实验室专注于雷达,这是一项有望扭转战局对抗德国人的技术。对它的研究是最重要的。另一个实验室,伺服机构实验室,专注于复杂系统的控制。(伺服机构或伺服系统通常是使用反馈进行精细控制的电机。)这些实验室多次更名,这使得跟踪变得困难。它或多或少地简化为该表中的两条下降线(缩进标识子组而不是重命名):
MIT was heavily funded in 1940 and set up two labs. The Radiation Lab concentrated on radar, a technology that promised to turn the tide of war against the Germans. Research on it was of the highest importance. The other lab, the Servomechanisms Lab, concentrated on control of complex systems. (A servomechanism, or servo, is typically a motor that uses feedback for fine control.) These labs changed names several times, which makes keeping track difficult. It simplifies more-or-less into the two lines of descent in this table (indentations identify subgroups not renamings):
|
辐射实验室下降 Rad Lab Descent |
伺服实验室下降 Servo Lab Descent |
|---|---|
|
辐射实验室'40 Radiation Lab ’40 |
伺服机构实验室'40 Servomechanism Lab ’40 |
|
电子研究实验室'46 Research Lab for Electronics ’46 |
数字计算机实验室'51 Digital Computer Lab ’51 |
|
林肯项目'51 Project Lincoln ’51 |
电子系统实验室'59 Electronic Systems Lab ’59 |
|
林肯实验室'52 Lincoln Lab ’52 |
CAD项目麻省理工学院'59 CAD Project MIT ’59 |
Whirlwind 计算机始于伺服实验室,于 1951 年进入数字计算机实验室,并于 1951 年被纳入林肯计划(在 Rad Lab 专栏中)。因此计算机图形学主要来自 Rad Lab,但不完全是。计算机辅助设计 (CAD) 项目于 1959 年在麻省理工学院作为电子系统实验室的一部分开始。所以很容易说计算机辅助设计起源于伺服实验室。但正如我们很快看到的那样,麻省理工学院的计算机图形学和计算机辅助设计故事比这更交织在一起。
The Whirlwind computer began in the Servo Lab, went into the Digital Computer Lab in 1951, and was subsumed into Project Lincoln (in the Rad Lab column) also in 1951. So computer graphics descends primarily from the Rad Lab, but not completely. The Computer-Aided Design (CAD) Project began at MIT in 1959 as part of the Electronic System Lab. So it’s tempting to say that computer-aided design descends from the Servo Lab. But the computer graphics and computer-aided design stories at MIT were more intertwined than that, as we soon see.
战后,麻省理工学院教授兼行政人员万尼瓦·布什发表了一篇重要且有影响力的论文:《As We May Think》出现在《大西洋月刊》上,并在《生活》杂志上再版。考虑到他甚至在计算机出现之前,甚至在互联网出现之前,布什就具有惊人的先见之明:
Just after the war, Vannevar Bush, a professor and administrator at MIT, published a significant and influential paper: “As We May Think” appeared in The Atlantic Monthly and was republished in Life magazine. Bush was astonishingly prescient, considering that he wrote before computers even, and well before the internet:
考虑未来的个人使用设备,它是一种机械化的私人文件和图书馆。它需要一个名字,而且,为了随机创造一个名字,“memex”就可以了。memex 是一种设备,个人在其中存储他的所有书籍、记录和通信,并且是机械化的,因此可以以超快的速度和灵活性对其进行查询。这是对他记忆的一种扩大的亲密补充。18
Consider a future device for individual use, which is a sort of mechanized private file and library. It needs a name, and, to coin one at random, “memex” will do. A memex is a device in which an individual stores all his books, records, and communications, and which is mechanized so that it may be consulted with exceeding speed and flexibility. It is an enlarged intimate supplement to his memory.18
他在这个著名的“memex 备忘录”中犯了很多错误。在上面引用的前一段中,他告诉我们 memex 是桌面大小的。而“memex”这个名字并没有留下来。但他的其他一些评论是对 75 年后未来的准确愿景——也就是说,现在:“全新形式的百科全书将会出现,准备好用贯穿其中的关联线索网。” 并且:“开拓者是一种新的职业,他们乐于通过大量的共同记录建立有用的路径。” 在某种程度上,这就是我对这本书所做的。19
He got a lot wrong in this famous “memex memo.” In the paragraph just before the one quoted above, he tells us that the memex is desk sized. And the name “memex” didn’t stick. But some of his other comments are dead-on accurate visions of the future 75 years hence—that is, now: “Wholly new forms of encyclopedias will appear, ready made with a mesh of associative trails running through them.” And: “There is a new profession of trail blazers, those who find delight in the task of establishing useful trails through the enormous mass of the common record.” In a way that’s what I’m doing with this book.19
布什(与美国总统没有关系)在建立曼哈顿计划和国家科学基金会方面发挥了重要作用。他是第一位担任总统科学顾问的人(富兰克林·D·罗斯福)。也许他在麻省理工学院最著名的学生是克劳德·香农。但另一个是弗雷德里克·特曼,他后来在斯坦福大学将大学土地出租给高科技公司,以创建现在被称为硅谷的地方。
Bush (no relation to the US presidents) was instrumental in setting up the Manhattan Project and the National Science Foundation. He was the first person to be the science adviser to a president (Franklin D. Roosevelt). Perhaps his most notable student at MIT was Claude Shannon. But another was Frederick Terman who would later, at Stanford University, lease university lands to high-tech firms to create what is now known as Silicon Valley.
1945 年在新墨西哥州的三一遗址进行的原子试验——紧随其后的是广岛和长崎爆炸——标志着战争的结束。与俄罗斯的冷战紧随其后。火上浇油的是美国物理学家克劳斯·富克斯(Klaus Fuchs),他出席了三一中心试验并将核机密传递给了苏联。而且,具有讽刺意味的是,在与超级爱国者约翰·冯·诺依曼合作研究美国的氢弹时,富克斯还向苏联人通报了其关键秘密。苏联在 1949 年引爆了他们的第一颗原子弹乔一号,并在 1953 年引爆了他们的第一颗氢弹乔四号。(这些是美国对炸弹的绰号——当然是以约瑟夫·斯大林的名字命名的。)
The atomic test conducted at the Trinity Site in New Mexico in 1945—followed shortly by the Hiroshima and Nagasaki bombings—signaled the war’s end. And the Cold War with Russia followed right on its heels. Pouring fuel on the fire was the American physicist Klaus Fuchs, who was present at the Trinity Site test and passed nuclear secrets to the Soviets. And, ironically, while working with super-patriot John von Neumann on America’s H-bomb, Fuchs also informed the Soviets about its crucial secrets. The Soviets exploded Joe One, their first A-bomb, in 1949 and Joe Four, their first H-bomb, in 1953. (These were American monikers for the bombs—named for Joseph Stalin, of course.)
然后是第二个震惊。1957 年,自满的美国人对苏联发射的太空卫星 Sputnik 感到震惊。尽管正如我们在前一章中看到的那样,采样定理的 Vladimir Kotelnikov 已经清楚地警告过我们这一点。美国的反应是于 1957 年在国防部成立高级研究计划署 (ARPA),并于 1958 年成立美国国家航空航天局 (NASA)。ARPA 将资助大部分成为主流计算机图形学的项目。对计算机图形学的未来有影响力的人将担任 ARPA 和 NASA 的管理员。其中第一个是 JCR “Lick” Licklider。
Then came the second shocker. In 1957 complacent Americans were stunned by the Soviet launch of space satellite Sputnik. This was in spite of the fact that Vladimir Kotelnikov of the Sampling Theorem had clearly warned us about it, as we saw in an earlier chapter. The US response was to form the Advanced Research Projects Agency (ARPA) in the Defense Department in 1957 and the National Aeronautics and Space Administration (NASA) in 1958. ARPA would fund much of what became mainstream computer graphics. People influential to the future of computer graphics would serve as administrators at both ARPA and NASA. The first of these was J.C.R. “Lick” Licklider.
1960 年,“Lick”Licklider 在IEEE Transactions on Human Factors in Electronics 上发表了一篇论文“人机共生” 。这篇论文与布什 1945 年的备忘录一样重要和有影响力。利克看到我们中间的新野兽,计算机,不是我们的奴隶,而是会与我们共生共存:
In 1960 “Lick” Licklider published a paper, “Man-Machine Symbiosis,” in the IEEE Transactions on Human Factors in Electronics. This paper was as significant and influential as Bush’s memex memo of 1945. Lick saw that the new beasts among us, the computers, were not to be our slaves but rather would work together symbiotically with us:
未来 10 年或 15 年的时间里,设想一个“思维中心”似乎是合理的,它将结合当今图书馆的功能以及信息存储和检索方面的预期进步以及本文前面提出的共生功能。这幅画很容易扩大到这样的中心网络,通过宽带通信线路相互连接,并通过租用线路服务与个人用户连接。在这样的系统中,计算机的速度将得到平衡,巨大的内存和复杂程序的成本将除以用户数量。20
It seems reasonable to envision, for a time 10 or 15 years hence, a “thinking center” that will incorporate the functions of present-day libraries together with anticipated advances in information storage and retrieval and the symbiotic functions suggested earlier in this paper. The picture readily enlarges itself into a network of such centers, connected to one another by wide-band communication lines and to individual users by leased-wire services. In such a system, the speed of the computers would be balanced, and the cost of the gigantic memories and the sophisticated programs would be divided by the number of users.20
在摩尔定律和互联网出现之前的那些日子里,利克并没有完全正确。早期的一些领导者认为分时计算机才是王道。不是一个用户一次访问一台大型计算机,而是几个用户显然可以同时访问。这只是“显然同时”,因为计算机的速度足以让它看起来像那样。十个用户每人将在十分之一秒的时间内获得大型计算机的资源。他们将“分时”这台大机器。21
Lick didn’t get it exactly right in those days before Moore’s Law and the internet. Some leaders in those early days thought that time-shared computers were the thing. Instead of one user at a time getting access to a big computer, several users would get access apparently at the same time. It was only “apparently at the same time” because the computer was fast enough to make it seem that way. Ten users would each get the big computer’s resources for a tenth of a second say. They would “time share” the big machine.21
Licklider 和任何其他有远见的人都没有看到摩尔定律会使所有计算机分时共享由单个用户运行的多个应用程序。也就是说,单个用户会感觉到他们所有的应用程序都在同时运行(实际上每台计算机有多个 CPU)。这些有远见的人也看不到计算机会变得如此之小,以至于不再需要共享一台大计算机。世界各地的个人用户也不会相互连接,而不仅仅是计算机中心。但直到 1965 年,摩尔定律才出现。
Neither Licklider nor any other visionary could yet see that Moore’s Law would make it possible for all computers to time-share multiple apps run by single users. That is, single users would perceive that all their apps were running simultaneously (and with multiple CPUs per computer it would actually be so). Nor could these visionaries see that computers would become so small that sharing one big one would no longer be necessary. Nor that individual users all over the world would be interconnected, not just computer centers. But then Moore’s Law didn’t exist until 1965.
Doug Engelbart 发表了第三篇论文,与 Bush 的 memex 备忘录和 Licklider 的共生论文一起,构成了我们所讲述的相互交织的故事的知识支柱。增强人类智力:一个概念框架由斯坦福研究所于 1962 年出版。在摩尔定律和第二纪元之前,恩格尔巴特也试图掌握我们人类如何应对我们中间的新恐龙:
Doug Engelbart published the third paper that, with Bush’s memex memo and Licklider’s symbiosis paper, formed the intellectual backbone of the intertwined stories we’re telling. Augmenting Human Intellect: A Conceptual Framework was published by Stanford Research Institute in 1962. Engelbart too tried, before Moore’s Law and Epoch 2, to grasp how we humans might deal with the new dinosaurs among us:
这是一个项目的初步总结报告,该项目采用一种新的、系统的方法来提高个人的智力效率。一个详细的概念框架探索了由个人组成的系统的性质,以及将他的基本能力与他的问题相匹配的工具、概念和方法。显示的工具之一最大的直接希望是计算机,它可以用于直接在线帮助,并与新的概念和方法相结合。22
This is an initial summary report of a project taking a new and systematic approach to improving the intellectual effectiveness of the individual human being. A detailed conceptual framework explores the nature of the system composed of the individual and the tools, concepts, and methods that match his basic capabilities to his problems. One of the tools that shows the greatest immediate promise is the computer, when it can be harnessed for direct online assistance, integrated with new concepts and methods.22
恩格尔巴特相当迂腐地一步一步地探索人类与机器智能交互的方式。然而,比他的文字更重要的是他向我们展示的内容。1968 年,在 ARPA 的资助下,他在旧金山湾区的一次计算机会议上上演了著名的“所有演示之母”,在那里他使用新的指点设备通过图形用户界面与远处的计算机进行了实时交互他发明了——他称之为老鼠。这是我们今天所熟悉的个人计算机界面的开始,使用的是我们今天仍然用来控制它的设备原型,即鼠标。
Engelbart rather pedantically steps his way through what a human interacting intelligently with a machine might be like. More important than his text, however, was what he showed us. In 1968 and funded by ARPA, he staged the famous “mother of all demos” at a computer conference in the San Francisco Bay Area where he interacted in real time with a computer at a distant location via a graphical user interface using a new pointing device he had invented—which he called a mouse. This was the beginning of the personal computer interface familiar to us all today, using the prototype of the very device, the mouse, that we still use today to control it.
接下来我们回到起点,专注于这个环境中特别影响计算机图形的部分。
Next we step back to the beginning and concentrate on the parts of this milieu that particularly affected computer graphics.
数字光在 1945 年美国原子弹和 1949 年苏联氢弹之间——二战和冷战之间——出现了。回想一下“数码光的黎明”一章,在 1940 年代在少数珍贵的计算机上拍照被认为是轻浮的。他们“应该”计算原子弹或氢弹的统计数据。尽管如此,1947 年,第一张数码照片 First Light 出现在 Manchester's Baby。1951 年和 1952 年在曼彻斯特和剑桥大学创建了两个最早记录的交互式视频游戏。1951 年,由空军资助的第一个有记录的计算机动画出现在麻省理工学院的旋风上。在所有这些早期案例中,几何模型都作为散布像素渲染到显示屏上,其中一些可以交互地更改图片。
Digital Light dawned between the American A-bomb of 1945 and the Soviet H-bomb of 1949—between World War II and the Cold War. Recall from the Dawn of Digital Light chapter that making pictures on the few precious computers in the 1940s was considered frivolous. They “should” be computing A-bomb or H-bomb statistics. Nevertheless, the first digital picture, First Light, appeared in 1947 on Manchester’s Baby. Two of the first documented interactive videogames were created in 1951 and 1952 at Manchester and Cambridge Universities. And the first documented computer animations appeared on Whirlwind at MIT in 1951, funded by the Air Force. In all these early cases, geometric models were rendered to a display screen as spread pixels, and some of them could change pictures interactively. Whirlwind is at the top of this chapter’s flow chart because it connects that early history to this Soviet-fueled, defense-funded next stage—one nevertheless not devoid of occasional frivolous picture making.
冷战催生了 1950 年代最冷血的野兽,或者更确切地说,这些野兽肩负着最冷血的使命——防御核攻击。当时最大、最可怕的是 Sage 计算机,它是旋风的直接继任者。空军与麻省理工学院和 IBM 合作实施 Sage,该项目的规模和成本可与曼哈顿或阿波罗计划相媲美。从 1958 年开始,建造了 20 多个中心,每个中心都有四层楼高,没有窗户,并装有两台 Sage 计算机。每台计算机造价 2.38 亿美元(约合今天的 20 亿美元),占地半英亩占地面积,重达100多吨。每个都有一个通常是黄色的图形显示器,带有一个用于交互的“光枪”。
The Cold War spawned the most cold-blooded beasts of the 1950s, or rather beasts with the most cold-blooded mission—defense against nuclear attack. The biggest and scariest at the time was the Sage computer, the immediate successor to Whirlwind. The Air Force worked with MIT and IBM to implement Sage, a project comparable in size and cost to the Manhattan or Apollo Projects. Starting in 1958 more than 20 centers were built, each four stories tall, windowless, and housing two Sage computers. Each computer cost $238 million (about $2 billion in today’s dollars), occupied half an acre of floor space, and weighed over 100 tons. And each featured an often-yellow graphical display with a “light gun” for interaction.
图 6.14
Figure 6.14
今天,Sage 剩下的文物包括那些图形站。图 6.14(右)中的军事用户,凝视着野兽张开的大嘴,似乎准备射击它——或者无论如何都要焊接它。为了对这种努力有一个正确的认识,想象一下一个房间里挤满了数十名军人和他们的枪,在排列整齐的展示站。
Among the remaining artifacts of Sage today are those graphics stations. The military user in figure 6.14 (right), staring into the gaping maw of the beast, appears ready to shoot it—or solder it anyway. To get a proper sense of this effort, picture a room filled with dozens of servicemen and their guns at display stations arranged in rank and file.
Sage 的正常业务端(图 6.15)描绘了飞机和导弹在粗糙边界线上的位置。显示右侧的虚线——一个“不明飞行物”——接近美国。但《大西洋月刊》在一篇题为“世界上第一个计算机艺术(这是一个性感的贵妇人)的前所未闻的故事”的文章中讲述了另一个故事。有人,当然是匿名的,使用价值 2.38 亿美元的机器来展示“禁果”——来自Esquire的少女海报,男性杂志。这篇文章声称,她是 1950 年代后期的某个时候,第一次在电脑显示器上描绘了一个人。这甚至可能是真的,但请记住第 4 章提到的可能在 1950 年代初在 Edsac 上的高地舞者的轶事。无论如何,这些图形是已经灭绝的书法或矢量品种,是失败者从长远来看,像素的光栅显示,现代形式。尽管 Sage 恐龙的体型很大,但它的图形很简单——但它们是互动的。24
The normal business end of Sage (figure 6.15) depicts aircraft and missile locations against crude borderlines. A dotted line at display right—an “unidentified flying object”—approaches the United States. But the Atlantic Monthly told an alternative story in an article titled “The Never-Before-Told-Story of the World’s First Computer Art (It’s a Sexy Dame).” Someone, anonymous of course, used the $238 million machine to display “forbidden fruit”—a girlie pinup traced from Esquire, the men’s magazine. The article claims that she was the first depiction of a person on a computer display, sometime in the late 1950s. This might even be true, but remember that anecdote of a Highland dancer on Edsac, probably in the early 1950s, mentioned in chapter 4. In any case these graphics were the calligraphic, or vector, variety that have come and gone extinct, losers in the long run to raster displays of pixels, the modern form. Despite the size of the Sage dinosaur, its graphics were simple—but they were interactive.24
准备好与否,计算机正在走向人们。这是个好消息,也许是自迷幻药以来最好的消息。. . . 这种趋势的健康归功于一系列奇怪的影响:设计计算机科学的怪胎的年轻热情和坚定的反建制主义;一个惊人的来自国防部最高层的开明研究计划;. . . 以及一种无法抑制的午夜现象,称为太空战。
Ready or not, computers are coming to the people. That’s good news, maybe the best since psychedelics. . . . The trend owes its health to an odd array of influences: The youthful fervor and firm dis-Establishmentarianism of the freaks who design computer science; an astonishingly enlightened research program from the very top of the Defense Department; . . . and an irrepressible midnight phenomenon known as Spacewar.
图 6.15
Figure 6.15
1950 年代末和 1960 年代初出现了一种新的反主流文化猫,它是由计算机革命带来的,并且是独一无二的。他们称自己为黑客。在当时,这是一个非常尊重的词,在选举操纵、身份盗用和勒索软件的世界中,它现在所受到的谴责丝毫没有。麻省理工学院的黑客完全爱上了旋风的孙子 TX-0。他们称之为“Tixo”。如果他们愿意自己解决(他们是)并且愿意在一天中最晦涩的时间向它求爱(他们是),那么这就是他们第一台完全属于他们的计算机。Tixo 是一只填满房间的小恐龙,但他们可以与它嬉戏。它有一个图形显示器和一支光笔。26
A new breed of countercultural cat appeared in the late 1950s and early 1960s, brought on by, and unique to, the computer revolution. They called themselves hackers. It was a term of deep respect then, without a trace of the opprobrium it now has in a world of election manipulation, identity theft, and ransomware. The hackers of MIT fell totally in love with TX-0, grandson of Whirlwind. They called it “Tixo.” It was the first computer that was completely theirs if they were willing to figure it out themselves (they were) and if they were willing to court it at the most obscure times of day (they were). Tixo was a baby dinosaur that filled a room, but they could romp with it. And it had a graphics display and a light pen.26
那些原始的黑客现在是传奇。邪教迅速蔓延到西海岸。斯图尔特布兰德是第一个在地上庆祝他们的人。在 1960 年代后期,他是嬉皮一代的产品圣经《全球目录》的著名出版商。他的下一个噱头是 1972 年在滚石杂志上发表的一篇文章,该文章将公众的注意力放在了黑客身上,并在一个名为施乐帕洛阿尔托研究中心 (PARC) 的地方引起了一些关注。它的标题定下了基调:“太空战争:计算机流浪者中的狂热生活和象征性死亡”。27
Those original hackers are legendary now. The cult quickly spread to the West Coast. Stewart Brand was the first to celebrate them above ground. In the late 1960s he was the noted publisher of the Whole Earth Catalog, the hippie generation’s product bible. His next stunt was a 1972 article in Rolling Stone magazine that put the public spotlight on hackers and raised a few eyebrows at a place called Xerox Palo Alto Research Center (PARC). Its title set the tone: “Spacewar: Fanatic Life and Symbolic Death Among the Computer Bums.”27
那时,至少有一名 MIT 原始黑客已经搬到 PARC,靠近嬉皮士的首都旧金山。纽约州北部施乐公司的三件套纽扣西装高管对他们研究中心的摇滚报道感到尴尬。电脑坏了!那些看起来和行为都像这样的人——比如我,当时我在那里——不可能有严肃的商业想法。这种无法跨越的文化鸿沟可能是施乐未能利用个人电脑的原因。正如我们现在所知,它是在 1970 年代初在 PARC 发明的——鼠标、基于 Windows 的界面、激光打印机、网络等等。通过那些流浪汉。28
At least one original MIT hacker had moved to PARC by then, near San Francisco, the capital of hippiedom. The three-piece button-down suit executives of corporate Xerox in upstate New York were embarrassed by the rock’n’roll coverage of their research center. Computer bums yet! People who looked and acted like that—like me, as I was there then—couldn’t possibly have serious business ideas. This uncrossable cultural divide might have been why Xerox failed to capitalize on the personal computer. It had been invented at PARC in the early 1970s just as we now know it—mouse, windows-based interface, laser printer, network, and all. By those bums.28
1984 年,记者 Steven Levy 发表了《黑客》,巩固了他们的名声。他的书讲述了这帮才华横溢、有影响力的恶作剧制造者的完整而奇妙的故事。我在本书中提到它们是因为他们在 MIT 的另一个特遣队在 TX-0 的儿子 TX-2(没有 TX-1)上做了一些非凡的事情之前就在计算机上制作了照片。29
In 1984 journalist Steven Levy published Hackers, cementing their fame. His book told the full and marvelous story of this gang of talented and influential mischief makers. I mention them in this book because they made pictures on computers slightly before another contingent at MIT did something pictorially remarkable on TX-2, son of TX-0 (there was no TX-1).29
在“数字光的黎明”一章中,我们了解到数字音频专家 Tom Stockham 教犹他大学的一代计算机图形师如何对他们的采样图片进行抗锯齿——如何消除“锯齿”。斯托克汉姆在麻省理工学院担任教授时受到了他在 TX-0 上制作音乐的黑客的启发。30
In the Dawn of Digital Light chapter, we learned that Tom Stockham, a digital audio expert, taught a generation of computer graphicists at the University of Utah how to antialias their sampled pictures—how to take the “jaggies” out. Stockham had been inspired to his audio calling while a professor at MIT by the hackers there making music on TX-0.30
但最令人难忘的黑客成就是一款名为Spacewar的二维互动游戏。他们使用 Tixo 的 CRT 图形显示器在 Tixo 上创建了几个“图形黑客”。但是大楼里最新的计算机很快就成为了黑客的宠儿:PDP-1。他们于 1962 年在其上创建了Spacewar。图 6.16 显示了一个打开动作。PDP-1 是一台价值 120,000 美元的计算机(今天略低于 100 万美元),它由数字设备公司提供给麻省理工学院,以试图打破巨头 IBM 在市场上的锁定。它本质上是 Tixo 的儿子,并且在各方面都更好。31
But the most memorable hacker achievement was a two-dimensional interactive game called Spacewar. They had created several “graphics hacks” on Tixo, using its CRT graphics display. But the newest computer in the building soon became the hackers’ darling: the PDP-1. They created Spacewar on it in 1962. Figure 6.16 shows an opening maneuver. The PDP-1, a $120,000 computer (that’s just shy of $1 million today), had been given to MIT by the Digital Equipment Corporation in an attempt to break giant IBM’s lock on the marketplace. It was essentially a son of Tixo and was better in every way.31
为了我们的目的,我们只需要知道Spacewar是交互式计算机图形。用户通过操纵杆和按钮与游戏互动。它有一个缓慢旋转的星域、两艘从鼻锥发射鱼雷(点)的卡通火箭飞船和一颗中央恒星。有重力和跳到超空间按钮。太空战争是游戏历史和实时计算机图形学中的重要事件。但在本书中,我们关注的是不受时间限制的计算机图形的数字光部分。
For our purposes we only need to know that Spacewar was interactive computer graphics. Users interacted with the game via joysticks and buttons. It featured a slowly rotating star field, two cartoon rocket ships that shot torpedoes (dots) from their nosecones, and a central star. There was gravity and a jump-to-hyperspace button. Spacewar was an important event in the history of games, and in real-time computer graphics. But in this book, we focus on the part of Digital Light that is computer graphics with no time constraints.
“实时”一词有多种含义,都与人类对时间流逝的感知有关。一种流行的含义是实时计时,就像在电子游戏中一样。其他是实时按需的,就像在计算机模型的“交互式”设计中一样。这些方便的术语可以帮助我们细分数字光的广阔范围。
The term “real time” has several meanings, all related to the human perception of the passage of time. One popular meaning is clocked real time, as in videogames. Another is real time on demand, as in the “interactive” design of computer models. These are handy terms that help us subdivide the vastness of Digital Light.
图 6.16
Figure 6.16
在电子游戏中,一个假想的时钟滴答作响,并且必须渲染一张新图片并准备好在每次滴答时显示。视频的自然“时钟”是每秒 30 帧的帧速率,之所以选择这个速率,是因为它近似于人类对时间流逝的感觉,并且与现实世界中的时间同步。因此,在电子游戏中,每三十秒必须显示一张新图片。
In videogames, an imaginary clock ticks, and a new picture must be rendered and ready for display at each tick. The natural “clock” for video is the frame rate of 30 frames per second, a rate chosen because it approximates the human sense of time passing smoothly and at the same pace as time in the real world. In videogames, then, a new picture must be displayed every thirtieth of a second.
电子游戏是现代世界时钟品种实时图形的压倒性例子。但在早期,飞行模拟器——每台花费数百万美元——是主要表现形式。战斗机飞行员将在飞行模拟器上进行训练,而宇航员将在航天器模拟器上进行训练。他们今天仍然这样做。虚拟现实 (VR) 是时钟实时类的最新成员,可在特殊护目镜内渲染到双显示器,以获得立体或所谓的 3D 效果。
Videogames are the overwhelming example of real-time graphics of the clocked variety in the modern world. But in the early days, flight simulators—costing millions of dollars each—were the principal expression. Fighter pilots would train on flight simulators, and astronauts on spacecraft simulators. They still do today. Virtual reality (VR) is the newest member of the clocked real-time class, rendering to dual displays inside special goggles for a stereo, or so-called 3D, effect.
非时钟或按需实时图形的一个主要示例是内部计算机模型的交互式设计。这只是另一种说法,“图片变化得足够快,足以让用户相信它在与计算机交互时‘即时’发生。”
A principal example of unclocked, or on-demand, real-time graphics is interactive design of internal computer models. That’s just another way of saying “pictures that change fast enough to convince users that it’s happening ‘instantaneously’ while they interact with the computer.”
另一个例子是几乎每个应用程序的每个界面。我只是单击了 Word 中的保存图标。当我将鼠标光标悬停在它上面时,图标“立即”亮起,然后当我单击鼠标并保存文件时,“时间正在消逝”的旋转图标“立即”出现。
Another example is almost every interface to every app. I just clicked on the Save icon in Word. The icon “instantly” lit up as I hovered the mouse cursor over it, then a “time-is-elapsing” rotating icon appeared “instantly” as I clicked the mouse and saved the file.
在时钟或非时钟情况下,实时的权衡要么是低图像质量,要么是高产品价格。在时钟的情况下,电子游戏仍然(截至 2020 年)显示在保持低消费价格的同时,没有足够的时间来计算完全渲染的图片的视觉伪影。
In either the clocked or unclocked case, the trade-off for real time is either low image quality or high product price. In the clocked case, videogames still (as of 2020) show the visual artifacts of insufficient time to compute a fully rendered picture while maintaining a low consumer price.
在非时钟情况下,模型交互设计中使用的图片质量通常仍低于如此设计的对象或场景的最终渲染。设计师可能会观看他们正在创建的对象或角色的线描显示 - 例如茶壶的金属丝网视图,而不是完全着色、彩色和纹理的茶壶。
In the unclocked case, the picture quality used in interactive design of models is still typically lower than the final rendering of the objects or scenes so designed. Designers might watch a line-drawing display of an object or character that they are creating—say a wire mesh view of a teapot rather than a fully shaded, colored, and textured teapot.
计算机图形学是我的职业,但我对它的历史只有一个摇摇欲坠的把握。我收到的版本大致是这样的:Ivan Sutherland 于 1962 年在麻省理工学院编写了第一个交互式计算机图形程序 Sketchpad。然后他于 1968 年进入盐湖城的犹他大学,开创了计算机图形学的王朝先驱者。事实上,这个总结有很多道理。例如,Ed Catmull 是 Sutherland 的学生之一,多年来我们在纽约理工学院、卢卡斯影业和皮克斯的许多同事都在犹他州接受过教育。我们使用的早期图形硬件是由 Evans & Sutherland 制造的,这家公司也是 David Evans 和 Ivan Sutherland 于 1968 年在盐湖城共同创立的。
Computer graphics is my profession, but I only had a shaky hold on its history. The version I received was roughly this: Ivan Sutherland wrote Sketchpad, the first interactive computer graphics program, it was said, at MIT in 1962. Then he went to the University of Utah in Salt Lake City in 1968 and fathered a dynasty of computer graphics pioneers. In fact, there’s a lot of truth in that summary. For example, Ed Catmull was one of Sutherland’s students, and many of our colleagues over the years at the New York Institute of Technology, Lucasfilm, and Pixar were Utah educated. And the early graphics hardware we used was manufactured by Evans & Sutherland, a company David Evans and Ivan Sutherland cofounded in Salt Lake, also in 1968.
但萨瑟兰的叙述与我们在“数码光之黎明”一章中所发现的不符:第一张数码图片、互动游戏和动画是在 1940 年代末和 1950 年代初出现在最早的计算机上的。Whirlwind 有一个光枪,可以让你与它的显示器互动。正如我们在本章中看到的那样,在 1950 年代后期,正在射击或焊接 Sage 的人正在与它的图形进行交互。Spacewar在 Sketchpad 之前就在麻省理工学院进行了互动。显然,故事中存在差异需要解释。
But the Sutherland narrative doesn’t fit what we’ve discovered in the Dawn of Digital Light chapter: The first digital pictures, interactive games, and animations were on the earliest computers in the late 1940s and early 1950s. Whirlwind had a light gun that let you interact with its display. As we’ve seen in this chapter, the fellow who was shooting, or soldering, Sage is interacting with its graphics in the late 1950s. And Spacewar was interactive at MIT slightly before Sketchpad. Obviously, there’s a discrepancy in the story that needs explanation.
像许多技术史一样,收到的版本省略了很多内容,并且过分强调了一个人。它忽略了该领域的两位著名创始人史蒂文·库恩斯(Steven Coons)和皮埃尔·贝塞尔(Pierre Bézier),他们比萨瑟兰早了一代人。然而,该领域非常了解这些创始人。几十年来,计算机图形学的最高奖项一直是 Coons 奖。几十年来,流行的应用程序 Adobe Illustrator 和 Adobe Photoshop 也采用了贝塞尔曲线。但是历史网络并没有顺利编织在一起。
Like many histories of technology, the received version omits great swaths, and overly emphasizes a single person. And it leaves out two well-known founding fathers of the field, Steven Coons and Pierre Bézier, who predated Sutherland by a generation. The field is quite aware of these founders, however. For decades, the highest award in computer graphics has been the Coons Award. And Bézier curves have been featured in the popular apps Adobe Illustrator and Adobe Photoshop for decades as well. But there’s been no smooth weaving together of the historical web.
简单的叙述实际上也不符合我个人所知的历史。我遇到并与之共事的第一个计算机图形学先驱是赫伯特·弗里曼,他不是犹他州的学校。他出生于德国的赫伯特弗里德曼并设法逃脱在阿尔伯特爱因斯坦的帮助下,纳粹的祸害。当赫伯的父母试图获得进入美国的许可时,只有他一个人被拒绝,被指控患有肺结核。这不是真的,但是爱因斯坦本人花了数年时间和三封信才让孩子及时克服官僚障碍并于 1938 年安全进入美国。1949 年,赫伯与爱因斯坦会面,并亲自感谢了爱因斯坦的巨大恩惠。32
The easy narrative actually doesn’t match the history I personally know, either. The first computer graphics pioneer I met and worked with was Herbert Freeman, who was not of the Utah school. He was born Herbert Friedmann in Germany and managed to escape the Nazi scourge with the help of Albert Einstein. When Herb’s parents tried to obtain permits for the family to enter the United States, he alone was disallowed, accused of having tuberculosis. It wasn’t true, but it took years and three letters from Einstein himself to get the child over the bureaucratic hurdles and safely into America in 1938, just in time. In 1949 Herb met and thanked Einstein personally for this tremendous favor.32
在遇到这位伟大的科学家前大约一年,赫布从哥伦比亚大学获得了电气工程硕士学位。1952 年,在麻省理工学院的一个暑期班上,他遇到了旋风,并对数字计算机产生了兴趣——以至于到了第二年,他在斯佩里公司设计了自己的计算机,称为 Speedac。1958 年,哥伦比亚大学的博士学位导致在麻省理工学院的伺服机构实验室和次年的林肯实验室工作。1960年他加入纽约大学。他的专长是计算机图形学,1972 年,他与人共同创办了最早的 Digital Light 学术期刊之一,这反映在其标题:Computer Graphics and Image Processing中。制作和服用。几何和像素。33
About a year before he met the great scientist, Herb got a master’s degree in electrical engineering from Columbia. At a summer class at MIT in 1952 he met Whirlwind and became excited by digital computers—so much so that by the next year, he had designed his own computer, called Speedac, at the Sperry Corporation. A doctorate from Columbia led to jobs at MIT with the Servomechanism Lab in 1958 and Lincoln Lab the following year. In 1960 he joined New York University. His specialty was computer graphics, and in 1972 he cofounded one of the earliest scholarly journals of Digital Light, as reflected in its title: Computer Graphics and Image Processing. Making and taking. Geometry and pixels.33
Herb 于 1969 年直接从斯坦福研究生院聘请我进入他在纽约大学的系。在我与他相处的四年里,他向我介绍了来自加拿大的 Ron Baecker 和 Marceli Wein,两位最早的计算机动画师,以及来自英国的 Robin Forrest。
Herb hired me straight out of Stanford graduate school in 1969 into his department at NYU. During my four years with him, he introduced me to Ron Baecker and Marceli Wein from Canada, two of the earliest computer animators, and to Robin Forrest from England.
罗宾,我最喜欢的苏格兰人,在我研究和写这本书的时候,从诺里奇来到伦敦,引导我了解我所在领域的早期历史。当我们整天在布卢姆斯伯里酒店的茶室里欢笑和回忆时,他开始这样做。34
Robin, my favorite Scot, came up to London from Norwich, while I was researching and writing this book, to guide me through the early history of my own field. Which he proceeded to do as we laughed and reminisced all day in the tearoom of a Bloomsbury hotel.34
“我第一次见到你是在 1971 年 11 月,”我们握手时他开口道。
“I first met you in November 1971,” he opened as we shook hands.
“而你是在 1990 年代把我卷入那些专利案件的魔鬼,”我取笑道。
“And you’re the devil who roped me into those patent cases in the 1990s,” I teased.
“我确实是。”
“Indeed I was.”
(计算机图形学同事和我曾在英国法庭上尽最大努力从英国硬件公司手中拯救一家英国软件公司。我们未能提出诉讼,软件公司被迫停业。但随后同一家硬件公司尝试了在美国法院对一家美国公司采取同样的法律手段。这次我们成功地帮助保护了 Adobe 及其旗舰 Photoshop 产品免受高额版税的侵害。法院仁慈地裁定所有五项专利均无效,并消除了该领域的祸害。)
(Computer graphics colleagues and I had tried our best in British court to save a British software company from a British hardware company. We failed to make our case, and the software company was forced out of business. But then the same hardware company tried the same legal maneuver against an American company in an American court. This time we successfully helped protect Adobe, and its flagship Photoshop product, from a crippling royalty. The court mercifully found all five patents invalid and removed a scourge from the field.)
“而我,”罗宾补充道,“首先把你介绍给了杰克·布雷森汉姆。”
“And I,” Robin added, “first introduced you to Jack Bresenham.”
Jack Bresenham 是来自新墨西哥州克洛维斯的另一位计算机图形师。罗宾和我开始跑步。35
Jack Bresenham was the other computer graphicist from Clovis, New Mexico. Robin and I were off and running.35
对于早期的历史,我再也找不到比这更好的指南了——当然不是更机智的了。Robin 在东英吉利大学工作了 40 多年,现在是名誉教授。罗宾自己经历了大部分早期历史。他曾多次与 Coons、Bézier 和 Sutherland 合作,并曾在早期的 MIT、剑桥和犹他大学中心工作。但他也告诉我一些鲜为人知的地方,比如雪铁龙、雷诺和通用汽车。36
I couldn’t have asked for a better guide through the early history—certainly not a wittier one. Robin has been with the University of East Anglia for over 40 years, now professor emeritus. Robin experienced much of the early history himself. He worked at various times with Coons, Bézier, and Sutherland, and had been at the early MIT, Cambridge, and Utah university centers. But he also told me about lesser known places such as Citroën, Renault, and General Motors.36
罗宾的故事很快阐明了基本的历史和定义问题。计算机图形学是关于物体的内部模型和它们的图片。计算机图形学的历史是从物体模型还是从它们的图片开始的?根据重点不同,历史有不同的版本。计算机图形学和计算机辅助设计的历史通常并且可以理解地纠缠在一起。
Robin’s tales soon elucidated the fundamental historical and definitional problem. Computer graphics is about both internal models of objects and pictures of them. Does the history of computer graphics begin with models of objects or with pictures of them? There are different versions of the history depending on the emphasis. The histories of computer graphics and computer-aided design are typically, and understandably, tangled together.
将 Coons 和 Bézier 称为计算机图形学的奠基人的问题在于,他们都没有制作图片,至少一开始也没有。Coons 在旧的 Chance Vought 公司创建了他在飞机行业的基础工作。贝塞尔在法国汽车制造商雷诺完成了他的工作。他们都在计算机内部使用了三维表面的几何模型,但都没有显示设备来查看图片。Coons 创造了实际的机身表面和 Bézier 实际的汽车车身表面。
The problem with calling Coons and Bézier the founding fathers of computer graphics is that neither made pictures, not at first, anyway. Coons created his foundational work in the aircraft industry at the old Chance Vought company. Bézier did his at Renault, the French automobile manufacturer. They both used geometric models of three-dimensional surfaces inside a computer, but neither had a display device to see pictures. Coons created actual airframe surfaces, and Bézier actual auto body surfaces.
他们并不关心图片本身。他们关心由真实材料制成的真实 3D 空间中的真实物体——汽车和飞机机身,或它们的模型。这又是创意空间与展示空间的区别。Coons 和 Bézier 有创意空间,但没有展示空间。或者换句话说,他们的展示是物体本身,而不是它们的照片。他们拥有计算机控制的机器,可以从真实材料中雕刻或切割实际物体。换句话说,他们是针对对象进行计算机辅助设计,而不是针对图片进行计算机图形设计。我们将在本章后面花时间解开这些领域。但毫无疑问,Coons 和 Bézier 都是两者的主张。他们是一个很好的起点。
They didn’t care about pictures per se. They cared about actual objects in real three-dimensional space made of real materials—automobile and airplane bodies, or maquettes for them. It’s the Creative Space versus Display Space distinction again. Coons and Bézier had Creative Space but no Display Space. Or to put it another way, their displays were the objects themselves, not pictures of them. They had computer-controlled machines that carved or cut actual objects from real materials. In other words, they were doing computer-aided design aimed at objects, not computer graphics aimed at pictures. We’ll spend time later in this chapter disentangling these fields. But there’s no question that Coons and Bézier are claimed by both. They are a good place to start.
Coons 让我兴奋,他让 Ivan Sutherland 兴奋。. . 他当得起几个正教授。
Coons turned me on, he turned Ivan Sutherland on, . . . he was worth several full professors.
——Timothy Johnson,麻省理工学院 Sketchpad III 37的创造者
—Timothy Johnson, creator at MIT of Sketchpad III37
图 6.17
Figure 6.17
Steven Coons 的照片,由他的麻省理工学院学生 Abbott Weiss 拍摄,1964 年。
Photo of Steven Coons, by his MIT student, Abbott Weiss, 1964.
Steven Anson Coons(图 6.17)不仅是一位知识领袖。他是一位有趣的讲师——他的学生们都很喜欢他。他很有趣。38
Steven Anson Coons (figure 6.17) was not only an intellectual leader. He was an entertaining lecturer—and his students loved him. He was fun.38
故事是这样的,大约在 1936 年,当 Coons 在麻省理工学院学习数学时或之后,他在 Chance Vought Aircraft 找到了一份“推扫帚”的工作。当他扫地时,他碰巧注意到一位老板陷入了飞机表面表示的数学问题。所以他秘密地想出了一个解决方案,这个解决方案被称为Coons 补丁,这个名字一直流传至今。从作为一名直观的数学家将飞机设计形式化的卑微开始,他成为计算机辅助设计和计算机图形学之父。39
The story goes that around 1936, while or after Coons was a mathematics student at MIT, he took a job “pushing a broom” at Chance Vought Aircraft. While he was sweeping the floors, he happened to notice that a boss was bogged down in the mathematics of an aircraft surface representation. So he secretly worked out a solution, which famously became known as the Coons patch, a name that stuck. From that humble beginning as an intuitive mathematician formalizing aircraft design, he became a father of both computer-aided design and computer graphics.39
库恩斯的职业生涯有过坎坷。年轻时,他“在不利条件下”仅仅一年后就不得不离开麻省理工学院的数学学习,并且从未获得正式学位。不利的条件可能是简单的贫困。尽管如此,由于他在飞机工业方面的成就,他于 1948 年被麻省理工学院聘为助理教授。最终,他晋升为副教授。但令他的同事们困惑的是,尽管他对麻省理工学院的其他先驱产生了深远的影响——尤其是对伊万·萨瑟兰和蒂姆·约翰逊(见流程图)——但他却没有得到进一步的提升。也许他没有博士学位是原因。尽管如此,他随后在雪城大学、犹他大学、密歇根大学和科罗拉多大学任职。40
Coons’s career had bumps. As a young man, he had to leave his mathematical studies at MIT after only a year “under adverse conditions,” and never obtained a formal degree. The adverse condition was probably simple poverty. Nevertheless, because of his accomplishments in the aircraft industry, he was hired as an assistant professor at MIT in 1948. Eventually, he advanced to associate professor. But to the puzzlement of his colleagues and despite his profound influence on other pioneers at MIT—in particular, on Ivan Sutherland and Tim Johnson (see the flow chart)—he was passed over for further advancement. Perhaps his lack of a PhD was the reason. Nevertheless, he subsequently held positions at the universities of Syracuse, Utah, Michigan, and Colorado.40
Robin Forrest 的职业生涯跨越了计算机辅助设计和计算机图形学。那天在布卢姆斯伯里,他给我讲了一个计算机辅助设计的成功故事,那是在计算机出现之前的时代。它涉及著名的喷火战斗机,它在 1940 年英国与德国空军德国空军的关键战役中发挥了如此突出的作用。喷火战斗机的主要设计是将一组横截面刻在铝板上,并存放在英格兰汉普郡某处的大桌子上。尽管可以从主人那里复制图纸,但它肯定没有安全地保存在计算机内存中,因为当时还不存在。德国空军在汉普郡的一次空袭将摧毁这架重要战斗机的规格。41
Robin Forrest’s career has straddled both computer-aided design and computer graphics. That day in Bloomsbury he told me an establishing story of computer-aided design, from the era just before computers. It concerned the famous Spitfire fighter aircraft that featured so prominently in the crucial 1940 Battle of Britain against the German air force, the Luftwaffe. The Spitfire’s master design was a set of cross-sections scored into aluminum sheets and stored on large tables somewhere in Hampshire, England. Although drawings could be reproduced from the master, it certainly wasn’t secured safely inside a computer memory, because none existed yet. One Luftwaffe strike at that Hampshire location would have destroyed the specifications for this important fighter.41
但罗宾的问题是:这些横截面之间的喷火战斗机翼形状是什么?嗯,它没有被定义,这是一个问题。需要一个插入连续横截面的光滑表面,但它还不存在。
But Robin’s question was this: What was the Spitfire wing shape between those cross-sections? Well, it wasn’t defined, and that was a problem. A smooth surface that interpolated successive cross-sections was required, but it didn’t yet exist.
这些话让我们想起了 Ravi Shankar 故事中的样条曲线。飞机设计师需要将样条曲线推广到表面。他们需要一个在连续曲线之间插值的光滑表面——比如喷火式的横截面。该解决方案称为补丁,即在两条曲线(例如两条样条曲线)之间平滑通过的一块曲面。两条曲线形成一个面片的相对边缘,其间的曲面从一个边缘的曲线到另一边的曲线连续变化,甚至是优雅的变化。Spitfire 工程师需要在这些金属板上刻痕的横截面之间有一个明确的补丁,以完全定义飞机的机翼。但这个概念在 1940 年还不存在。
These words remind us of the spline in the Ravi Shankar story. Aircraft designers needed to generalize the spline to a surface. They needed a smooth surface that interpolated between successive curves—such as the Spitfire cross-sections. The solution is called a patch, a piece of surface that smoothly passes between two curves—two splines, say. The two curves form opposite edges of a patch, and the surface between varies continuously, even gracefully, from the curve at one edge to the curve at the opposite edge. The Spitfire engineers needed a well-defined patch between the cross-sections scored on those metal sheets to completely define the plane’s wing. But the concept didn’t exist yet in 1940.
将补丁引入飞机设计的人是史蒂文·库恩斯。补丁是他的话。他没有在喷火战斗机上工作,但他确实在航空业工作,并试图解决这个迫在眉睫的问题。他定义的 Coons 补丁是上面描述的补丁,但有两对对边。所示的 Coons 补丁示例在图 6.18 中,它类似于一张皱巴巴但没有褶皱的薄纸。每条边沿两个不同的方向平滑弯曲。平滑起伏的曲面在两个方向上连接或插入相反的边缘曲线。
The man who introduced patches to aircraft design was Steven Coons. Patch was his word. He didn’t work on the Spitfire, but he did work in the aviation industry and sought to solve this looming problem. The Coons patch he defined is the patch described above but with two pairs of opposite edges. The Coons patch example shown in figure 6.18 resembles a rumpled, but not creased, piece of tissue paper. Each edge bends smoothly in two different directions. And a smoothly undulating surface joins, or interpolates, opposite edge curves in both directions.
图 6.18
Figure 6.18
在 Coons 的定义中,补丁可以有任何形状的边缘,而不仅仅是图中所示的简单曲线。例如,一条边上的曲线可能是您手写的名字,而另一边可能是您的姓氏。只要您提供一种将一个名称混合到其相反名称的方法,它仍然是一个 Coons 补丁。但这种混合功能可能是一件棘手的事情。42
In the generality of Coons’s definition, a patch could have edges of any shape, not just simple curves as shown in the figure. For example, the curve on one edge might be your first name in handwriting, and the opposite edge your surname. So long as you provide a method for blending one name into its opposite, it’s still a Coons patch. But that blending function can be tricky business.42
为了在计算机图形中制作复杂的表面,例如茶壶、角色或飞机,我们设计了一组贴片,这些贴片沿着边缘平滑地相互连接,并覆盖所需的表面——比如被子——包括它的角落和缝隙。然后我们通过沿每条边递增的方式将每个补丁细分为四边的“补丁小”,如上图所示。像这样进行细分,直到小片变得足够小,可以被视为平面多边形。就我们的目的而言,这些扁平小片中的每一个都像以前一样被分成两个带有对角线的三角形。所以,我们又回到了只需要理解一个三角形的问题上。
To make a complex surface in computer graphics, like a teapot, a character, or an airplane, we design a set of patches that join one another smoothly along their edges and cover the desired surface—like a quilt—including its nooks and crannies. Then we subdivide each patch into four-sided “patchlets” by stepping along each edge in increments, as shown in the preceding figure. Subdivision proceeds like this until the patchlets become small enough to be considered flat polygons. For our purpose each of these flat patchlets is then divided into two triangles with a diagonal, as before. So, we’re back to having to understand only one triangle again.
显示三角形很容易,使用 Amplification 显示由数千个三角形组成的模型也很容易。但是没有办法将建造的难度降到最低首先是一个模型。建模是雕刻的一种形式,没有简单的方法来教授雕刻。这是专业建模师的任务。
Displaying a triangle is easy, and so is displaying a model made of thousands of them using Amplification. But there’s no way to minimize the difficulty of building a model in the first place. Modeling is a form of sculpting, and there’s no easy way to teach sculpting. That’s the task of professional modelers.
计算机图形学中最负盛名的奖项旨在表彰 Coons 补丁的发明者。Steven Anson Coons 奖由最大和最重要的年度计算机图形会议 Siggraph 颁发。它的名字是计算机图形和交互技术特别兴趣组的缩写,它是大型专业计算机科学组织的一部分,古朴地称为计算机协会 (ACM)。几十年来,Siggraph 每年都是成千上万的爱好者不容错过的会议。
The most prestigious award in computer graphics honors the inventor of the Coons patch. The Steven Anson Coons Award is presented by Siggraph, the largest and most important annual computer graphics conference. Its name is short for the Special Interest Group on Computer Graphics and Interactive Techniques, a part of the large professional computer science organization quaintly called The Association for Computing Machinery (ACM). Siggraph is the not-to-miss conference for tens of thousands of enthusiasts every year, as it has been for decades.
我们将这个奖项和这次会议都归功于另一位从纳粹手中拯救出来的早期计算机图形先驱 Bertram Herzog (1929-2008)。赫尔佐格被犹太儿童的 Kindertransport 计划救出。它把他安全地送到了英格兰的寄养家庭。1946 年,他从那里移居美国,并于 1961 年在密歇根大学获得博士学位。几年后,他遇到了库恩斯,库恩斯成为了他的朋友,并将他转化为计算机图形学。Bert 在 1969 年创立 Siggraph 方面发挥了重要作用。他帮助他的朋友将 Siggraph 的最高奖项命名为 Coons 奖。43
We owe both the award and the conference, in part, to another early computer graphics pioneer who was saved from the Nazis, Bertram Herzog (1929–2008). Herzog was rescued by the Kindertransport program for Jewish children. It got him safely to a foster home in England. From there he emigrated to the United States in 1946 and earned his PhD in 1961 at the University of Michigan. A couple of years later he met Coons, who befriended him and converted him to computer graphics. Bert was instrumental in founding Siggraph in 1969. And he helped name Siggraph’s highest prize the Coons Award for his friend.43
他被描述为具有放荡精神的快活,一个理性的不墨守成规者。在他的环境中,他简直就是“天才”。
He’s described as jovial with a libertine’s spirit, a reasoned nonconformist. In his milieu he’s simply “a genius.”
——关于皮埃尔·贝塞尔
—about Pierre Bézier
从那以后,我不可避免地被视为一个危险的疯子,被允许逍遥法外太久。
Since then I was inevitably seen as a dangerous lunatic who had been allowed to go free for too long.
——皮埃尔·贝塞尔,关于他自己44
—Pierre Bézier, about himself44
皮埃尔·艾蒂安·贝塞尔(Pierre Étienne Bézier),据说是一个非常机智的人,是弗兰克人的图形计算机图形学和计算机辅助设计之父,但只有一半的 CAD 实践者。像 Coons 一样,Bézier 在有图片之前就已经对表面进行了数学计算。他为汽车车身设计提出了类似的补丁创意。图 6.19 中的他的肖像是用贝塞尔曲线绘制的,以他的名字命名。45
Pierre Étienne Bézier, by all accounts a wickedly witty man, was a Franks father of picture-oriented computer graphics and computer-aided design, but a practitioner of the CAD half only. Like Coons, Bézier worked out a mathematics of surfaces before there were pictures of them. He came up with a similar patch idea for auto body design. The portrait of him in figure 6.19 is made with Bézier curves, named for him.45
贝塞尔是一个彻头彻尾的汽车人。作为一名工程师,他在 23 岁时进入雷诺并在那里度过了他的整个职业生涯。和 Coons 一样,他从 1933 年开始做工具设置员,然后在 1934 年晋升为工具设计师。这导致了他于 1945 年成为工具设计办公室的负责人。到 1948 年,他担任生产工程部主任,然后于 1957 年担任机床部主任。
Bézier was a car man, through and through. Educated as an engineer, he entered Renault at age 23 and spent his entire career there. Like Coons, he started small, as a tool setter in 1933. Then he worked his way up to a tool designer in 1934. This led to his becoming Head of the Tool Design Office in 1945. By 1948 he was Director of Production Engineering and then Director of the Machine Tool Division in 1957.
图 6.19
Figure 6.19
贝塞尔与贝塞尔。© 安东尼·黑尔,2010。
Bézier with Béziers. © Antony Hare, 2010.
这一切听起来像是一个顺利展开的职业生涯,但我遇到了一个令人费解的空白。雷诺在线历史记录称,“雷诺工程师皮埃尔·贝塞尔在德国战俘期间改进了通用汽车在战前引入的自动机器原理。” 直到这本书的截止日期前不久,我才知道更多关于这个神秘时期的信息。在法国 Facebook 页面的最后一分钟发帖后,一位联系人解开了这个谜团:Bézier 被囚禁在德国 Offiziersläger(军官战俘营),可能是 Osterode am Harz 的 Oflag XI-A,大约一年从 1940 年开始。46
This all sounds like a smoothly unwinding career, but I encountered a puzzling lacuna. An online Renault history states, “Pierre Bézier, a Renault engineer who, while a prisoner of war in Germany, improved upon the automatic machine principle introduced before the war by GM.” I’d been unable to learn anything more about this mysterious period until shortly before this book’s deadline. A last-minute posting to a French Facebook page resulted in a contact who resolved the mystery: Bézier was held prisoner in a German Offiziersläger (prisoner of war camp for officers), probably Oflag XI-A at Osterode am Harz, for about a year starting in 1940.46
Bézier 负责为著名的 4CV 汽车生产大部分机械零件,这是第一辆销量超过 100 万辆的欧洲汽车(图 6.20,左)。但这发生在计算机辅助设计出现之前。1960年开始从事CAD研究,主要研究方向为交互式曲线曲面设计、粘土模型和大师的三维铣削。到 1968 年,他完善了名为 Unisurf 的系统,并在雷诺投入生产。中间照片中的雷诺 10 可能使用了这个 CAD 系统。他确实有绘图机,但他的明确目标是制造汽车。它们是他的终极展示。雷诺“大师”最右边的照片就是一个例子。47
Bézier was responsible for producing most of the mechanical parts for the famous 4CV automobile, the first European car to sell over a million units (figure 6.20, left). But that happened before there was computer-aided design. He started his research in CAD in 1960, focusing on interactive curve and surface design, and three-dimensional milling of clay models and masters. By 1968 he had perfected his system, called Unisurf, and launched it into production at Renault. The Renault 10 in the center photo probably used this CAD system. He did have drawing machines for pictures, but his clear goal was the manufacture of automobiles. They were his ultimate displays. The rightmost picture of a Renault “master” is an example.47
图 6.20
Figure 6.20
1969 年,Robin Forrest 拜访了 Bézier。“他有一个可以切割全尺寸汽车面板的系统,我们对此印象非常深刻。” Forrest 讲述了 Bézier 如何让他的工程师接受计算机辅助设计:
Robin Forrest visited Bézier in 1969. “He had a system that could cut full-size car panels, and we were very impressed by that.” Forrest tells how Bézier got his engineers to embrace computer-aided design:
贝塞尔是雷诺生产工程副总裁,可以对他的员工说:“你可以停止使用粘土模型,现在你将使用我的方法。” 但他告诉我们他没有这样做。. . . 贝塞尔制造了这台机器,你可以用它来制造汽车面板,但他只是离开了它。他有一两个明星设计师感兴趣,但想知道这是什么东西。他告诉他们如何使用它。他们中的一些人被说服并玩弄它。他说:“有一天早上,我进来了,这个美丽的木雕就在我的门外[cf. 图 6.21],那是当我意识到我已经赢得了战斗。因为这可以做艺术。” 这就是引入这些技术的方式。你不强迫它。你让人们自己找到它并做出令人惊奇的事情,然后他们做事,你会想,“他们到底是怎么用我的系统做到这一点的?我不知道!” 这就是这种工作的好处。48
Bézier was vice-president of production engineering at Renault, and was in a position to say to his staff: “You can stop using clay models and now you will use my method.” But he told us he didn’t do this. . . . Bézier built this machine with which you could build car panels, but he just left it. He got one or two star designers who were interested but wondered what the thing was. He told them how to use it. Some of them were convinced and played around with it. He said “one morning I came in, and this beautiful wooden sculpture was outside my door [cf. figure 6.21], and that’s when I realized I had won the battle. Because this can do art.” And this is the way to introduce these technologies. You don’t force it. You let people find it for themselves and do amazing things, and then they do things and you are left thinking, “how the heck did they do that with my system? I don’t know!” That’s the nice thing about this kind of work.48
贝塞尔在晚年变得严肃学术。1975 年退休几年后,他在巴黎大学获得了数学博士学位。他于 1999 年去世,刚刚错过了新千年,比 Coons 活了 20 年。
Bézier became seriously academic late in life. A couple of years after he retired in 1975, he got his doctorate in mathematics at the University of Paris. He died in 1999, just missing the new millennium, and outliving Coons by 20 years.
Siggraph——一年一度的计算机图形学会议——在 1985 年授予他第二个 Coons 奖,第一个奖是在 1983 年授予 Coons 的一位直接知识继承人 Ivan Sutherland。面向图片的计算机图形学没有贝塞尔奖,但有一个计算机辅助设计贝塞尔奖(由实体建模协会授予)。
Siggraph—the annual computer graphics conference—awarded him the second ever Coons Award in 1985, the first having gone to one of Coons’s direct intellectual heirs, Ivan Sutherland, in 1983. There’s no Bézier prize in picture-oriented computer graphics, but there’s a Bézier Award in computer-aided design (awarded by the Solid Modeling Association).
图 6.21
Figure 6.21
蒂娜·梅兰登摄。
Photo by Tina Merandon.
因此,我的脑海中开始萌生想用数学方法研究车身形状的想法。. . 这要么是绝对的轻率,以免称其为疯狂,要么是一种惊人的把戏。. . . 法语单词carrosserie中有rosserie,代表车体(rosserie意为nastiness),真是太真实了!
Therefore the idea began to stir in my mind to go through the car body forms mathematically . . . It was either absolute thoughtlessness, in order not to call it madness, or else a phenomenal trick. . . . It is only too true that there is rosserie in the French word carrosserie, standing for car body (rosserie meaning nastiness)!
——Paul de Casteljau,关于他自己49
—Paul de Casteljau, about himself49
Paul de Faget de Casteljau 是该领域的另一位法兰克人之父(图 6.22)。和贝塞尔一样,他也从事汽车行业,也有一种自嘲的幽默感。1958 年,他在 Citroën 开发了用于汽车设计的数学系统。类似于贝塞尔稍后在雷诺的工作。与贝塞尔不同,他经常被忽视,尽管贝塞尔本人优先考虑他。不幸的是,对于 de Casteljau,Citroën 直到 1974 年才允许他公开他的发现。到那时,两人都起源的曲线被称为贝塞尔曲线,因此它们仍然存在——斯蒂格勒定律再次发挥作用。具有讽刺意味的是,de Casteljau 是 2012 年计算机辅助设计领域的贝塞尔奖得主。50
Paul de Faget de Casteljau was another Franks father of the field (figure 6.22). Like Bézier he was also in the auto industry and also had a self-deprecating sense of humor. He developed mathematical systems for car design at Citroën in 1958 that were quite similar to Bézier’s slightly later work at Renault. Unlike Bézier, he is often overlooked, although Bézier himself gave him priority. Unfortunately for de Casteljau, Citroën wouldn’t allow him to publicize his findings until 1974. By then the curves that both men had originated were called Bézier curves, and so they’ve remained—Stigler’s Law in action once more. Ironically, de Casteljau was the 2012 Bézier Award winner in the computer-aided design field.50
图 6.22
Figure 6.22
Bézier 和 de Casteljau 都将计算机视为提高汽车制造效率的一种方式。他们似乎独立地开发了另一种表示表面的数学方法,即贝塞尔补丁。这些不是 Coons 贴片,但与它们相似,因为它们也可以平滑地连接在边缘——可以说是绗缝——形成复杂的表面。Bézier 补丁是另一种建模表面的方法,然后可以将其细分为多边形和三角形,以便随后渲染到显示器。
Both Bézier and de Casteljau saw the computer as a way to increase the efficiency of automobile manufacture. They developed, independently it seems, the mathematics of another way to represent surfaces, the Bézier patch. These were not Coons patches but similar to them in the sense that they also could be attached smoothly at the edges—quilted, so to speak—to form complex surfaces. Bézier patches are another way to model surfaces that can then be subdivided into polygons and triangles for subsequent rendering to a display.
图 6.23
Figure 6.23
Bézier(或 de Casteljau)的数学在这里并不重要,但对它的直觉很重要。回想一下 Ravi Shankar 的演示,以及平板点的水平和垂直坐标是如何使用具有两个负“叶”的扩展器展开的,以便通过平板点获得样条曲线。它被称为 Catmull-Rom 吊具(图 6.7,底部)。如果我们使用图 6.23 中的扩展器,没有负波瓣,那么我们会得到一个稍微平滑的样条曲线。计算机图形学家将其称为B 样条曲线(对于如此漂亮的曲线而言相当笨拙),其中 B 代表“基础”,但在其他方面没有任何信息。图 6.23 是 B 样条扩展器。
Bézier’s (or de Casteljau’s) mathematics isn’t important here, but an intuition about it is. Recall the Ravi Shankar demonstration, and how the horizontal and vertical coordinates of the tablet points were spread with a spreader that has two negative “lobes” to get a spline through the tablet points. It was called a Catmull-Rom spreader (figure 6.7, bottom). If we use the spreader in figure 6.23 instead, with no negative lobes, then we get a slightly smoother spline. Computer graphicists call it—rather clunkily for such a pretty curve—a B-spline, where the B stands for “basis” but is otherwise uninformative. Figure 6.23 is the B-spline spreader.
两条样条曲线在图 6.24 中并排显示。两者都源自完全相同的点,即来自 Ravi Shankar 演示中的平板电脑的点。尽管您可能需要费力才能看到它,但新曲线(右侧)比旧曲线更优美。它通过仅在数位板点附近而不是通过它们来实现这一点。因此,它是近似样条,而不是插值样条。
The two splines are shown side by side in figure 6.24. Both are derived from exactly the same points, the ones from the tablet in the Ravi Shankar demo. Although you probably have to strain to see it, the new curve (on the right) is more graceful than the older one. It accomplishes this by passing only near the tablet points, not through them. It’s therefore an approximating spline, not an interpolating one.
Bézier(或 de Casteljau)给了我们一条两者兼而有之的曲线,尽管他(他们)不这么认为。下一张图片(图 6.25)显示了两条贝塞尔曲线——一条连接最左边的点和中间的一条,另一条连接中间的点和最右边的一条。Adobe Illustrator 和 Photoshop 有一个特殊的工具(钢笔工具),用于从像这样的贝塞尔线段创建平滑曲线。设计师从最左边的点开始画一条线,这里用虚线表示,在该点给出所需曲线的倾斜度。我们称之为切线。设计师通过旋转(虚线)切线来控制倾斜的角度,使用给定的点作为枢轴。它们通过延长或缩短切线来控制曲线的松紧度——通过将曲线外点移入或移出。
Bézier (or de Casteljau) gave us a curve that’s a little bit of both, although he (they) didn’t think of it that way. The next picture (figure 6.25) shows two Bézier curves—one that connects the leftmost point to the middle one, and another that connects the middle point to the rightmost one. Adobe Illustrator and Photoshop have a special tool (the pen tool) for creating smooth curves from Bézier segments like these. A designer begins at say the leftmost point and draws out a line, shown dashed here, that gives the desired curve’s slant at that point. We call it a tangent line. Designers control the slant’s angle by rotating the (dashed) tangent line, using the given point as a pivot. They control the curve’s tightness by lengthening or shortening the tangent line—by moving the off-curve point in or out.
图 6.25 中的左侧曲线是通过旋转和缩放两条切线的长度创建的,一条用于最左边的点,一条用于中间点。右侧曲线同样是通过旋转和缩放显示的另外两条切线创建的。
The left curve in figure 6.25 was created by pivoting and scaling the lengths of two tangent lines, one for the leftmost point and one for the middle point. The right curve was similarly created by pivoting and scaling the two other tangent lines shown.
在所有情况下,虚切线的斜度都与曲线通过给定点时的斜度相匹配。贝塞尔曲线通常按如下方式连接在一起以获得完全优雅:第二条曲线的第一个点的切线只是一个第一条曲线的最后一点的切线的延伸。它的长度完全相同,并以相同的角度倾斜,但方向相反。
In all cases, the slant of a dashed tangent line matches the slant of the curve as it passes through a given point. Bézier curves are typically joined together as follows for full gracefulness: the tangent line for the first point of the second curve is just an extension of the tangent line for the last point of the first curve. It’s exactly the same length and slanted at the same angle, but in the opposite direction.
图 6.24
Figure 6.24
图 6.25
Figure 6.25
图 6.26
Figure 6.26
通过戴夫科尔曼。
By Dave Coleman.
Bézier 会将此过程描述为使用四条切线进行控制,对最左边、中间和最右边的点进行插值。但在数学上这相当于指定图中的七个点。四个偏离曲线点定义了四个切线的长度和角度。平滑连接两条贝塞尔曲线形成的曲线通常只描述为一系列贝塞尔曲线。但它可以被称为贝塞尔样条,我建议它应该是。然后我们可以说,图中的贝塞尔样条曲线插入了七个点中的三个,并逼近了另外四个——两者都有一点。
Bézier would have described this process as interpolating the leftmost, middle, and rightmost points, using the four tangent lines for control. But mathematically this is equivalent to specifying the seven points in the figure. The four off-curve points define the length and angle of the four tangent lines. The curve that’s formed by smoothly joining two Bézier curves is usually just described as a sequence of Bézier curves. But it could be called a Bézier spline, and I suggest that it should be. Then we could say that the Bézier spline in the figure interpolates three of the seven points and approximates the other four—a little of both.
您现在正在阅读的文字字母很有可能是用贝塞尔曲线设计的。图 6.26 显示了曲线的一个有趣使用,“贝塞尔曲线”是用贝塞尔曲线设计的。短直线显示曲线连接处的倾斜(所有水平或垂直,顺便说一下)。
Chances are good that the text letters you are reading now were designed with Bézier curves. And figure 6.26 shows an amusing use of the curves, “Beziers” designed with Bézier curves. Short straight lines show the slants where the curves join (all horizontal or vertical, incidentally).
贝塞尔面片是一个面片,其每条边由贝塞尔曲线(或德卡斯泰尔约)定义。它是另一个用于复杂曲面建模的工具。在图 6.27 中,Martin Newell 的茶杯和茶托——不像他的茶壶那么有名——是用 26 个 Bézier 补丁建模的。从左到右,补丁被细分为越来越小的“补丁”,以显示在计算机图形学中如何处理曲率的外观。不在茶杯或碟子表面上的点网是近似的点通过补丁。与内插的 Coons 补丁不同,Bézier 补丁(部分)近似。
A Bézier patch is a patch with each edge defined by a Bézier (or de Casteljau) curve. It’s yet another tool for modeling complex surfaces. In figure 6.27 Martin Newell’s teacup and saucer—not so famous as his teapot—are modeled with 26 Bézier patches. From left to right, the patches are subdivided into smaller and smaller “patchlets” to show how the appearance of curvature is approached in computer graphics. The web of dots that are not located on the teacup or saucer surfaces are the points approximated by the patches. Unlike Coons patches, which interpolate, Bézier patches (partially) approximate.
图 6.27
Figure 6.27
通过米歇尔·博西。
By Michele Bosi.
罗宾·福雷斯特翻译了贝塞尔的一本书,并从他那里收到了一份法文版,题为:“对于罗宾·福雷斯特,我欠他的可能比他想象的要多。” 罗宾说:“我还没有解开这个谜团。” 这可能与罗宾向贝塞尔和世界展示了贝塞尔最初使用的数学实际上与谢尔盖·纳塔诺维奇·伯恩斯坦(Sergei Natanovich Bernstein)引入的复杂数学有关——另一位伟大的俄罗斯人。伯恩斯坦是多个领域的专家,但这里相关的是近似理论。他之于近似理论就像埃德蒙·惠特克爵士之于插值理论一样。51
Robin Forrest translated one of Bézier’s books and received from him a copy of the French version dedicated: “For Robin Forrest to whom I owe more than he perhaps thinks.” Robin says, “I’ve not unraveled that enigma.” It pertains perhaps to Robin’s having showed Bézier and the world that the mathematics originally used by Bézier was actually related to the sophisticated mathematics introduced by Sergei Natanovich Bernstein—yet another great Russian. Bernstein was an expert in several fields, but the pertinent one here is approximation theory. He was to approximation theory what Sir Edmund Whittaker was to interpolation theory.51
黎明一章的一个教训是,数码光始于 1947 年,并在 1950 年代初期蓬勃发展——包括计算机图形学,数码光的一个分支,它将内部几何模型渲染成可见的图片。计算机图形学的早期十年,就像 Coons 和 Bézier 早期的 CAD 工作一样,几乎从未被提及。相反,该领域的通常历史始于 Sketchpad。我们的部分工作是阐明是什么让 Sketchpad 如此重要。
A lesson from the Dawn chapter is that Digital Light began in 1947 and flourished in the early 1950s—including computer graphics, the branch of the Digital Light that renders internal geometric models into visible pictures. That early decade of computer graphics, like the earlier CAD work of Coons and Bézier, is hardly ever mentioned. The usual history of the field starts, instead, with Sketchpad. Part of our job is to articulate what made Sketchpad so important.
Ivan Edward Sutherland 于 1962 年在麻省理工学院展示了著名的 Sketchpad,并完成了它并于 1963 年 1 月作为他的博士论文发表。这是一个以用户交互为特色的二维几何设计程序。它当时受到高度吹捧,现在仍然是——而且应该是。但计算机图形学的荣耀是在二维透视图中查看三维场景和物体。52
Ivan Edward Sutherland famously demonstrated Sketchpad in 1962 at MIT and completed it and published it in January 1963 as his PhD thesis. It was a two-dimensional geometrical design program that featured user interaction. It was highly touted then and still is—and should be. But the glory of computer graphics is three-dimensional scenes and objects, viewed in two-dimensional perspective.52
是 Sutherland 的研究生 Timothy Edward “Tim” Johnson 将 Sketchpad 放入了三个维度和透视图。他将他的程序命名为 Sketchpad III,并于 1963 年 5 月发表了他的硕士论文。“III”是三个尺寸,而不是第三版。(没有 Sketchpad II。)为什么 Sketchpad III 没有以同等的力量被记住?可以说,从二维转换为三维并没有那么大的变化,实际上是一个相当明显的变化。但观点是巨大的、不平凡的、不明显的。Sketchpad III 采用了 Johnson 从另一位研究生 Lawrence Gilman “Larry” Roberts 那里学到的透视解决方案。罗伯茨于 1963 年 6 月完成了他的博士论文。因此,1963 年是计算机图形学三巨头的一年,所有这些都在麻省理工学院的林肯实验室:伊万·萨瑟兰、蒂姆·约翰逊和拉里·罗伯茨。两个,萨瑟兰和约翰逊,是史蒂文库恩斯的学生。
It was Sutherland’s fellow graduate student Timothy Edward “Tim” Johnson who put Sketchpad into three dimensions and perspective. He called his program Sketchpad III and published his master’s thesis on it in May 1963. The “III” was for three dimensions, not third version. (There was no Sketchpad II.) Why isn’t Sketchpad III remembered with equal force? One can argue that converting from two dimensions to three wasn’t that big a change, indeed a rather obvious one. But perspective was huge, nontrivial, and nonobvious. Sketchpad III incorporated the solution for perspective that Johnson learned from yet another fellow graduate student, Lawrence Gilman “Larry” Roberts. Roberts completed his PhD thesis in June 1963. So 1963 was the year of the Triumvirate of computer graphics, all at MIT’s Lincoln Lab: Ivan Sutherland, Tim Johnson, and Larry Roberts. And two, Sutherland and Johnson, were students of Steven Coons.
图 6.28 显示了代表三个各自成就的图标,Sutherland 画板的正方形,Johnson 画板 III 的立方体,以及 Roberts 对 Sketchpad III 贡献的透视立方体。
Figure 6.28 shows icons representing the three respective achievements, the square for Sutherland’s Sketchpad, the cube for Johnson’s Sketchpad III, and the cube in perspective for Roberts’s contribution to Sketchpad III.
图 6.29 以相同的顺序显示了 MIT 同学三巨头的照片:萨瑟兰、约翰逊、罗伯茨。53
And figure 6.29 displays photos of the Triumvirate of MIT classmates in the same order: Sutherland, Johnson, Roberts.53
图 6.28
Figure 6.28
图 6.29
Figure 6.29
Triumvirate 在 TX-2 上完成了他们的工作,Tixo 的儿子和旋风的曾孙。1940 年代末和 1950 年代早期的计算机大多采用光栅显示器。然后书法显示器开始使用了几十年,并分散了计算机图形师的注意力——我在第 4 章中提到的书法绕道。千禧年的大数字融合重新引入了光栅显示,它现在已成为世界标准。
The Triumvirate did their work on TX-2, son of Tixo and great-grandson of Whirlwind. The early computers of the late 1940s and 1950s had mostly raster displays. Then calligraphic displays came into use for several decades and distracted computer graphicists—the calligraphic detour that I mentioned in chapter 4. The millennium’s Great Digital Convergence reintroduced the raster display, which is now the world standard.
TX-2 显示器是一种跨界显示器。它是书法的,但只能以固定的阵列显示点。Ivan Sutherland 1963 年的 Sketchpad 论文将其描述为 1024 x 1024 的点阵列,这暗示了光栅显示。但是这些点可以按随机顺序打开,而不是逐行顺序。如果不刷新,这些点就会关闭,这只是由于阴极射线管屏幕上荧光粉的自然衰减。
The TX-2 display was a crossover kind of display. It was calligraphic but could only display dots in a fixed array. Ivan Sutherland’s Sketchpad thesis of 1963 describes it as a 1024 by 1024 array of dots, which suggests a raster display. But the dots could be turned on in random order, not row-by-row order. The dots would turn off if they weren’t refreshed, simply by the natural decay of the phosphors on the cathode-ray-tube screen.
在数码光的黎明章节中,有两种书法展示的图片。最明显的“书法”,如手写,是在运动方向上画出光线的笔迹。另一种类型是沿着这样的路径放置点,而不是连续的笔画。图 6.30(左,从黎明章节重复)是书法的。它是点状的,但这些点并不限于确切的网格位置。
In the Dawn of Digital Light chapter are pictures of two types of calligraphic display. The most obviously “calligraphic,” as in handwriting, is the one that draws strokes of light in the direction of motion. The other type lays down spots, not continuous strokes, along such a path. Figure 6.30 (left, repeated from the Dawn chapter) is calligraphic. It’s dotted, but the spots aren’t restricted to exact grid locations.
图 6.30
Figure 6.30
图 6.30(右)看起来像一个光栅显示——但有一个很大的不同:这些点是以书法顺序显示的,而不是光栅顺序。所以这个显示不同于前面的任何一个。它的斑点不是散布像素。它们是书法笔画的固定网格上的近似值。TX-2 显示器就是这种书法风格。以下是 TX-2 中实际发生的情况:按顺序绘制了一系列线段。每一个都通过类似 Bresenham 的渲染算法转换为光点位置,并且这些位置的光点由显示电路顺序打开。
Figure 6.30 (right) looks like a raster display—but with a big difference: the spots are displayed in calligraphic order instead of raster order. So this display differs from any of the preceding ones. Its spots aren’t spread pixels. They are approximations on a fixed grid of a calligraphic stroke. The TX-2 display was this calligraphic variety. Here’s what actually happened in TX-2: A sequence of line segments was drawn in order. Each one was converted into spot positions by a Bresenham-like rendering algorithm, and the spots in those positions were sequentially turned on by the display circuitry.
有时一定很不愉快,因为萨瑟兰煞费苦心地描述防止屏幕闪烁的方法。可以绘制一些不闪烁的线段,但随着线段数量的增加,显示将无法跟上并开始闪烁。他介绍了只显示每八分之一的技巧,然后稍后再返回以类似间隔的方式显示它们之间的其他七个,但这导致线条“由爬行的点组成”。这是一种交错显示的形式,但用于书法而不是光栅显示。他还介绍了点的随机显示,使屏幕“闪烁”而不是爬行。54
It must have been unpleasant sometimes because Sutherland goes to pains to describe methods to keep the screen from flickering. A few line segments could be drawn without flickering, but as the number of them increased the display could no longer keep up and would start to flicker. He introduced the trick of displaying only every eighth point and then going back later to display the other seven between them in a similarly spaced out way, but this caused lines to “be composed of crawling dots.” It was a form of interlaced display, but for a calligraphic, not a raster, display. He also introduced random display of the dots which made the screen “twinkle” instead of crawl.54
毫不奇怪,当 Sutherland 后来与 David Evans 共同创立了 Evans & Sutherland 公司时,它的第一批产品之一是真正的书法展示——笔画而不是斑点,而且绝对不是限制在网格中的斑点。它被称为 LDS-1,代表画线系统,而不是某些人认为的后期圣徒,因为联合创始人埃文斯是虔诚的摩门教徒,而 E&S 位于盐湖城。LDS-1 于 1969 年首次出货。该公司的下一个版本是流行的图片系统。纽约理工学院的计算机图形实验室(包含后来成为皮克斯的小组)于 1974 年开始使用 E&S 的机器,第一个是书法图片系统。55
Not surprisingly, when Sutherland later cofounded, with David Evans, the company Evans & Sutherland, one of its first products was a true calligraphic display—with strokes not spots, and definitely not spots constrained to a grid. It was called LDS-1, for Line Drawing System—not Latter-Day Saints as some thought, given that cofounder Evans was a devout Mormon and E&S was located in Salt Lake City. LDS-1 first shipped in 1969. The company’s next version was the popular Picture System. The Computer Graphics Lab at the New York Institute of Technology—containing the group that would later become Pixar—began in 1974 with machines from E&S, the first one a calligraphic Picture System.55
以下是如何看待当今的计算机图形,无论它在哪里使用——电影、游戏、VR 等等:一个虚构的世界是在计算机内存中建模的。这是模型,不是图片。它是标准的三维几何 á la Euclid 和其他早期希腊人。它不可见。这个世界的图像是二维的。所以为了拍一张照片,一个虚构的相机被放置在虚构的世界中。摄像头是虚拟的。它的机身、镜头、三脚架等没有建模。我们只关心虚拟摄像机在场景中的位置、指向的方向以及向上的方向。就像一个真正的相机一样,这个虚拟相机有一个取景器,可以捕捉到它所看到的虚构世界的矩形视图。我们称取景器为透视视口 在计算机图形学中——只是viewport,简称。Tim Johnson 首先在 Sketchpad III 中实现了(透视)视口。56
Here’s how to think about computer graphics today, regardless of where it’s used—in movies, games, VR, or so forth: A fictitious world is modeled inside a computer memory. It’s a model, not a picture. It’s standard three-dimensional geometry á la Euclid and other early Greeks. It’s not visible. A picture of this world is two-dimensional. So to make a picture, a fictitious camera is placed in the fictitious world. The camera is virtual. Its body, lenses, tripod, and so forth are not modeled. All we care about is where the virtual camera is located in the scene, what direction it’s pointed, and which way is up. Like a real camera, this virtual one has a viewfinder that captures a rectangular view of the fictitious world it’s looking at. We call the viewfinder a perspective viewport in computer graphics—just viewport, for short. Tim Johnson first implemented a (perspective) viewport in Sketchpad III.56
虚拟相机在其视口中捕获的虚幻世界部分被展平为二维 - 就像真实相机在其取景器中将现实世界展平为二维图像一样。还有一件非常重要的事情:视口以透视的方式看到了虚幻的世界——就像真实相机的取景器一样。这与我们人类感知视觉世界的视角相同。Johnson 在 Sketchpad III 的视口中使用了 Larry Roberts 的透视解决方案。
The portion of the unreal world that the virtual camera captures in its viewport is flattened into two dimensions—just like a real camera flattens the real world into a two-dimensional image in its viewfinder. And one further, very important, thing: the viewport sees the unreal world in perspective—just like a real camera’s viewfinder does. It’s the same perspective through which we humans perceive the visual world. Johnson used Larry Roberts’s perspective solution in the viewport of Sketchpad III.
我称其为计算机图形学的中心法则,因为它不必如此。毕竟,计算机是人类发明的最具延展性的工具。几何不一定是欧几里得,但它在中心法则中。它可能是科捷利尼科夫的祖父所鼓吹的洛巴乔夫斯基式——没有平行线(见第 2 章)。最重要的是,视角不一定是文艺复兴时期的视角,但中央教条就是这样。简而言之,中心法则代表了一个不真实的世界,就像我们人类感知的真实世界一样。这是虚拟相机对虚幻世界的透视图,全部在计算机内部,最终被渲染成像素,以便我们可以实际看到它。
I call this the Central Dogma of computer graphics because it doesn’t have to be that way. After all, a computer is the most malleable instrument ever invented by humankind. The geometry doesn’t have to be Euclidean, but it is in the Central Dogma. It could be Lobachevskian—with no parallel lines—as trumpeted by Kotelnikov’s grandfather (see chapter 2). Most importantly the perspective doesn’t have to be Renaissance perspective, but the Central Dogma has it so. In short, the Central Dogma represents an unreal world exactly as we humans perceive the real world. It’s the virtual camera’s perspectival view of the unreal world, all inside the computer, that is finally rendered into pixels so that we can actually see it.
MC Escher 的艺术展示了扭曲的视角会变得多么糟糕。在图 6.31 中,受 Escher 的启发,在没有计算机的情况下完成,直梁显然必须弯曲,以使它们的网格在透视中消失,朝向无限远的两点。这两个消失点在三维空间中彼此垂直的线上,但它们在一个平面中沿着一条线出现。这在透视图中并不罕见。但是这幅画的目的是让从下消失点发出的扩散线在看向上消失点时变得明显不断地间隔开。需求如此之大,以至于从较低的消失点朝向观察者的直线必须向上弯曲以适应它。而那些来自上消失点的人必须向下弯曲。这是非人的观点。我们看不到直线弯曲,中央教条也不允许。(这张图片,来自中心教条之外,被使用了 38 年作为年会的封面计算机科学程序的基础。)
The art of M. C. Escher shows just how screwy perspective can get. In figure 6.31, inspired by Escher and done without a computer, the straight beams have to bend, apparently, to let a grid of them vanish in perspective toward two points at infinity. The two vanishing points are on lines perpendicular to one another in three-dimensional space, but they appear along a single line in one plane. That’s not unusual in perspective drawings. But the picture’s intent is to have spreading lines that emanate from the lower vanishing point become apparently constantly spaced as seen looking toward the upper vanishing point. The demand is so severe that straight lines coming toward the viewer from the lower vanishing point have to bend upward to accommodate it. And those coming from the upper vanishing point have to bend downward. That’s a nonhuman perspective. We don’t see straight lines bend, and the Central Dogma doesn’t allow it. (This picture, from outside the Central Dogma, was used for 38 years as the cover for the annual Foundations of Computer Science proceedings.)
计算机辅助设计中计算机图形学的早期起源,例如,在 Coons、Bézier 和 de Casteljau 的工作中,促成了中心教条。在 CAD 中,设计的对象必须存在于现实世界中,这是必不可少的。但是,尽管中心法则是几乎总是在计算机图形学中实践的学科,但它肯定不是必需的。计算机艺术家从一开始就违反了它。从某种意义上说,这就是他们作为艺术家的角色——在没有人为限制的情况下运用数字光的媒介,并向我们其他人展示他们的发现。但是有即使在中心教条学科中也有很多创造力。拍摄皮克斯、梦工厂、蓝天和其他制作动画故事片的电影。学科内有如此多的创意空间,以至于许多艺术家从不考虑在它之外冒险。
The early origins of computer graphics in computer-aided design, in the work of Coons, Bézier, and de Casteljau, for instance, contributed to the Central Dogma. It’s a necessity in CAD where the objects designed must exist in the real world. But although the Central Dogma is the discipline that’s nearly always practiced in computer graphics, it’s certainly not required. Computer artists have violated it since the beginning. In a sense, that’s their role as artists—to exercise the medium of Digital Light without artificial limits and show the rest of us what they find. But there’s been a lot of creativity even within the Central Dogma discipline. Take any movie by Pixar, DreamWorks, Blue Sky, and others creating animated feature films. There’s so much Creative Space within the discipline that many artists never consider venturing outside it.
图 6.31
Figure 6.31
突触,© Alvy Ray Smith,1973。
Synapse, © Alvy Ray Smith, 1973.
这是妙语。1963 年,麻省理工学院的约翰逊和罗伯茨向我们介绍了现在使用的中心法则(尽管他们没有这么称呼它)。他们应该得到比他们往往得到的更多的荣誉。特别是,他们获得的信用比萨瑟兰少。但在某种程度上,这三个人都参与其中。这就是为什么我称他们为三巨头。在扩展这三位领导者之前,让我们简要回顾一下计算机图形学中透视的历史,因为约翰逊和罗伯茨并不是第一个使用透视的人。他们也不是首先使用中央教条。
Here’s the punch line. Johnson and Roberts at MIT in 1963 were the ones who introduced us to the Central Dogma as it’s now used (although they didn’t call it that). They deserve more credit than they tend to get. In particular, they get less credit than Sutherland. But all three were in on it at some level. That’s why I call them the Triumvirate. Before expanding on these three leaders, let’s briefly review a history of perspective in computer graphics, because Johnson and Roberts weren’t the first with perspective. Nor were they first with the Central Dogma.
动画对于计算机图形学来说是很自然的,因此可以大大扩展。. . . “艺术机器”的能力——计算机图形学是官方命名法——可以最好地描述为从任何所需的观察位置与空间中任意数量的点相关联。
Animation is a natural for computer graphics and could be greatly expanded because of it. . . . The capabilities of “the art machine”—computer graphics is the official nomenclature—could best be described as the relating of any number of points in space from any desired viewing position.
——威廉·费特,“艺术机器”,1962 年 2 月57
—William Fetter, “The Art Machine,” February 196257
在 1963 年有影响力的 Triumvirate 贡献之前一年多,堪萨斯州威奇托波音飞机公司的威廉·费特 (William Fetter, 1928-2002) 申请了在计算机上执行透视的专利。他于 1961 年 11 月向研究数学的同事沃尔特·伯恩哈特提出申请。该专利包含一架飞机的图纸,图 6.32,这可能是有史以来第一个以透视渲染的计算机模型。58
Over a year before the influential Triumvirate contributions of 1963, William Fetter (1928–2002) at the Boeing aircraft company in Wichita, Kansas, filed for a patent on perspective as executed on a computer. He filed in November 1961 with coworker Walter Bernhart, who did the mathematics. The patent contained the drawing of an airplane, figure 6.32, probably the first computer model rendered in perspective ever published.58
从上面的题词可以明显看出,Fetter 在 1962 年 2 月之前制定了计算机图形学的中心法则。用他的话来说,“计算机图形学...... . . 是空间中任意数量的点[模型]与任何所需观察位置的关联。” 他假设了观点,所以这符合我们的中心法则定义。平心而论,波音公司的费特和伯恩哈特首先实践了它。但是没有人从他们那里继承了中心法则。正如我在在线注释中详细解释的那样,它以蒂姆·约翰逊和拉里·罗伯茨在 1963 年提出的形式继承下来。59
As evident from the epigraph above, Fetter had formulated the Central Dogma of computer graphics by February 1962. In his words, “computer graphics . . . is the relating of any number of points in space [a model] from any desired viewing position.” He assumed perspective, so this fits our Central Dogma definition. In all fairness then, Fetter and Bernhart at Boeing practiced it first. But nobody inherited the Central Dogma from them. It was inherited instead in the form Tim Johnson and Larry Roberts presented in 1963, as I explain in detail in the online annotation.59
题词中提到“计算机图形”是该重要术语的最早用法之一。在同一篇文章中,费特说:“计算机图形学[他的斜体字] 诞生于波音公司军用飞机系统部门的威奇托分公司。” 他后来澄清说,这个词最初是由他的上司使用的在波音公司,凡尔纳 L.哈德逊 (1915-2001)。到 1962 年初,我们可以放心和保守地把这个词归功于 Hudson。Fetter 确实努力推广它,并在 1962 年经常使用它。60
The mention of “computer graphics” in the epigraph is one of the earliest uses of that important term. In that same article Fetter said, “Computer graphics [his italics] was born at the Wichita Branch of the Military Aircraft Systems Division of The Boeing Company.” He clarified later in life that the term was first used by his supervisor at Boeing, Verne L. Hudson (1915–2001). We can comfortably and conservatively give Hudson credit for the term by early 1962. Fetter certainly worked to popularize it and was using it frequently in 1962.60
图 6.32
Figure 6.32
Fetter 的一个有趣的主张,特别是对于这本书,是他在 1960 年制作了第一部计算机动画电影:“[I] 制作了 60 年的第一部透视电影动画(海军驾驶舱能见度)。” 但在一份单独获得的他的电影清单中,最早的日期是“Est. 年”1962 年。A4B–F4B,航母着陆,最早与他自己的描述大致相符的是 1964 年,AMSA 驾驶舱能见度。保守的约会将第一部三维动画电影归功于 Fetter,大概是在 1962 年。
An interesting claim by Fetter, particularly for this book, is that he made the first computer-animated movie in 1960: “[I] produced the first perspective motion picture animation (Naval cockpit visibility) ’60.” But in a separately obtained list of his films, the earliest is dated “Est. Year” 1962. A4B–F4B, Carrier Landing, and the earliest that roughly matches his own description is dated 1964, AMSA Cockpit Visibility. Conservative dating gives Fetter credit for the first three-dimensional animated movie, presumably in perspective, probably in 1962.
我们在“数字光的黎明”一章中了解到,已知的第一部数字动画是在 1951 年的旋风中。它们在电视上播出,但没有录制到电影中。Whirlwind 动画实际上在电视上移动,这意味着 Whirlwind 可以实时动画。最大的区别在于 Fetter 的动画是从透视的角度来看的 3D 模型,但 Whirlwind 的模型只是二维的。即使是旋风后的 10 年,也就是 1962 年,要实时观看 3D 模型移动的唯一方法就是将帧记录到电影中,然后实时投影电影。
We learned in the Dawn of Digital Light chapter that the first known digital animations were on Whirlwind in 1951. They were broadcast on television, but not recorded to movie film. The Whirlwind animations actually moved on television, which means Whirlwind could animate in real time. The big distinction is that Fetter’s animation was from a three-dimensional model viewed in perspective, but Whirlwind’s models were only two-dimensional. Even 10 years after Whirlwind, in 1962, the only way to see a three-dimensional model move in real time was to record frames to film, and then project the film in real time.
图 6.33
Figure 6.33
在著名的贝尔实验室,Edward E. Zajac 得出了另一种透视解决方案。他于 1963 年 10 月将其提交出版,并于次年 3 月出版。根据他论文中的一个脚注,他当时已经制作了一部 16 毫米的电影,其中的三维物体在透视中移动。因此,有时人们认为他制作了 1963 年的第一部电脑动画电影。但由于费特 1962 年的电影(可能)已经存在,我们将第二部动画电影归功于 Zajac。61
At the famed Bell Labs, Edward E. Zajac derived another perspective solution. He submitted it for publication in October 1963, and it was published the following March. According to a footnote in his paper, he had made a 16 mm movie of a three-dimensional object moving in perspective by that time. He is therefore sometimes credited with the first computer-animated film, dated 1963. But since Fetter’s 1962 film (probably) already existed, we credit Zajac with the second animated film.61
Zajac 电影帧根本没有在计算机显示器上看到。它们被直接(并且缓慢地)逐帧写入电影。图 6.33 显示了运动物体的所有帧在一张图片中相互叠加。
The Zajac movie frames weren’t seen on a computer display at all. They were written directly (and slowly) to film, frame by frame. Figure 6.33 shows all the frames of the moving object written atop one another in one picture.
Zajac 说:“制作透视图所需的基本转换在数学上是微不足道的。” 确实如此,而且他的解决方案在数学上等同于 Tim Johnson 和 Larry Roberts 在 1963 年使用的解决方案。但 Zajac 的解决方案,就像 Bernhart-Fetter 的解决方案一样,并没有被传给现代计算机图形学。与 Zajac、Bernhart-Fetter 和 Roberts 透视解决方案相关的详细信息显示在注释中。62
Zajac said, “The basic transformation needed to make a perspective drawing is mathematically trivial to state.” It is, and his solution is mathematically equivalent to the one Tim Johnson and Larry Roberts used, also in 1963. But Zajac’s solution, like Bernhart-Fetter’s, is not the one that was passed down to modern computer graphics. Details relating the Zajac, Bernhart-Fetter, and Roberts perspective solutions appear in the annotation.62
如果您曾经在会议中遇到过 Ivan,您就会知道与 Ivan 的每一次会面都是一次相遇。
If you’ve ever encountered Ivan in a meeting, you’ll know that every meeting with Ivan is an encounter.
——史蒂文·A·库恩斯63
—Steven A. Coons63
Ivan,我为你制造了 TX-2。
I built TX-2 for you, Ivan.
——韦斯利·A·克拉克64
—Wesley A. Clark64
像 Steven Coons 一样,Ivan Sutherland 这个名字在计算机图形学中一次又一次地出现。我的同事 Ed Catmull 在 Sutherland 手下学习,多年来向我讲述了他。我什至和萨瑟兰在同一个房间里去过几次,但我从来没有真正了解过这个人。因此,2017 年 5 月 9 日,我在俄勒冈州波特兰市的我位于英格兰剑桥的公寓里与他进行了 Skype 通话——根据他的要求,他的时间是早上 5 点,这是他开始新一天的通常时间。
Like Steven Coons, the name Ivan Sutherland shows up again and again in computer graphics. My colleague Ed Catmull studied under Sutherland and told me about him over the years. I had even been in the same room as Sutherland a couple of times, but I’d never really gotten to know the man. So, on May 9, 2017, I Skyped him in Portland, Oregon, from my flat in Cambridge, England—at 5 a.m. his time per his request, the usual time he starts his days.
我们一起度过了一个半小时,笑声比我预期的要频繁得多。萨瑟兰并不是我所期望的那种严厉的人。是的,他最初的举止暗示了一种阴郁的性格,但我很快就发现了一丝微笑,几乎是隐藏的。偶尔会出现一些诙谐的评论——带着有趣的一口。他对我的开场白提醒我,Sketchpad 的发展发生在笨重的恐龙计算机时代,这个时代充满了电子塔。他告诉我,他必须步行穿过TX-2 才能在 Sketchpad 上工作。
We spent an hour and a half together, chuckling much more often than I had anticipated. Sutherland was not the stern man I expected from reports. Yes, his initial demeanor suggested a saturnine personality, but I soon detected a slight smile, almost hidden. And there was the occasional witty remark—with a funny bite to it. His opening salvo to me was a reminder that Sketchpad’s development occurred in the era of hulking dinosaur computers, this one filling a room with towers of electronics. He had to walk, he told me, through TX-2 to work on Sketchpad.
麻省理工学院的 TX-2 可能是当时世界上最强大的单用户计算机。它的家是林肯实验室,一个高度安全的秘密设施(再次,一个军事暴君提供掩护)。但作为林肯实验室的员工和麻省理工学院的学生,萨瑟兰可以接触到这只野兽。他必须自己使用它,就好像它是他自己的一样。满屋子的电子设备只对他有反应。TX-2 是他自己的私人霸王龙,带有图形显示器和光笔。萨瑟兰可以用笔操纵显示器上的点。
TX-2 at MIT was probably the world’s most powerful single-user computer at the time. Its home was Lincoln Lab, a secret facility with high security (once more, a military tyrant offers cover). But as a Lincoln Lab employee and MIT student, Sutherland had access to the beast. And he got to use it by himself as if it were his own. The whole roomful of electronics responded only to him. TX-2 was his own personal T Rex, with a graphics display and a light pen. Sutherland could manipulate points on that display with the pen.
他将线段模型存储在 TX-2 的内存中,并编写了一个程序,将这些不可见的二维模型渲染为可见的二维TX-2 的光栅书法杂交显示器上的图片。如果他让光笔悬停在显示器上的某个点附近——比如线段的末端——那么他可以抓住端点并将其移动到新位置。存储在内存内部模型中的端点坐标会发生变化。显示屏将显示更改模型的更新图片。
He stored models of line segments in the memory of TX-2 and he wrote a program that rendered these invisible two-dimensional models into visible two-dimensional pictures on TX-2’s raster-calligraphic crossbreed display. If he let the light pen hover in the vicinity of a point on the display—say the end of a line segment—then he could grab the endpoint and move it to a new location. The endpoint coordinates stored in the internal model in memory would change. And the display would show an updated picture of the changed model.
萨瑟兰还首次展示了橡皮筋。他会抓住线段的一端并将其拖到新位置。旧线段消失,因为新线段被立即绘制到新位置。因此,随着他移动光笔,线段被重新绘制。它会随着新端点的需要和用户指示的任何方向延长或缩短。该技术及其效果令观众惊叹不已。现在看起来很明显,但以前没有人见过。
Sutherland also showed rubberbanding for the first time. He would grab one end of a line segment and drag it to a new location. The old line segment disappeared as a new line segment was drawn instantaneously to the new location. So the line segment was redrawn as he moved the light pen. It would lengthen or shorten as the new endpoint required and in whatever direction the user indicated. The technique and its effects amazed viewers. It seems so obvious now, but nobody then had seen it before.
Sutherland 的二维 Sketchpad 强调了几何约束的力量以及对他的模型进行应力分析和其他物理测试的能力。这使 Sutherland 直接进入了计算机辅助设计开发的主线。
Sutherland’s two-dimensional Sketchpad emphasized the power of constraints on geometry and the ability to do stress analysis and other physical tests on his models. This put Sutherland directly in the main line of computer-aided design development.
麻省理工学院三巨头的另一位成员蒂姆·约翰逊(Tim Johnson)对我来说,可以这么说,萨瑟兰是这样看待的。我在下面的故事中保留了工程(计算机辅助设计)的讨论,这也让我们想起了 Coons 的影响:
Tim Johnson, another member of the MIT Triumvirate, put Sutherland into perspective, so to speak, for me. I’ve left the engineering (computer-aided design) talk intact in the following story, which also reminds us of Coons’s influence:
史蒂夫库恩斯出现了一晚。. . 第一次看到 Ivan 的图形约束在起作用。Coons 被“恒定长度”约束收回,该约束固定了行长。他 [库恩斯] 随便注意到。. . 他可以绘制一个桁架并显示应变,只需为每条受约束的线添加一个文本显示,以显示该线正在经历的拉伸/压缩量。伊万从来没有预料到会有这样的用途。他为下一个演示添加了文本,史蒂夫开始绘制经典结构来测试它。那一刻标志着伊万工作的巨大力量。65
Steve Coons showed up one night . . . to see Ivan’s graphical constraints in action for the first time. Coons was taken back by the “constant length” constraint, which fixed a line length. He [Coons] casually noted . . . that he could draw a truss and show the strain just by adding a text display for each constrained line that showed the amount of stretch/compression the line was undergoing. Ivan had never anticipated such a use. He added the text for the next demo and Steve went to work drawing classic structures to test it. That moment marked the immense power of Ivan’s work.65
抛开限制不谈,Sketchpad 中的图形显示水平按照今天的标准似乎几乎是微不足道的,但在 1962 年没有人见过这样的东西。或者他们见过吗?像往常一样,一项技术的历史并不像收到的版本那么简单。与此同时,还有另一个交互式计算机图形和计算机辅助设计程序正在开发中。计算机增强设计 (DAC-1) 是在 IBM 的帮助下创建的,仅供底特律通用汽车公司内部的设计师和工程师使用。它的合同已出租(授予的法律术语)) 于 1960 年在纽约金斯敦的 IBM 进行开发,直到 1963 年 4 月 IBM 将该系统交付给 GM。它始终是一个三维系统。GM 知道 Sketchpad,但认为二维线段不足以满足其设计目的。他们需要三维曲线。66
Constraints aside, the level of graphic display in Sketchpad seems almost trivial by today’s standards, but nobody had seen anything like it in 1962. Or had they? As usual the history of a technology isn’t as simple as the received version. There was another interactive computer graphics and computer-aided design program in development at the same time. Design Augmented by Computers (DAC-1) was created, with IBM’s help, for exclusive use by designers and engineers internal to General Motors in Detroit. The contract for it was let (legalese for awarded) in 1960 and development occurred at IBM in Kingston, New York, until IBM delivered the system to GM in April 1963. It was always a three-dimensional system. GM was aware of Sketchpad but considered two-dimensional line segments insufficient for its design purposes. They needed three-dimensional curves.66
起初并没有推动系统公开。也就是说,直到 1963 年 Sketchpad 和 Sketchpad III 出版。通用汽车很快得到了 1964 年出版的 DAC-1 来分享在荣耀中。但很少有人记得它或它的作者 Edwin Jacks、Barrett Hargreaves 和许多其他人。67
At first there was no push to make the system public. That is, not until Sketchpad and Sketchpad III published in 1963. GM quickly got DAC-1 published in 1964 to share in the glory. But few remember it or its authors, Edwin Jacks, Barrett Hargreaves, and many others.67
在我准备本章时,Barrett Hargreaves 自己告诉我:
Here’s what Barrett Hargreaves himself told me as I prepared this chapter:
是的,您可以使用光笔输入线段。设计师可以输入两个位置并要求它们之间有一条直线。或者有一些计算机图形对话程序可以让他开发曲线。例如,他可以输入现有的 3-D 表面,并将线或表面与该表面或与原始表面的给定距离相匹配。最终结果可能是驱动数控机床的磁带。
DAC-1 系统是一个非常早期的开发,它聘请了工程师和设计师与 GM Research 的计算机专家和数学家一起工作。工程师告诉我们他们需要什么,我们对他们的要求进行编程响应。工程师确实使用 DAC-1 来设计车辆部件,主要是引擎盖和挡泥板等车身部件。
DAC-1 对 GM 最重要的贡献可能是,在 1960 年代初期,它向 GM 工程师和 GM 工程管理人员证明了计算机图形可以有效地用于设计和工程。计算机用于燃油经济性计算、车辆操纵计算、凸轮应力分析等的案例很多,但 DAC-1 证明,使用计算机可以极大地协助车身部件和其他面向图形的工程。68
Yes, you could use the light pen to enter line segments. The designer could enter two locations and request a straight line between them. Or there were a number of computer graphic dialog routines that allowed him to develop curved lines. He could for instance, enter an existing 3-D surface and match a line or surface to that surface or a given distance from the original surface. The end result could be a tape that drove a numerically controlled machine tool.
The DAC-1 system was a very early development that employed engineers and designers working along with GM Research computer specialists and mathematicians. The engineers told us what they needed and we programmed responses to their requests. The engineers did use DAC-1 to work on the design of vehicle parts, mostly body parts like hoods and fenders.
Probably the most important contribution of DAC-1 to GM was that, in the very early 1960s, it demonstrated to GM engineers and GM engineering management that computer graphics could effectively be used in design and engineering. There were numerous cases where computers were used for fuel economy calculations, vehicle handling calculations, cam stress analysis, etc. but DAC-1 proved that body parts and other graphic oriented engineering could be greatly assisted using the computer.68
根据哈格里夫斯的说法,通用汽车与麻省理工学院合作开发了 DAC-1 和光笔的软件。麻省理工学院和通用汽车集团会互相了解。这里有一些涉及 DAC-1 的有趣历史线索,值得进一步调查。DAC-1 帐户中缺少的一件事是确切的日期。比如,画板只有二维线条图的时候,有没有三维曲线?在约翰逊的画板 III 之前它有 3D 交互图形吗?DAC-1 于 1963 年 4 月的交付早于 Sketchpad III 于 1963 年 5 月的出版,这表明它确实如此,但这些都是外部日期,不一定表示内部发展。我们确实知道 DAC-1 没有透视显示。69
According to Hargreaves, GM worked with MIT on software for DAC-1 and the light pen. The MIT and GM groups would have known about one another. There are intriguing historical hints here involving DAC-1 that deserve further sleuthing. One thing lacking in DAC-1 accounts is exact dates. For example, did it have three-dimensional curves when Sketchpad had only two-dimensional line drawings? Did it have three-dimensional interactive graphics before Johnson’s Sketchpad III? That DAC-1’s delivery in April 1963 predates Sketchpad III’s publication in May 1963 suggests that it did, but these are both external dates and not necessarily indicative of internal developments. We do know that DAC-1 did not display in perspective.69
哈格里夫斯还提供了以下惊喜——通用汽车公司的早期计算机动画的证据显示给沃尔特迪斯尼本人,但不是在 DAC-1 上:
Hargreaves also delivered the following surprise—evidence of an early computer animation at GM shown to Walt Disney himself, but not on DAC-1:
沃尔特迪斯尼在 1960 年初的某个时间访问了通用汽车研究实验室计算机技术部。一位名叫 Hugh Brouse 的计算机图形程序员同事为迪斯尼先生开发了一部米老鼠的自动化电影。迪斯尼先生着迷了。当他在我们小小的计算机部门走来走去时,我们都目瞪口呆。70
Walt Disney visited the GM Research Laboratories Computer Technology Department sometime in the early 1960 time frame. A fellow computer graphics programmer named Hugh Brouse had developed an automated movie of Mickey Mouse for Mr. Disney. Mr. Disney was fascinated. We all stood agape as he walked around our little computer department.70
同样,日期很柔和,缺乏细节。休·布鲁斯去世了。因此,如果没有确凿的证据证明并非如此,并使用我们保守的约会计划来确定优先级,让我们假设此后在 Sketchpad 与 DAC-1 的比赛中,萨瑟兰是第一名。毫无疑问,他的 Sketchpad 广为人知,而 DAC-1 却没有。但同样清楚的是,DAC-1 几乎同时是一个交互式计算机辅助设计程序。71
Again, the dates are soft and details lacking. And Hugh Brouse has died. So, without hard evidence that proves otherwise, and using our conservative dating scheme for establishing priority, let’s assume henceforth in the Sketchpad versus DAC-1 contest that Sutherland was first. It’s certainly true that his Sketchpad was publicized far and wide, and DAC-1 was not. But it’s also clear that DAC-1 was an interactive computer-aided design program at about the same time.71
但是,如果我们给他,萨瑟兰首先做了什么?它不是交互式计算机图形。十年前,克里斯托弗·斯特拉奇(Christopher Strachey)和他的草稿(跳棋)电子游戏以及桑迪·道格拉斯(Sandy Douglas)和他的三字棋(井字棋)电子游戏已经做到了这一点。1950 年代早期的这两个程序都允许用户交互地更改,例如,将一个空的棋盘正方形更改为一个持有 X 或 O 的棋盘。更新了内部棋盘模型,并重新绘制了显示以显示新棋盘配置锯齿状地呈现 Xs 和 Os。
But what exactly had Sutherland done first, if we give him that? It wasn’t interactive computer graphics. That had already been done a decade earlier—by Christopher Strachey and his draughts (checkers) videogame and by Sandy Douglas and his noughts and crosses (tic-tac-toe) videogame. Both programs from the early 1950s enabled a user to interactively change, say, a board square from an empty one to one holding an X or an O. The internal board model was updated, and the display was redrawn to show the new board configuration with jaggedly rendered Xs and Os.
这确实是 Sutherland 的创新:Sketchpad 交互式渲染,强调渲染。当您移动您的手时,该程序会以交互方式更新内部几何模型。但 Strachey 和 Douglas 的游戏也做到了这一点。重要的新事物是 Sketchpad在您移动您的手时将更新的模型呈现到显示器上。它不仅改变了模型。它也重新渲染了它。画板不知道下一条线可能在哪里绘制,不知道它会多长,也不知道它会处于什么角度。它必须像用户的手移动端点位置一样快地渲染它。因此,用户在交互式地更改几何模型方面具有完全的代理感。
This was really Sutherland’s innovation: Sketchpad rendered interactively, with emphasis on rendered. The program updated an internal geometric model interactively, as you moved your hand. But Strachey’s and Douglas’s games did that too. The important new thing was that Sketchpad rendered the updated model to the display while you moved your hand. It didn’t just change the model. It re-rendered it too. Sketchpad had no notion of where the next line might be drawn, nor how long it would be, nor at what angle it would lie. And it had to render it as fast as the user’s hand moved the endpoint locations. Thus the user had a sense of full agency in changing the geometric model interactively.
Strachey 的草稿程序在曼彻斯特古老的 Mark I 计算机上运行,显示了预渲染的几何元素——棋盘、Xs 和 Os。Mark I 的速度还不够快,甚至无法以交互速度渲染 X。道格拉斯在剑桥古老的 Edsac 上跑步的 noughts 和 crosss 也同样处于不利地位。但是大约10 年后,麻省理工学院的 TX-2速度足够快,可以瞬间渲染几十条线段,无论如何都是人类所感知的。
Strachey’s draughts program, running on the ancient Mark I computer at Manchester, displayed pre-rendered geometrical elements—the board, Xs, and Os. The Mark I wasn’t fast enough to render even an X at interactive speeds. Douglas’s noughts and crosses running on the ancient Edsac at Cambridge was similarly disadvantaged. But 10 or so years later TX-2 at MIT was fast enough to render several dozen line segments instantaneously, as perceived by a human anyway.
Sutherland 拥有巨大的 TX-2,并且是第一个以图形方式利用其速度的人。我们已经讨论过橡皮筋。他还让 Sketchpad 做一些事情,例如保持线段的一个端点固定,同时围绕它旋转另一个端点。效果是旋转线段——正如你所看到的——而用户(萨瑟兰)在显示器表面上移动光笔。或者他可以在旋转旋钮的同时实时旋转由多个线段组成的整个对象。这款游戏与 1950 年代初期的互动游戏的主要区别在于,线段的渲染是瞬间发生的,或者显然是瞬间发生的。Sketchpad 程序不知道新线段可能位于何处,因此无法预渲染它们。
Sutherland had giant TX-2 to himself and was the first to exploit its speed graphically. We’ve already discussed rubberbanding. He also caused Sketchpad to do things such as hold one endpoint of a line segment fixed while rotating the other endpoint about it. The effect was to rotate the line segment—as you watched—while the user (Sutherland) moved the light pen on the display’s surface. Or he could rotate an entire object, consisting of several line segments, in real time while twirling a knob. The key difference between this and interactive games in the early 1950s was that the rendering of line segments happened instantaneously, or apparently so. The Sketchpad program had no idea of where new line segments might be located, so couldn’t have pre-rendered them.
Sutherland 使用 Sketchpad 完成的是第一个交互式渲染的计算机图形。它不像 Sutherland 和 Sketchpad 经常被认为的“第一个交互式计算机图形”那样顺利地从舌头上滚下来,但它具有准确的优势。这个概念是渲染到显示器的几何模型立即被模型的另一个渲染替换,该模型包含依赖于用户输入的变化,因此程序无法预测。TX-2 是第一台具有足够快显示屏的单用户计算机,而 Sutherland 则跃跃欲试地采用了这种方式。
What Sutherland accomplished with Sketchpad was the first interactively rendered computer graphics. It doesn’t roll off the tongue as nicely as “first interactive computer graphics”—with which Sutherland and Sketchpad are often credited—but it has the advantage of being accurate. The notion is that a geometric model rendered to a display is instantaneously replaced with another rendering of the model, which incorporates changes that depend on a user’s input and hence can’t be predicted by the program. TX-2 was the first single-user computer with a display that was fast enough, and Sutherland leapt to use it that way.
但是 Sketchpad 有一些新的东西:交互式渲染使之成为可能但没有解释的东西;在这个交互式渲染的讨论中还没有捕捉到一些东西。好奇的?新的东西是这样的:用户自己感觉好像他(通常还不是她)正在通过“触摸”显示器上的图片来改变模型。我们称之为图片即界面的概念。早期的交互式棋盘游戏通过打字来交互地改变内部模型,而不是通过触摸图片本身。早期的 Edsac 游戏“羊与门”通过挥手中断 Edsac 纸带阅读器的光束来工作。但是作为Sketchpad的用户,新的体验是你自己通过触摸来改变图片. 如果您是设计师,您可以第一次在创建模型时看到它。DAC-1 几乎在同一时间允许同样的事情。
But there was something new about Sketchpad: something that interactive rendering made possible but doesn’t explain; something that hasn’t yet been captured in this discussion of interactive rendering. Curious? The something new was this: the user himself felt as if he (not yet she, generally) were changing the model by “touching” a picture of it on the display. We call this the picture-as-interface notion. The early interactive board games changed the internal model interactively by typing, not by touching the picture itself. And the early Edsac game called “sheep and gates” worked by interrupting the light beam of Edsac’s paper tape reader with a hand wave. But as a user of Sketchpad, the new experience was for you yourself to change the picture by touching it. If you were a designer you could, for the first time, see your model while it was being created. DAC-1 allowed the same thing at about the same time.
我在这里非常宽松地使用“触摸”,包括将光笔或光枪靠近计算机显示屏。由于使用鼠标进行光标操作对我们来说就像用光标触摸某物一样,所以我也将该模式包括为触摸。同样,我还包括通过在触摸板上移动轨迹球、操纵杆、手指或在虚拟现实中挥动魔杖来进行光标定位。
I’m using “touch” here quite loosely, to include bringing a light pen or light gun into close proximity to a computer display screen. Since cursoring with a mouse feels to us like touching something with the cursor, I also include that mode as touch. Similarly, I include cursoring by moving a trackball, joystick, your finger on a touchpad, or waving a wand in virtual reality.
实际上用一根或多根手指触摸屏幕,就像我们今天在手机和触摸板上所做的那样,似乎是过去十年左右的一个相当新的发展。但事实并非如此。由伊利诺伊大学的 Dan Alpert、Don Bitzer 和其他人策划的 Plato 项目从 1972 年开始让用户直接触摸其等离子面板显示器。这些二进制光栅显示器的显示元素以发出橙色的光而闻名。最近出版的这个项目的历史, Brian Dear的 The Friendly Orange Glow,应该会在现代计算历史中重建柏拉图的发展。72
Actually touching a screen with a finger or fingers, as we do on cellphones and touchpads today, would appear to be a fairly recent development of the last decade or so. But that’s not true. The Plato project masterminded by Dan Alpert, Don Bitzer, and others at the University of Illinois let users directly touch its plasma panel displays, starting in 1972. The display elements of these binary raster displays famously glowed orange. A recently published history of this project, The Friendly Orange Glow by Brian Dear, should reestablish the Plato development in modern computing history.72
在我向人们展示现场演示之前的早期,我会描述在桌面上移动鼠标是如何改变显示器的。我会在每次谈话中花大约 15 分钟来解释这确实有效。人们感到惊讶的是,如果你在一个地方移动并导致另一个地方的光标以严格的模仿方式移动,你会感觉好像你是在显示器上移动,而不是在桌面上移动。1980 年代初个人电脑的出现消除了这个问题。突然之间,每个人都从个人经验中知道了鼠标是如何连接到光标的。
In the early days before I could show people a live demo, I would describe how moving a mouse on a desktop made a change on the display. I would spend about 15 minutes in every talk explaining that this really worked. People were surprised that if you were moving in one place and causing a cursor in another place to move in rigid mimicry, it would feel as if you were moving up there on the display, not down on the desktop. The advent of personal computers in the early 1980s banished that question. Suddenly everyone just knew, from personal experience, how a mouse connected to a cursor.
无论您是通过移动鼠标还是通过实际触摸屏幕来使屏幕上发生某些事情,您都认为您的手是改变画面的代理。感觉是这样,但实际情况并非如此。实际发生的情况是:“触摸”设备导致向正在运行的程序发出命令——Sketchpad 说。该程序使计算机内存中的几何模型更改,然后这会导致更改后的模型重新显示(重新渲染)到刚刚“触摸”的显示。
Whether you cause something to happen on a screen by moving a mouse or by actually touching the screen, you perceive that your hand is the agent that changes the picture. It feels that way, but that’s not what actually happens. What actually happens is this: The “touching” device causes commands to be issued to a running program—Sketchpad say. The program causes the geometric model in computer memory to change, and then that causes a re-display of the changed model—a re-rendering of it—to the display that has just been “touched.”
从今天的角度来看,使用二维几何——例如正方形、三角形或圆形——听起来并不多,但萨瑟兰首先出现了,他必须解决无数问题。他必须创建一个数据结构来表示模型中对象的拓扑结构:这条线段连接到那个线段,并在运动过程中保持连接。
From today’s vantage point, working with two-dimensional geometry—such as a square, a triangle, or a circle—doesn’t sound like much, but Sutherland was there first and had to solve myriad problems. He had to create a data structure that represented the topology of the objects in his model: this line segment is connected to that one—and stays connected during movements.
当 TX-2 进行 Sketchpad 工作时,他必须让显示设备显示物体的图片。也就是说,他必须考虑一个与主计算进程分开运行的显示进程。这就是现代显示器的工作原理,但萨瑟兰不得不直面它。
He had to cause a display device to display a picture of the objects while the TX-2 was doing Sketchpad work. That is, he had to think about a display process running separately from the main computation process. This is how modern displays work, but Sutherland had to confront it head on.
他必须创建一种算法,将线段作为一组点呈现到显示器上。这与 1962 年 Bresenham 的著名算法做同样事情的时间大致相同,但 Sutherland 独立解决了它并且不考虑效率,因为 TX-2 非常快。
He had to create an algorithm for rendering a line segment to the display as a set of points. This was about the same time as Bresenham’s famous algorithm in 1962 for doing the same thing, but Sutherland solved it independently and without regard for efficiency because the TX-2 was so fast.
他必须弄清楚如何在显示器上跟踪光笔。他之后的人,比如蒂姆约翰逊,可以从许多已经解决的问题开始。仅二维几何听起来并没有多大贡献,但 Sutherland 还首次创建了交互式渲染计算机图形的管道(可能还记得 DAC-1)。
He had to figure out how to track a light pen on a display. People after him, like Tim Johnson, could just start with many of these problems already solved. Two-dimensional geometry alone doesn’t sound like much of a contribution, but Sutherland also created the plumbing of interactively rendered computer graphics for the first time (probably, remember DAC-1).
对于计算机辅助设计,他贡献了约束、拓扑保存、准确性和对象测试等重要概念,我们在此不再赘述。73
And for computer-aided design, he contributed the important notions of constraints, topology preservation, accuracy, and testing of his objects that we won’t further pursue here.73
但最重要的是,萨瑟兰向我们展示了通过“触摸”它的显示屏并看到某些东西瞬间发生变化的感觉来控制计算机的力量。萨瑟兰可能并不完全是第一个,但几乎没有人看到,甚至不知道更早的例子。例如,圣人是最高机密。DAC-1 是通用汽车内部的。但麻省理工学院在营销方面很聪明。画板的电影演示被广泛传播。您仍然可以在 YouTube 上观看 Alan Kay 讲述(事后)1962 年 Sketchpad 的电影演示,感受最初的兴奋。光是橡皮筋就足以震惊世界,在当时肯定是新事物。74
But most importantly, Sutherland showed us the power of feeling in control of a computer by “touching” its display and seeing something change instantaneously. Sutherland might not have entirely been first, but hardly anybody saw, or was even aware of, earlier instances. Sage, for example, was top secret. And DAC-1 was internal to GM. But MIT was smart about marketing. Film demos of Sketchpad were distributed far and wide. You can still watch Alan Kay on YouTube narrate (well after the fact) a 1962 film demo of Sketchpad and sense the original excitement. The rubberbanding alone was enough to astonish the world, and it was certainly new at the time.74
在 Sketchpad 中这种交互性的使用似乎是我们现在所说的图形用户界面的戏剧性起源。我在 Skype 通话中向 Sutherland 询问了这个问题。他还没准备好走那么远。他的程序允许用户通过光笔通过“触摸”来控制物体的图片。
This use of interactivity in Sketchpad appears to have been the dramatic origin of what we now call the graphical user interface. I asked Sutherland about this in our Skype call. He wasn’t ready to go that far. His program allowed a user to control the picture of an object through “touch” via a light pen.
给我们完整的图形用户界面的最后一个比喻是用户可以通过触摸显示器来控制任何东西,而不仅仅是几何图形的图片。对象。在用户触摸下发生变化的内部模型可以是,例如,用户计算机的文件或文件夹系统。文件夹的图标是计算机内存中实际文件夹的显示版本。它不是它的图片,因为那里没有任何东西可以用来制作图片。移动文件夹的图标实际上会将文件夹移动到内存中的某个新位置。
The final metaphor that gave us the full graphical user interface was the notion that a user could control anything through touching a display, not just pictures of geometrical objects. The internal model that changes under user touch could be, for example, the file or folder system of the user’s computer. An icon of a folder is the displayed version of an actual folder in the computer memory. It is not a picture of it, because there is nothing there to make a picture of. Moving the folder’s icon actually moves the folder somewhere new in the memory.
不幸的是,蒂姆约翰逊看起来很像 1960 年代初期的伊万萨瑟兰。他的笑容比萨瑟兰更大、更热情,但同样的头发、眼镜和窄脸。今天的许多在线照片,标题为 Sutherland 在 Sketchpad 的控制下,实际上是 Johnson 在 Sketchpad III 的控制下。当我在 2017 年 3 月下旬联系约翰逊时,他善意地接受了这种情况。他说,他现在已经辞职了。他还能做什么?我向他保证我会尽我所能扭转局面。
Tim Johnson had the misfortune of looking a lot like Ivan Sutherland in the early 1960s. He had a bigger, readier smile than Sutherland but the same hair, glasses, and narrow face. Many online photos today, captioned as Sutherland at the controls of Sketchpad, are actually Johnson at the controls of Sketchpad III. When I contacted Johnson in late March 2017, he good-naturedly accepted the situation. He’s now resigned to it, he said. What else could he do? I promised him I would do my bit to turn it around.
Johnson 的 Sketchpad III 是计算机辅助设计开发的主线。正如我们所提到的,他介绍了计算机辅助设计建模师流行的四窗格窗口布局:三个显示对象的顶视图、前视图和侧视图,没有透视图,第四个是视口,显示对象使用罗伯茨透视解决方案从任何角度和透视。
Johnson’s Sketchpad III was in the main line of computer-aided design development. With it he introduced, as we’ve mentioned, the four-pane window layout popular with computer-aided design modelers: three showing top, front, and side views of an object without perspective, and the fourth, the viewport, showing the object from any angle and in perspective using the Roberts perspective solution.
考虑一下那个视口。假设它填满了整个显示器。这就是您在每部皮克斯电影的每一帧中看到的视图。其他三个窗格,包括顶视图、前视图和侧视图,仅在设计阶段使用,以方便建模者。
Consider that viewport for a moment. Assume that it fills the entire display. That’s the view you see in every frame of every Pixar-like movie. Those other three panes, with the top, front, and side views, are used during the design phase only, for the convenience of modelers.
在图 6.34 的左上角,Johnson(不是 Sutherland!)在 Sketchpad III 的控制之下。每个显示器的特写显示所有四个窗格,视口位于每个窗格的右上角。Tim 从一个简单立方体的三个面开始(在右上图)。然后,他使用光笔在正面 F(左下方)的顶部添加了一个三角形,当他添加它时,该三角形会显示在其他窗格中。然后,他在侧面 S 上添加(右下)一个倾斜的矩形,并且可能在正面 F 上添加另一个矩形。75
In figure 6.34, upper left, Johnson (not Sutherland!) is at the controls of Sketchpad III. The closeups of each display show all four panes, with the viewport in the upper right of each. Tim started with three faces of a simple cube (in the upper right figure). He then added, using a light pen, a triangle at the top of the front face F (lower left), which shows in the other panes as he adds it. He then added (lower right) a skewed rectangle to the side face S and perhaps is adding another to front face F.75
视口是 Johnson 的创新:“Ivan [Sutherland] 通过将我指向拉里·罗伯茨的方向来实现同质化。我很快就意识到他(罗伯茨)的方法是多么干净(和出色)。. . . 透视视口是我的想法。” 而那个(透视)视口概念是计算机图形学的关键。76
The viewport was Johnson’s innovation: “Ivan [Sutherland] got the homogeneous thing going by pointing me in Larry Roberts’s direction. I quickly appreciated how clean (and brilliant) his [Roberts’s] approach was. . . . The perspective view port was my notion.” And that (perspective) viewport notion is key to computer graphics.76
我问约翰逊,他是否在 Sketchpad III 中实施了 Coons 补丁,因为 Coons 是他的硕士论文导师。“我将史蒂夫的补丁作为一个快速而肮脏的独立 TX-2 程序,它不是 Sketchpad III 的一部分。” 77
I asked Johnson if he had implemented Coons patches in Sketchpad III, given that Coons was his master’s thesis adviser. “I did Steve’s patches as a quick and dirty stand-alone TX-2 program, it was not part of Sketchpad III.”77
图 6.34
Figure 6.34
从那些早期开始,他对自己做了什么?约翰逊在 Sketchpad III 之后从事建筑事业。在麻省理工学院建筑系,他将萨瑟兰的约束思想应用于建筑规划,并在那里获得了教授职位。然后他在麻省理工学院校园建造了一座示范太阳能建筑。他通过创办一家成功的企业结束了他的职业生涯,该企业对建筑进行了程式化的“照片级写实”渲染。也就是说,约翰逊在 Digital Light 的计算机辅助设计分支开始了他的职业生涯,并在计算机图形分支中结束了他的职业生涯。但他从未获得过任何一个奖项。78
And what had he done with himself since those early days? Johnson pursued a career in architecture after Sketchpad III. In MIT’s Department of Architecture, he applied Sutherland’s constraint ideas to architectural plans, leading to a professorship there. Then he built a demonstration solar building on the MIT campus. He ended his professional career by starting a successful business that did stylized “photorealistic” renderings of architecture. That is, Johnson started his professional career in the computer-aided design branch of Digital Light and ended it in the computer graphics branch. But he’s never been honored with an award by either.78
拉里·罗伯茨看起来不像他在麻省理工学院的同学伊万·萨瑟兰和蒂姆·约翰逊。他的头发较黑,没有戴眼镜。而且他没有写过 Sketchpad 的版本。事实上,他并不是从计算机图形学开始的。罗伯茨最初在 Digital Light 的图像处理部门工作。他研究了一张花花公子杂志的照片,在作为像素栅格的数字形式,以了解他可以省略每个像素多少位并仍然保持图像质量。
Larry Roberts didn’t look like his MIT classmates Ivan Sutherland and Tim Johnson. He had darker hair and didn’t wear glasses. And he didn’t write a version of Sketchpad. In fact, he didn’t start in computer graphics. Roberts initially worked in the image processing branch of Digital Light. He studied a Playboy magazine photograph, in digital form as a raster of pixels, to understand how many bits per pixel he could omit and still maintain image quality.
但他更令人印象深刻的作品涉及识别数字化照片中的 3D 形状——不是花花公子兔子,而是透视拍摄的立方体和棱镜等简单物体。他通过检测这些物体的直线边和角提取了这些物体的线条图,同时考虑了透视。然后他推断出它们的三维结构并将其显示在 TX-2 显示器上,然后又回到 Digital Light 的计算机图形分支进行这部分工作。他必须掌握透视才能做到这一点,而他这样做的方式成为他对计算机图形学的基本贡献。79
But his far more impressive work involved the recognition of three-dimensional shapes in digitized photographs—not of Playboy Bunnies but of simple objects like cubes and prisms photographed in perspective. He extracted line drawings of these objects by detecting their straight-line edges and corners, taking the perspective into account. Then he deduced their three-dimensional structure and displayed it on the TX-2 display, crossing back over into the computer graphics branch of Digital Light for this part of his work. He had to master perspective to accomplish this, and the way he did so became his fundamental contribution to computer graphics.79
他的透视解决方案在当今的计算机图形学中普遍使用。它来自一个名为射影几何的深奥数学,它利用了奇怪的齐次坐标。这不是一个明显或直观的步骤。
His perspective solution is used universally in computer graphics today. It’s from an esoteric math called projective geometry, and it utilizes the oddly named homogeneous coordinate. It wasn’t an obvious or intuitive step.
该技术要求我们将第四个坐标附加到几何中的每个点。我的高中教科书的平面几何使用具有两个坐标的点,第一个用于水平位置x,第二个用于垂直位置y。这就是萨瑟兰画板的几何形状,无论是内部还是展示。
The technique asks us to append a fourth coordinate to each point in our geometry. The plane geometry of my high-school textbook uses points with two coordinates, the first for horizontal location x and the second for vertical location y. That’s the geometry of Sutherland’s Sketchpad, both internally and in display.
像我这样的学生在高中也学了一点立体几何或三维几何。它将第三个坐标附加到每个点,它在三维空间中的深度位置z 。立体几何是 Johnson 的 Sketchpad III 的内部结构。为了显示,Johnson 只需要二维点,但在他最有趣的转折中,他让 Sketchpad III 也以透视的方式显示内部模型。这就是他的同学罗伯茨的透视解法发挥作用的地方。
Students like me learned a smidgen of solid, or three-dimensional, geometry in high school too. It appends a third coordinate to each point, its depth location z in three-dimensional space. Solid geometry is what’s internal to Johnson’s Sketchpad III. For display, Johnson needed only two-dimensional points, but in his most interesting twist, he had Sketchpad III also display the internal model in perspective. This is where the perspective solution of his classmate Roberts came in.
罗伯茨技术将奇怪的第四个“同质”坐标附加到内部模型中的每个点。我们称之为h。罗伯茨世界中的一个缩略点——在射影几何中——变成了 ( x , y , z , h )。前三个坐标只是空间中一个点的通常位置。但是第四个坐标是什么?我们已经讨论过时空,其中一个点具有第四个坐标,即它的时间位置。但是齐次坐标不是时间。它的意思是:给定一个通常位于内部几何模型中 ( x , y , z ) 的点,使用该点 (x / h , y / h ) 以在模型显示的透视图中定位该点。换句话说,透视一个点的方法是将它的前两个坐标除以它的第四个坐标h(并且简单地忽略第三个坐标)。这并不明显,是吗?文艺复兴时期的艺术家和建筑师当然不知道这种算法。
The Roberts technique appended that strange fourth, “homogeneous,” coordinate to every point in an internal model. Let’s call it h. An abbreviated point in Roberts’s world—in projective geometry—becomes (x, y, z, h). The first three coordinates are just the usual location of a point in space. But what is that fourth coordinate? We’ve talked about spacetime where a point has a fourth coordinate, which is its location in time. But the homogeneous coordinate isn’t time. What it means is this: given a point normally located at (x, y, z) in an internal geometric model, use the point (x / h, y / h) to locate that point in perspective on the model’s display. In other words, the way to get a point into perspective is to divide its first two coordinates by its fourth coordinate h (and simply ignore the third coordinate). That’s not obvious, is it? The Renaissance artists and architects certainly didn’t know this algorithm.
但罗伯茨走得更远,约翰逊也将这些其他想法融入到 Sketchpad III 中。罗伯茨介绍了当今计算机图形学中普遍使用的空间转换机制。我们所说的空间变换是指移动、旋转或调整对象大小。除了说它在 Roberts 用他的透视解法引入的四维点上使用四维乘法外,我不会进一步解释它——其中第四个坐标是齐次坐标。进一步解释将带我们进入“矩阵”代数的数学杂草。关于罗伯茨要记住的重要一点是,他以矩阵形式将透视和空间变换结合在一起,就像我们今天普遍采用的那样。他没有创建齐次坐标或矩阵代数。但是将两者结合起来是深刻的。以下是罗伯茨自己的发现:
But Roberts went even further, and Johnson incorporated these other ideas into Sketchpad III as well. Roberts introduced the spatial transformation machinery that’s used universally in computer graphics today. By spatial transformation we mean moving, rotating, or resizing an object. I won’t explain it further other than to say that it uses four-dimensional multiplication on the four-dimensional points that Roberts introduced with his perspective solution—where the fourth coordinate is the homogeneous one. To explain further would take us into the mathematical weeds of “matrix” algebra. The important point to remember about Roberts is that he combined both perspective and spatial transformations together in matrix form, as we do universally today. He didn’t create either homogeneous coordinates or matrix algebra. But combining the two was profound. Here is Roberts’s discovery in his own words:
事实证明,当时在美国或世界上都没有整合矩阵和透视几何的技术。不知怎的,两人在整个世界的时间和空间上完全分开了。所以我回到了德语教科书,发现透视几何是如何完成的,并且没有矩阵知识。当然,我去其他教科书上找到了有关矩阵的知识,然后将两者放在一起,创建了四维齐次坐标变换,今天广泛用于透视变换。这篇论文甚至可能是最初论文中所有工作中最为人所知的,因为它提供了一个单一的四维变换,可以对物体进行任何透视显示。80
It turned out there was no technology in the US or in the world at that point in time integrating both matrices and perspective geometry. Somehow the two had been totally separated in time and space throughout the world. So I went back to the German textbooks and found out how perspective geometry was done and that had no knowledge of matrices. I went to other textbooks and found out about matrices, of course, and put the two together and created the four dimensional homogeneous coordinate transform, which is widely used today for perspective transformations. This paper probably is even best known of all of the work that was in this original thesis because it provides, with a single four dimensional transform any perspective display of an object.80
为什么没有罗伯茨奖?拉里·罗伯茨怎么了?你可能会感到惊讶。他成为互联网发明背后的主要力量!但这是一个需要背景的故事。
Why isn’t there a Roberts Award? And what happened to Larry Roberts? You might be surprised. He became a major force behind the invention of the internet! But that’s a story that needs a context.
您可能还记得,JCR Licklider 在他 1960 年的“人机共生”论文中设想了互联网。因此两年后 ARPA 抢购“Lick”并让他成为新信息处理技术办公室的第一任主任也就不足为奇了。在一系列强有力的领导者的领导下,IPTO 将成为我们故事中的一支主要力量。特别是,它将刺激互联网、个人计算机和计算机图形学的发展。
J.C.R. Licklider, you may recall, imagined the internet in his “Man-Machine Symbiosis” paper of 1960. So it’s not surprising that two years later ARPA snapped up “Lick” and made him the first director of the new Information Processing Techniques Office. IPTO would become, under a succession of strong leaders, a major force in our story. In particular, it would spur development of the internet, personal computers, and computer graphics.
Lick 立即开始资助项目,这些项目可能会实现他关于人与机器和谐工作的愿景。他在这方面非常自由,并获得了真正的远见卓识。他资助的第一批项目之一是 Doug Engelbart 在斯坦福大学附近的斯坦福研究所的“增强型”人机通信项目。这个项目导致了图形用户界面的第一个完整实现。如前所述,恩格尔巴特在著名的“所有演示之母”中展示了这一点——他用一种叫做鼠标的新设备来驱动它。
Immediately, Lick started funding projects that might realize his vision of man and machine working in harmony. He had a remarkably free hand at this and attained true visionary status with it. One of the first things he funded was Doug Engelbart’s “augmented” man-machine communications project at the Stanford Research Institute near Stanford University. This project led to the first full implementation of a graphical user interface. As noted earlier, Engelbart showed it off in the famous “mother of all demos”—which he drove with a new device, called a mouse.
NASA 的罗伯特·泰勒同样对恩格尔巴特感兴趣,也投入了资金。形成了一个有远见的联系——ARPA 的 Licklider、NASA 的 Taylor 和 EngelbartSRI——谁会影响这个技术爆炸性十年和下一个十年的所有相互交织的故事。
Similarly intrigued by Engelbart, Robert Taylor at NASA also pitched in funds. A nexus of visionaries formed—Licklider at ARPA, Taylor at NASA, and Engelbart at SRI—who would affect all the intertwined stories of this technically explosive decade and the next.
Licklider、Engelbart 和 Taylor 非常了解 1962 年至 1964 年在麻省理工学院的 Triumvirate 的 Sketchpad 和 Sketchpad III 开发。他们引用它们作为他们集体人机视觉的证据。毫不奇怪,ARPA IPTO 的第二任主任是 1963 年的 Ivan Sutherland。第三任主任是 1965 年的 Bob Taylor。第四任主任是 1966 年的 Larry Roberts。ARPA 的资金帮助这些人不仅影响了 Digital Light,而且影响了肤色我们整个现代世界。
Licklider, Engelbart, and Taylor were quite aware of the Triumvirate’s Sketchpad and Sketchpad III developments at MIT from 1962 to 1964. They cited them as evidence of their collective man-machine vision. Not surprisingly then, the second director of ARPA’s IPTO was Ivan Sutherland in 1963. The third director was Bob Taylor in 1965. And the fourth director was Larry Roberts in 1966. ARPA’s funding helped these men influence not only Digital Light, but also the complexion of our entire modern world.
在 Ivan Sutherland 在 IPTO 工作期间,他继承并继续资助伯克利的 David Evans。当埃文斯随后在犹他州成立图形部门时,他敦促萨瑟兰加入他的行列。Sutherland 终于在 1968 年这样做了,同时两人在盐湖城共同创立了计算机图形硬件公司 Evans & Sutherland。该公司,尤其是该部门将对随后的计算机图形学历史产生巨大影响。
While Ivan Sutherland was at IPTO he inherited and continued to fund David Evans in Berkeley. When Evans subsequently founded the graphics department at Utah, he urged Sutherland to join him. Sutherland finally did so in 1968, and at the same time the two cofounded the computer graphics hardware company Evans & Sutherland in Salt Lake City. The company and especially the department would have a tremendous influence on the subsequent history of computer graphics.
1970 年,鲍勃·泰勒(Bob Taylor)在 IPTO 分配 ARPA 资金后,在施乐 PARC(帕洛阿尔托研究中心)创立了著名的实验室。几年后我会在那里为他工作。这是创建我们现在所理解的个人计算的实验室,它集成了个人计算机、基于 Windows 的图形用户界面、鼠标、激光打印机、光栅图形和以太网。
In 1970 Bob Taylor, after his stint handing out ARPA funds at IPTO, founded the famous lab at Xerox PARC (Palo Alto Research Center). I would work for him there a few years later. This is the lab where personal computing as we now understand it was created, integrating the personal computer, a windows-based graphical user interface, mouse, laser printer, raster graphics, and Ethernet.
拉里·罗伯茨(Larry Roberts)利用他在 ARPA 的 IPTO 领导职位创建了后来成为互联网的 ARPAnet。互联网现在是使用在施乐 PARC 的泰勒实验室发明的以太网组件来实现的。ARPAnet 上最早的四个节点中有两个是斯坦福研究所和犹他大学。
Larry Roberts used his IPTO leadership position at ARPA to cause the creation of the ARPAnet, which became the internet. The internet is now implemented using the Ethernet components that were invented at Taylor’s lab at Xerox PARC. Two of the four earliest nodes on the ARPAnet were Stanford Research Institute and the University of Utah.
在我撰写本章的初稿(2017 年 4 月)时,罗伯茨被选为加州计算机历史博物馆的研究员。他的官方介绍没有提到他在计算机图形学及其中心法则中的创始角色。他因在创建互联网中所扮演的角色而备受赞誉——这对任何人来说都是足够的成就。仅 IEEE 就获得了 1976 年的 Harry M. Goode 纪念奖、1990 年的 W. Wallace McDowell 奖和 2000 年的 Internet 奖。他是美国国家工程院院士,2001 年授予他查尔斯奖斯塔克德雷珀奖。但他从未因其对计算机图形学的基本贡献而获得同样的荣誉。81
As I wrote an early draft of this chapter (April 2017), Roberts was inducted as a Fellow of the Computer History Museum in California. His official induction made no mention of his founding role in computer graphics and its Central Dogma. He’s celebrated entirely for his role in founding the internet—quite enough accomplishment for any one man. He received from the IEEE alone the Harry M. Goode Memorial Award in 1976, the W. Wallace McDowell Award in 1990, and the Internet Award in 2000. He was a member of the National Academy of Engineering, which in 2001 awarded him the Charles Stark Draper Prize. But he was never similarly honored for his fundamental computer graphics contributions.81
动画是本书的一个持续主题。尽管萨瑟兰主要以计算机辅助设计而闻名,但他在 1963 年的画板中暗示了动画论文。图 6.35 是论文的一部分,是一个女孩和她眼睛的三个位置的简单绘图。这个概念是,如果你连续替换三个眼睛位置,她会眨眼。值得引用萨瑟兰的话说,看看我们已经走了多远:
Animation is a continuing theme of this book. Even though Sutherland is primarily known for computer-aided design, he hinted at animation in his 1963 Sketchpad thesis. Figure 6.35, which was part of the thesis, is a simple drawing of a girl and three positions of her eye. The notion is that if you substitute in the three eye positions in succession, she’ll wink. It’s worth quoting Sutherland to see how far we’ve come:
图 6.35
Figure 6.35
卡通化的一种方式是替换。例如,显示的女孩“Nefertite [原文如此]”。. . [上图]可以通过改变三种眼睛中的哪一种放在她原本没有眼睛的脸上的位置来眨眼。在电脑显示器上这样做让许多参观者感到很开心。
第二种卡通化方法是通过运动。通过适当地应用约束,可以制作一个简笔画来踩自行车。类似地,Nefertite 的头发也可以摆动。这是电影中更常见的卡通形式。82
One way of cartooning is by substitution. For example, the girl “Nefertite [sic]” shown . . . [above] can be made to wink by changing which of the three types of eyes is placed in position on her otherwise eyeless face. Doing this on the computer display has amused many visitors.
A second method of cartooning is by motion. A stick figure could be made to pedal a bicycle by appropriate application of constraints. Similarly, Nefertite’s hair could be made to swing. This is the more usual form of cartooning seen in movies.82
萨瑟兰错误地认为,这种第二种形式,通过受约束的运动,在电影中很常见。Cel 动画使用了中间形状的替换,直到千禧年它都是常用的形式。即使在今天,它仍然是通常的形式,如果用替换来表示在三个维度上的中间形状的插值。
Sutherland was wrong that this second form, by constrained motion, was usual in the movies. Cel animation used substitution of inbetween shapes, and it was the usual form until the millennium. And it’s still the usual form even today if substitution is taken to mean the interpolation of inbetween shapes in three dimensions.
在完成 MIT 论文后,Sutherland 加入了 ARPA 并资助了正如我们所见的 David Evans。然后他从 ARPA 辞职,去了哈佛几年,并于 1968 年加入了 Evans 创立的犹他大学计算机图形系。许多现代计算机图形学研究人员从该系毕业,每个人都讲述了萨瑟兰的首要地位的故事。尽管 Sutherland 没有直接从事动画,但犹他州的毕业生对于接下来章节中介绍的计算机动画行业来说是基础。
After his MIT thesis, Sutherland proceeded to join ARPA and fund, as we’ve seen, David Evans. Then he resigned from ARPA, went to Harvard for a few years and, in 1968, joined the University of Utah department of computer graphics that Evans had founded. Many researchers in modern computer graphics graduated from that department, each telling the story of Sutherland’s primacy. Although Sutherland didn’t directly pursue animation, Utah graduates were fundamental to the computer animation industry treated in the next chapters.
除非他阅读了与所有作品相关的所有注释,否则任何参观展览的人都不会知道他正在看的是艺术家、工程师、数学家还是建筑师制作的东西。
No visitor to the exhibition, unless he reads all the notes relating to all the works, will know whether he is looking at something made by an artist, engineer, mathematician, or architect.
—Jasia Reichardt,Cybernetic Serendipity策展人,1968 83
—Jasia Reichardt, Cybernetic Serendipity curator, 196883
贝尔实验室是我们在 1963 年观看 Edward Zajac 的计算机动画电影的所在地。它也是早期计算机动画制作系统的所在地。1964 年,贝尔实验室的研究员 Ken Knowlton 设计了一种计算机语言,用于以光栅模式缓慢生成电影,一次一帧地拍摄。它后来被称为 Beflix。它不是交互式的。它假设一帧在“高分辨率”模式下被分成 252 x 184 个小方块。“在打字机模式下”的小字符可以写到每个方块上。相机是散焦的,因此角色是不同强度的斑点。也就是说,它们是粗略的散布像素,在网格上且没有重叠。一部由诺尔顿在 1964 年以这种方式制作的原始电影可以在网上看到。Zajac 和一名学生在 1964 年和 1965 年使用诺尔顿的语言制作的一个,也可以在网上看到。84
Bell Labs was home as we’ve seen to Edward Zajac’s computer animated film in 1963. It was also home to an early computer animation production system. In 1964 the Bell Labs researcher Ken Knowlton devised a computer language for slowly generating movies—in raster mode—one frame at a time to film. It came to be known as Beflix. It was not interactive. It assumed a frame was divided, in “high-resolution” mode, into 252 by 184 little squares. Tiny characters “in typewriter mode” could be written to each square. The camera was defocused so that the characters were blobs of different intensities. That is, they were crude spread pixels, on a grid and without overlap. A primitive movie made this way by Knowlton in 1964 can be seen online. One made by Zajac and a student in 1964 and 1965, using Knowlton’s language, can also be seen online.84
锣声在此响起。艺术家们开始与贝尔实验室和其他地方的技术人员合作。这些是受过艺术家训练的艺术家,而不是计算机科学家,他们嗅到了空气中的新事物。他们是一个新品种,他们将计算视为一种可以在雕塑、音乐、诗歌和绘画艺术中探索的新鲜物质。我们在下一章中再次见到的一位是斯坦·范德贝克,他是一位实验电影制作人,他在 1960 年代在贝尔实验室制作电影,与肯·诺尔顿合作。
And here a gong sounds. Artists began to work with the technologists at Bell Labs and other places. These were artists trained as artists, not computer scientists, who sniffed something new in the air. They were a new breed who perceived computation as a fresh substance to explore in sculpture, music, poetry, and pictorial art. One, whom we meet again in the next chapter, was Stan Vanderbeek, an experimental filmmaker, who made movies at Bell Labs in the 1960s, working with Ken Knowlton.
这是著名的六十年代,定义受到质疑。一些计算机科学家将自己视为艺术家,这在艺术界引起了沮丧。争论直到今天,我不会在这里解决它们。Ken Knowlton,无论你称他为艺术家与否,都开始了一生对各种展示元素的实验。他使用任何东西——多米诺骨牌、骰子、玩具车和贝壳——创作了数十张数码照片,以传播他的像素。1990 年代,在他的第一部电影之后 34 年对于散布像素,Knowlton 仍然在介质中工作——使用茶壶碎片作为显示元素(图 6.36)。85
This was the famous Sixties, and definitions were being questioned. Some computer scientists saw themselves as artists, causing dismay in the artistic community. Arguments rage to this day, and I won’t settle them here. Ken Knowlton, whether you call him an artist or not, began a lifetime of experimentation with various display elements. He created dozens of digital pictures using anything—dominoes, dice, toy cars, and seashells, say—to spread his pixels. In the 1990s, 34 years after his first movie with spread pixels, Knowlton was still working in the medium—with teapot shards as display elements (figure 6.36).85
图 6.36
Figure 6.36
这不是茶壶,© Ken Knowlton,1998 年。Laurie M. Young 收藏。
This Is Not Not a Teapot, © Ken Knowlton, 1998. Collection Laurie M. Young.
尽管 1960 年代后期的许多人不认为计算机是一种艺术工具,但有一位女士认为,她 1968 年的展览已载入史册。Jasia Reichardt 的开创性展览 Cybernetic Serendipity于当年在伦敦开幕。图 6.37 中的目录封面(左)和海报(右)现在是收藏品。即便如此,她还是小心翼翼地避免称作品的创作者为“艺术家”。五十年后,这在某些圈子中仍然是一个雷区,实际诉讼悬而未决。86
Although many people in the late 1960s didn’t consider the computer an artistic tool, one woman did, and her 1968 exhibition has gone down in history. Jasia Reichardt’s seminal exhibition Cybernetic Serendipity opened in London that year. The catalog cover (left), and poster for it (right), in figure 6.37 are collector’s items now. Even then she carefully avoided calling the creators of the works “artists.” Fifty years later this is still a minefield in certain circles, with actual lawsuits pending.86
但是 Robin Forrest 没有问题地避开这个术语,尽管他在图 6.37 海报的右侧贡献了扭曲的线框补丁。“我从不认为我的形象是艺术,但她 [Reichardt] 做到了。所以,一定是艺术!但为什么是那个图像?” 87
But Robin Forrest has no problem eschewing the term, despite his having contributed the contorted wireframe patch on the right side of the figure 6.37 poster. “I never considered my image to be art, but she [Reichardt] did. So, it must be art! But why that image?”87
2005 年,Reichardt 采用了间接的方式来描述创作者,他重复了另一位作者的话:
In 2005 Reichardt took an indirect route to describing the creators, by repeating another author’s words:
他还指出,1967 年存在的大部分照片主要是出于业余爱好,他讨论了 Michael Noll、Charles Csuri、Jack Citron、Frieder Nake、乔治尼斯和惠普帕特森。作为计算机艺术史的先驱,我们今天对所有这些名字都很熟悉。. . . 计算机诗歌和艺术的可能性在 1949 年首次被提及。到 1950 年代初,它已成为大学和科学机构的话题,当计算机图形学问世时,艺术家已成为科学家、工程师、建筑师. 88
He also pointed out that most of the pictures in existence in 1967 were produced mainly as a hobby and he discussed the work of Michael Noll, Charles Csuri, Jack Citron, Frieder Nake, Georg Nees, and H. P. Paterson. All these names are familiar to us today as the pioneers of computer art history. . . . The possibility of computer poetry and art was first mentioned in 1949. By the beginning of the 1950s it was a topic of conversation at universities and scientific establishments, and by the time computer graphics arrived on the scene, the artists were scientists, engineers, architects.88
图 6.37
Figure 6.37
© Cybernetic Serendipity,1968 年,由 Franciszka Themerson 设计。
© Cybernetic Serendipity, 1968, design by Franciszka Themerson.
本章中的人物,除了罗宾福雷斯特(也作为《控制论机缘巧合》的创作者)之外,还有威廉·费特、肯·诺尔顿、斯坦·范德贝克和爱德华·扎亚克。89
People in this chapter, in addition to Robin Forrest, who also appeared as creators in Cybernetic Serendipity were William Fetter, Ken Knowlton, Stan Vanderbeek, and Edward Zajac.89
随着鳄鱼开始在 TX-2 屏幕上嬉戏,图片驱动的动画成为现实。
As crocodilesses began to cavort across the TX-2 screen, picture-driven animation became a practical reality.
——Ron Baecker,博士论文,麻省理工学院,1969 90
—Ron Baecker, PhD thesis, MIT, 196990
在我的讲述中,Ronald Michael Baecker 是麻省理工学院 TX-2 计算机的第四个主要受益者。他直接受到前三个中的两个,伊万萨瑟兰和蒂姆约翰逊的影响。我记得六十年代色彩缤纷的贝克尔是一个穿着 dashiki 的加拿大人,有一个很酷的新节目。91
Ronald Michael Baecker is the fourth major beneficiary of the TX-2 computer at MIT in my telling. He was directly influenced by two of the first three, Ivan Sutherland and Tim Johnson. I remember the colorful Baecker from the Sixties as a dashiki-clad Canadian, with a cool new program.91
1966 年末,贝克尔在 TX-2 上开始了一个简笔画动画程序——一台 Epoch 1 机器。然后,他开始与来自哈佛卡彭特视觉艺术中心的迷人而有才华的动画师 Eric Martin 合作,掌握动画动态的控制。这项工作的灵感来自 Sutherland 和 Johnson 使用“波形”来控制运动的建议。结果是 Genesys ,用于 Generalized-cel 动画系统。92
In late 1966 Baecker began a stick-figure animation program on TX-2—an Epoch 1 machine. He then began working with Eric Martin, a charming and talented animator from Harvard’s Carpenter Center of the Visual Arts, on mastering the control of animation dynamics. This work was inspired by suggestions from Sutherland and Johnson to use “waveforms” to control movements. The result was Genesys, for Generalized-cel animation System.92
Baecker 将波形概念推广到他所谓的“p 曲线”。这些曲线定义了通过时空改变位置的路径,而不是定义角色形状的曲线。如果他想让狗跳起来,他会在显示器上画一条曲线来显示时间的运动——他实际上是在时间上画出跳的。然后一幅狗的画就会沿着这条路走。如果路径是一跳,那么狗就跳了。如果他用一张女士鳄鱼的画代替狗,那么“没有鳄鱼”的人就会跳起来。Baecker 于 1969 年完成了 Genesys,使其成为最早的交互式计算机动画程序。93
Baecker generalized the waveform notion to what he called “p-curves.” These curves define paths of changing positions through spacetime, as opposed to curves that define a character’s shape. If he wanted a dog to hop, he drew a curve on the display showing the motion in time—he actually drew the hops through time. Then a drawing of a dog would follow that path. If the path was a hop, then the dog hopped. If he substituted a drawing of a lady crocodile for the dog, then the “crocodiless” hopped. Baecker completed Genesys in 1969, making it the earliest interactive computer animation program.93
但据我的老朋友兼同事、新泽西素描艺术家 Ephraim Cohen 说,Genesys “当时让大多数艺术工作者感到困惑”。以法莲非常擅长素描,有时他可以在服务员为他服务的时候画一个女服务员的肖像来免费用餐。他会毫不费力地捕捉到她的个性。
But Genesys “was kind of confusing for most art persons at that time,” according to my long-time friend and colleague Ephraim Cohen, a New Jersey sketch artist. Ephraim was so skilled at sketching that he could sometimes get a free meal by drawing a waitress’s portrait while she served his table. He would effortlessly capture her personality.
在最近的一封电子邮件中,Ephraim 告诉我,“我是由一位共同的朋友 Lynn Smith 介绍给 Ron 的,他当时是哈佛大学卡彭特中心的动画师。林恩和我是高中的朋友。罗恩正在寻找使用他的动画系统的人。” Ephraim 是一位数学家、程序员和艺术家,他并没有被 p 曲线弄糊涂。他解释说:“我很适合,所以我们被介绍了。这一切都是在林肯实验室的 TX-2 上完成的。另外,我在那里玩了一个下午玩Spacewar。我做的动画并不多。我想这一切都在两天内完成。”
In a recent email, Ephraim told me, “I was introduced to Ron by a mutual friend, Lynn Smith, then an animator at the Carpenter Center at Harvard. Lynn and I were friends in high school. Ron was looking for people to use his animation system.” Ephraim, a mathematician and programmer as well as an artist, wasn’t confused by the p-curves. He explained, “I was a natural fit, so we were introduced. It was all done on the TX-2 in Lincoln Labs. Also, I killed an afternoon there playing Spacewar. The animation I did was not much. I think it was all done in two days.”
他帮助 Baecker 制作了第一批 Genesys 动画作品,尽管该系统的绘图功能(参见图 6.38 中的研究)远远不能充分体现 Ephraim 的素描技巧。在接下来的章节中,我们将再次遇到 Ron Baecker、Eric Martin 和 Ephraim Cohen(分别是程序员、动画师和艺术家)。94
He helped Baecker with one of the first Genesys animated productions, although the system’s drawing capabilities (see the studies in figure 6.38) fell far short of doing justice to Ephraim’s sketching skills. We’ll reencounter Ron Baecker, Eric Martin, and Ephraim Cohen (respectively, the programmer, the animator, and the artist) in the next chapters.94
Baecker 的波形或 p 曲线类型的动画不是通常的动画,这就是它令人困惑的原因。Genesys 并没有像传统的在关键帧之间的 cel 动画中那样进行插值,也没有像 Baecker 所说的那样对“关键帧”进行插值:
Baecker’s waveform or p-curve type of animation wasn’t the usual one, which is what made it confusing. Genesys didn’t interpolate as was traditionally done in cel animation between keyframes, or “critical frames” as Baecker called them:
当关键动画师要求他的助手填充中间到一对关键帧的图片时,就会发生插值。有人建议这个过程的一部分可以机械化。我们不会在本文中进一步考虑这个问题。95
Interpolation occurs when the key animator asks his assistants to fill in the pictures intermediate to a pair of critical frames. It has been suggested that part of this process could be mechanized. We do not consider further that problem in this paper.95
然而,我们确实在这里进一步考虑插值。那是下一个。
We do consider interpolation further here, however. That’s next.
图 6.38
Figure 6.38
2016 年 6 月 12 日,Marceli Wein 和他的妻子 Susan 在安大略省南部我公婆的农场接我,然后驱车前往 Gananoque,在那里我们登上了一艘摩托艇,前往他们位于千岛群岛之一的家中。在圣劳伦斯河。那是一个寒冷的日子,所以我们围坐在壁炉旁,在经历了 40 年的不同方向之后,继续各自的生活。这位绅士给我讲了一个最神奇的故事:
On June 12, 2016, Marceli Wein and Susan, his wife, picked me up at my in-laws’ farm in southern Ontario and drove to Gananoque, where we boarded a motorboat for the short ride to their home on one of the Thousand Islands in the St. Lawrence River. It was a chilly day, so we sat around a fireplace and caught up on our separate lives after 40 years of going different directions. This gentle man told me a most amazing story:
还记得史蒂文·斯皮尔伯格的电影《辛德勒的名单》(1993),它告诉我们一个贪婪的德国商人奥斯卡·辛德勒如何在奥斯威辛集中营从纳粹恐怖中拯救了一千多名犹太人?好吧,Marceli 的父亲 Wolf Wein 是一位裁缝大师,在这份名单上排名第五。但在这些事件发生之前,沃尔夫·韦恩救了他 8 岁的儿子马塞利。用马塞利自己的话来说:
Remember Steven Spielberg’s movie Schindler’s List (1993), which told us how a greedy German businessman, Oskar Schindler, saved more than a thousand Jews from the Nazi horror at Auschwitz? Well, Marceli’s father, Wolf Wein, was a master tailor who became number 5 on that list. But before those events unfolded, Wolf Wein had saved his 8-year-old son, Marceli. In Marceli’s own words:
1943 年春天,我因猩红热被送往克拉科夫隔都的一家医院。. . . 我父亲听说医院要关闭,里面的每个人都会被杀。那天晚上他来找我,把我裹在毯子里,然后偷偷带我出去。. . . 我记得我和我父亲以及一群犹太工人走出去,他们从贫民区到一家奴工工厂。在路上,他把我交给了沿途等候的一位女士。接我的人是一位漂亮的女士,Zofia Jezierska,我后来称她为姑姑。我和她一起去了克拉科夫的一个公寓。几天后,我和她一起搬到了华沙。我现在是一个“隐藏的孩子”。96
In the spring 1943 I was sent to a hospital in Krakow ghetto with scarlet fever. . . . My father heard that the hospital was being shut down and everyone in it would be killed. He visited me that night, wrapped me in a blanket, and smuggled me out. . . . I remember walking out with my father and a group of Jewish workers, as they went from the ghetto to a slave labour factory. On the way, he handed me to a woman who was waiting along the route. The person to whom I was handed over was a fine lady, Zofia Jezierska, whom I then called my aunt. I went with her to a flat in Krakow. After a few days I moved with her to Warsaw. I was now a “hidden child.”96
Zofia 将 Marceli 培养为罗马天主教徒,并以 Marek Czach 为名。与此同时,他的哥哥被枪杀,他的母亲死在集中营。但多亏了辛德勒,他的父亲沃尔夫幸免于难。他和马塞利最终于 1952 年团聚并定居在蒙特利尔。
Zofia raised Marceli as a Roman Catholic with the nom de guerre Marek Czach. Meanwhile his older brother was shot and killed, and his mother died in a concentration camp. But thanks to Schindler, his father Wolf survived. He and Marceli eventually reunited and settled in Montreal in 1952.
Marceli 在那里的麦吉尔大学学习,并在攻读博士学位期间接触到了计算机成像的潜力。1966 年,他加入了加拿大国家研究委员会的 Nestor Burtnyk,从事早期计算机图形研究,这让他兴奋不已。“我们对非技术人员如何与计算机交互感兴趣。” 97
Marceli studied at McGill University there and was exposed to the potential of computer imaging during his PhD studies. Excited by the possibilities he joined Nestor Burtnyk in 1966 at Canada’s National Research Council doing early computer graphics research. “We were interested in how non-technical people could interact with computers.”97
Burtnyk 在 1969 年的计算机图形会议上听取了迪斯尼动画师的演讲。动画师解释了我们之前在电影章节中讨论的 cel 动画过程: 动画师用铅笔轮廓绘制关键帧。然后中间帧,关键帧之间,由中间帧创建。Inkers 将印度墨水中的铅笔线描摹到 cels(赛璐珞片材)上,而遮光剂则用颜色填充轮廓。Burtnyk 和 Wein 决定使用计算机创建一个 cel 动画助手。
Burtnyk heard a Disney animator talk at a computer graphics conference in 1969. The animator explained the cel animation process that we discussed previously in the chapter on movies: A head animator draws keyframes in pencil outline. Then inbetween frames, between the keyframes, are created by inbetweeners. Inkers trace the penciled lines in India ink onto cels (celluloid sheets), and opaquers fill the outlines with color. Burtnyk and Wein decided to create a cel animation assistant using a computer.
Burtnyk 编写了二维插值程序,该程序将在关键帧中获取一条线,在下一个关键帧中获取相应的线,并在中间帧的适当位置插入一条线到另一条线。也就是说,计算机将成为关键帧动画系统中的中间人。因此,他们在 1970 年创建了第三个记录在案的二维计算机动画系统,这是在诺顿和贝克尔之后——所有实际用于制作的系统。98
Burtnyk wrote the two-dimensional interpolation program that would take a line in a keyframe and the corresponding line in the next keyframe and interpolate one to the other with lines in appropriate positions in the inbetween frames. That is, the computer would become the inbetweener in a system called keyframe animation. Thus they created in 1970 the third documented two-dimensional computer animation system, after Knowlton’s and Baecker’s—all systems that were actually used in productions.98
Knowlton 的 Beflix 系统是第一个完全面向像素的系统,无需插值几何。Baecker 的 Genesys 沿着曲线移动了固定的几何对象,但没有对它们进行插值。Burtnyk 和 Wein 的系统是第一个插值或中间的计算机动画系统。
Knowlton’s Beflix system, the first, was completely pixel oriented, with no geometry to interpolate. Baecker’s Genesys moved fixed geometrical objects along curves but didn’t interpolate them. Burtnyk and Wein’s system was the first interpolating, or inbetweening, computer animation system.
Burtnyk 和 Wein 于 1996 年被评为加拿大计算机动画技术之父。他们在 1997 年获得了美国技术学院奖,以表彰他们的贡献。
Burtnyk and Wein were honored in 1996 as the Fathers of Computer Animation Technology in Canada. And they received a technical Academy Award in the United States in 1997 for their contribution.
摩尔定律于 1965 年问世。它的宣布开启了计算加速的第二个时代。它带来了我们现在所知道的 Digital Light 成果。
Moore’s Law arrived in 1965. Its announcement ushered in Epoch 2 of computation speedup. It brought Digital Light as we now know it to fruition.
“法律”——因为它不是真正的法律——以世界上最成功的计算机芯片公司英特尔的联合创始人戈登·摩尔命名。英特尔是加利福尼亚硅谷的基石公司,其知识起源直接追溯到晶体管。晶体管导致了集成电路——单个芯片上的许多晶体管——以及摩尔定律。在摩尔定律之前,计算机变得越来越强大,因为它们变得越来越强大。之后,它们变小了。也就是说,它们变得更密集。
The “Law”—because it isn’t really a law—was named for Gordon Moore, cofounder of Intel, the most successful computer chip company in the world. Intel, a cornerstone company of California’s Silicon Valley, traces its intellectual origins directly to the transistor. The transistor led to the integrated circuit—lots of transistors on a single chip—and to Moore’s Law. Before Moore’s Law, computers got bigger as they got more powerful. After it, they got smaller. That is, they got denser.
摩尔这样制定他的“定律”:集成电路芯片上的元件数量每 18 个月翻一番。实际上,他先是说 12,然后是 24,但是平均卡住。毕竟这是“法律”,而不是法律。这只是 1965 年的一次观察——仅基于四个微薄的数据点。99
Moore formulated his “Law” this way: The number of components on an integrated circuit chip doubles every 18 months. Actually, he first said 12, then later 24, but the average stuck. It’s a “Law,” and not a law, after all. It was simply an observation in 1965—based on just four meager data points.99
他还预测——这只是事后看来很幽默——“没有理由相信它不会在至少 10 年内保持几乎不变。” 但它现在已经保持了55年。它已成为法律,尽管事实上没有理由以物理学为基础相信它确实是法律。100
He also predicted—it’s only humorous in hindsight—that “there is no reason to believe it will not remain nearly constant for at least 10 years.” But it’s held constant now for 55 years. It’s become the Law, despite the fact that there’s no reason grounded in physics to believe it really is one.100
我之前说过摩尔定律的一个方便的重新表述:关于计算机的所有优点每五年都会提高一个数量级:“10 Xin 5”很容易记住它(发音为“10 ex in 5”)。图 6.39 是 Epoch 2 的图片,左侧是 1965 年的第一年。
I stated a handy reformulation of Moore’s Law earlier: Everything good about computers gets an order of magnitude better every five years: “10X in 5” is an easy way to remember it (pronounced “ten ex in five”). Figure 6.39 is a picture of Epoch 2, with its Year One, 1965, on the left.
脚踏实地的商界称摩尔定律曲线为“曲棍球棒”。这是一个值得死去的利润图表。以显示的最后一个角度延伸曲线(接近垂直)以查看曲棍球棒。这是一个指数增长的画面。指数意味着爆炸。摩尔定律描述并预测了指数级增长计算速度或内存密度,或者成本和大小的指数级下降——计算机的所有优点都会以指数级的方式变得更好。
The down-to-earth business world calls the Moore’s Law curve a “hockey stick.” It’s a profits chart to die for. Extend the curve at the last angle shown—approaching vertical—to see the hockey stick. This is a picture of exponential increase. Exponential means explosive. Moore’s Law describes and predicts an exponential increase in computational speed or memory density, or an exponential decrease in cost and size—everything good about computers gets exponentially better.
图 6.39
Figure 6.39
摩尔定律是推动世界的阿基米德杠杆。人类能力的放大在第一纪元达到百万倍。然后摩尔定律在第二纪元中利用了另一个千亿倍——到 2025 年将达到万亿倍。自计算机发明以来,人类能力的放大将达到五亿分之一到那时折叠——18 个数量级!这是不可想象的 - 和愚蠢的 - 像天翻地覆一样,但它是真实的。
Moore’s Law is the Archimedean lever that has moved the world. Amplification of human capabilities reached a millionfold in Epoch 1. Then Moore’s Law in Epoch 2 has leveraged the factor another hundred-billionfold—a trillionfold by 2025. Amplification of human capabilities since the invention of the computer, all told, will have been a quintillionfold by then—18 orders of magnitude! That’s as unimaginable—and as silly—as skydillionfold, but it’s real.
任何现代计算方面的历史——尤其是数字光——都不能忽视摩尔定律的巨大作用。这是过去五年中所有特定发现和进步的爆炸性背景——没有它,其中大多数都是不可行的。随着我们在接下来的章节中继续阅读像素的传记,摩尔定律所扮演的角色将越来越明显。在这种情况下,概念的谱系并没有脱离历史时间——脱离摩尔定律时钟的沉重滴答声。
No history of any modern aspect of computing—of Digital Light in particular—can ignore the spectacular role of Moore’s Law. It’s the explosive background against which all specific discoveries and advances of the last five decades have taken place—most of them infeasible without it. As we proceed through the biography of the pixel in the next chapters, the role Moore’s Law plays will be increasingly evident. The genealogy of concepts in this case is not divorced from historical time—from the heavy ticking of the Moore’s Law clock.
我们也不能忽视当前的滴答作响。“定律”仍在发展超新星。事实上,它正在超越。一颗超新星的亮度可以比它的起源恒星亮 100 亿倍,但计算机很快就会比原来的机器强大一万亿倍——仅在 Epoch 2 中——。掌握摩尔定律的最高级概念,无论多么微不足道,都是理解计算和计算机以及数字光的核心。
Nor can we disregard that ticking clock in the present. The “Law” is still going supernova. In fact, it’s going beyond. A supernova can shine 10 billion times brighter than its originating star, but computers will soon be a trillion times more powerful—in Epoch 2 alone—than the original machines. Getting a handle, however slight, on the superlatives of Moore’s Law is at the heart of understanding computation and computers—and Digital Light.
我们已经看到了摩尔定律到底是什么——但为什么会这样呢?部分答案是,实现比特没有迫在眉睫的物理障碍。它只是某种东西的存在或不存在——比如电压。它没有大小。这只是一个区别,仅此而已。这是纯粹的信息。答案的其余部分必须反映人类可以创新的最大速度。给定技术的指数级改进——计算机芯片技术中的摩尔定律——衡量一大群有创造力的人在竞争下改进技术的最终速度,当没有最终的物理障碍阻碍它的改进时当技术必须以自己的方式付费时。
We’ve seen what Moore’s Law is exactly—but why is it? A partial answer is that there’s no imminent physical barrier to the realization of a bit. It’s merely the presence or absence of something—say a voltage. It has no size. It’s just a distinction and nothing more. It’s pure information. The rest of the answer must reflect the maximum rate at which humans can innovate. The exponential improvement of a given technology—Moore’s Law in the case of computer chip technology—measures the ultimate speed at which a large group of creative humans can proceed to improve a technology, under competition, when there is no ultimate physical barrier to its improvement and when the technology must pay its own way.
从表面上看,摩尔定律是一个谜。如果我们相信它,那么我们为什么要为干预步骤而烦恼呢?如果我们知道计算机将在三年内提高四倍,为什么还要先建立两倍的提高倍数呢?如果我们知道计算机将在 10 年内提高 100 倍,那么为什么还要为 5 年内只有 10 个版本的因素而烦恼呢?为什么不直接去更高的因素?
On the face of it, Moore’s Law is a puzzler. If we believe it, then why should we bother with the intervening steps? If we know that computers will improve by a factor of four in three years, why bother building the factor of two improvement first? If we know that computers will improve by a factor of 100 in 10 years, then why bother with the factor of only 10 version in 5 years? Why not go directly to the higher factor?
这个问题的极端形式使其荒谬性显而易见。如果我们在 1965 年就知道计算机在 2020 年会好上一千亿倍——就像现在一样——为什么我们是否费心制造在 1970 年好 10 倍、在 1975 年好 100 倍、在 1980 年好 1000 倍等等的计算机?为什么我们不直接开始制造 2020 年的机器,跳过所有年份和 pokey 机器之间的时间?这种形式的问题显示了缺陷。1965 年,假设我们对新的“法律”有信心,我们根本无法想象 2020 年的计算机——更不用说如何建造它了。工程师必须到达每个级别,然后才能开始想象到达下一个级别的方法,然后创建它。我们不能跳过中间步骤。
An extreme form of this question makes its absurdity obvious. If we knew in 1965 that computers would be a hundred billion times better in 2020—as they are—why did we bother to build the computers that were 10 times better in 1970, 100 times better in 1975, 1,000 times better in 1980, and so forth? Why didn’t we just proceed to build the 2020 machines, skipping all the years—and pokey machines—between? The question in this form shows the flaw. In 1965, assuming that we had faith in the new “Law,” we were simply unable to imagine the computer of 2020—much less how to build it. Engineers have to arrive at each level before they can even begin to imagine a way to reach the next one, and then create it. We can’t skip the intervening steps.
不,我们必须遵循摩尔定律逐步改进芯片技术的路径,才能想象下一个改进可能是什么。这就像生物的进化。微小的变化最终会聚合成巨大的变化——生物的生存能力在每一步都完好无损。从细菌到婴儿不可能一步一步直接飞跃。就像在达尔文进化论中一样,摩尔定律的变化提高了拟合度——在计算机的情况下朝着更便宜、更小、更密集和更快的方向发展。在任何一种情况下,我们都看不到累积的变化将走向何方,因为没有目的论。但是,当涉及到技术时,我们会实施每一步,看看它是否真的有效,然后获得勇气、洞察力和对工程的掌握,以进行下一步。这也是我们如何评估进行下一步所必需的金融赌博的方式。我们需要知道它在可行的范围内。
No, we have to follow the Moore’s Law path of incremental improvement of chip technology to even imagine what the next improvement could be. It’s like the evolution of living things. Tiny changes aggregate into eventually massive changes—with the viability of the living thing intact at every step. There couldn’t have been a direct one-step leap from a bacterium to a baby. Just as in Darwinian evolution, Moore’s Law changes improve the fit—toward cheaper, smaller, denser, and faster in the case of computers. And we can’t see where the accumulated changes are heading in either case because there is no teleology. But, when it comes to technology, we implement each step to see if it actually works, then gain the courage, the insight, and the engineering mastery to proceed to the next step. It’s also how we can assess the financial gamble that’s necessary to proceed to the next step. We need to know that it’s within feasible bounds.
摩尔定律将向我们表达的硬件现象描述为放大。曾经深不可测的变得可行,然后变得平凡。
Moore’s Law describes the hardware phenomenon that expresses itself to us as Amplification. What was once unfathomable becomes feasible, then ordinary.
然而,实际上,他正在检查的不是迪亚斯帕。他在记忆细胞中穿行,看着这座城市的梦幻形象。. . . 对于计算机、记忆电路和所有创造阿尔文所看图像的众多机制来说,这只是一个简单的透视问题。他们“知道”城市的形态;因此他们可以展示它,就像它从外面看到的一样。
Yet it was not, in reality, Diaspar he was examining. He was moving through the memory cells, looking at the dream image of the city. . . . To the computers, the memory circuits, and all the multitudinous mechanisms that created the image at which Alvin was looking, it was merely a simple problem of perspective. They “knew” the form of the city; therefore they could show it as it would appear from the outside.
——Arthur C. Clarke,《城市与星辰》,1956 年,摘自 Jim Blinn 的博士论文,1978 年101
—Arthur C. Clarke, The City and the Stars, 1956, as excerpted in Jim Blinn’s PhD dissertation, 1978101
当然,最终的展示将是一个房间,计算机可以在其中控制物质的存在。摆在这样的房间里的椅子足以坐下来。摆在这样的房间里的手铐会限制人,而摆在这样的房间里的子弹会是致命的。通过适当的编程,这样的展示实际上可以是爱丽丝走进的仙境。
The ultimate display would, of course, be a room within which the computer can control the existence of matter. A chair displayed in such a room would be good enough to sit in. Handcuffs displayed in such a room would be confining, and a bullet displayed in such a room would be fatal. With appropriate programming such a display could literally be the Wonderland into which Alice walked.
—Ivan Sutherland,《终极展示》,1965 102
—Ivan Sutherland, The Ultimate Display, 1965102
带注释的爱丽丝梦游仙境,由马丁·加德纳于 1960 年撰写,是一代人的必备读物,他们着迷于自己的心灵旅行和神奇的蘑菇。所以毫不奇怪,Ivan Sutherland 对 1965 年终极展示的描述读起来像是一个迷幻的梦——并唤起了爱丽丝。1968 年,萨瑟兰在哈佛实现了这一梦想的第一次通过,这一举动巩固了他作为 60 年代计算机图形学主要领导者的名声。他称其为头戴式显示器. 佩戴它的用户会看到一个简单的 3D 计算机生成场景,即“虚拟现实”,与用户周围的真实世界相混合。虚拟现实 (VR) 是计算机生成部分的矛盾现代造词。VR 与现实世界的混合称为增强现实 (AR),即由 VR “增加”或“改进”的现实。这两个术语都是对“现实”的奇怪看法,但一直存在。
The Annotated Alice in Wonderland, written in 1960 by Martin Gardner, was de rigueur reading for a generation fascinated with their own mind trips and magic mushrooms. So it’s no surprise that Ivan Sutherland’s description of the ultimate display in 1965 reads like a psychedelic dream—and invokes Alice. In an act that cemented his fame as the dominant leader of computer graphics in the Sixties, Sutherland implemented a first pass of that dream at Harvard in 1968. He called it a head-mounted display. A user who wore it was treated to a simple three-dimensional computer-generated scene, a “virtual reality,” mixed with the real world in the user’s surround. Virtual reality (VR) is the oxymoronic modern coinage for the computer-generated part. The mixture of a VR with the real world is called augmented reality (AR)—that is, reality “increased” or “improved” by the VR. Both these terms are odd takes on “reality” but have stuck.
有人认为 Sutherland 的头戴式显示器是 VR 或 AR 的首次实现。有早期的头戴式显示器,但这是第一个近乎实时地跟踪头部位置并调整虚拟场景以适应用户不断变化的视角的显示器。图 6.40 显示了它的光学系统(这个人不是Sutherland)。103
Some consider Sutherland’s head-mounted display the first realization of VR or AR. There had been earlier head-mounted displays, but this was the first that tracked head position and adjusted the virtual scene, in close to real time, to accommodate the user’s always changing perspective. Figure 6.40 shows its optics system (the man is not Sutherland).103
萨瑟兰的头戴式显示器远不能控制“物质的存在”,但它确实呈现了一个由直线段创建的三维世界的立体视图。这个视角是拉里·罗伯茨的视角,它结合了齐次坐标和矩阵操作。Sutherland 1963 年的 Sketchpad 没有采用计算机图形学的中心法则,但他 1968 年的头戴式显示器做到了。104
Sutherland’s head-mounted display was far short of controlling “the existence of matter,” but it did present a stereo view of a three-dimensional world created from straight line segments in perspective. And the perspective was Larry Roberts’s perspective, the one that combined homogeneous coordinates and matrix manipulations. Sutherland’s Sketchpad of 1963 didn’t embrace the Central Dogma of computer graphics, but his head-mounted display of 1968 did.104
摩尔定律使 VR 成为可能。头戴式显示器的发展早在 Epoch 2 之后——在 Gordon Moore 于 1965 年制定“法律”之后。事实上,Sutherland 在他的头戴式显示器设计中使用了集成电路芯片。105
Moore’s Law enabled VR. The head-mounted display development occurred early in Epoch 2—after Gordon Moore formulated the “Law” in 1965. Indeed, Sutherland used integrated circuit chips in his head-mounted display design.105
据传闻,萨瑟兰随后著名地声称,计算机图形学中的所有问题都已解决!这对于年复一年继续解决计算机图形问题的几代贡献者来说是一个惊喜,而且仍然如此——Siggraph 会议上到处都是他们的论文。在我与萨瑟兰的谈话中,他告诉我他永远不会发表那种声明。真正与他的说法背道而驰的是萨瑟兰在 1966 年写的一篇名为“计算机图形学中的十个未解决问题”的论文。但传闻中的说法与他给犹他州另一位杰出毕业生詹姆斯·卡吉亚的建议一致:
Sutherland then famously claimed, according to rumor, that all the problems in computer graphics had been solved! That’s a surprise to generations of contributors who have continued to solve computer graphics problems year after year, and still do—the Siggraph conference is full of their papers. During my conversation with Sutherland he told me he would never have made that statement. And truly belying the claim that he did is a 1966 paper Sutherland wrote called “Ten Unsolved Problems in Computer Graphics.” But the rumored claim is consistent with advice he gave James Kajiya, another outstanding Utah graduate:
进行研究的最好方法是选择一个每个人都认为非常困难的问题。找到一种全新的方式来看待它,让 90% 的事情变得简单。解决简单的 90%。然后其他人都会努力工作 10% 并参考你。106
The best way to do research is to pick a problem that everyone thinks is really hard. Find a fresh way of looking at it that makes 90% of it easy. Solve the easy 90%. Then everyone else will work on the hard 10% and reference you.106
图 6.40
Figure 6.40
萨瑟兰本人在一个完全不同的领域转向了一个非常困难的问题。他与 Carver Mead(创造了摩尔定律一词)合作,解决了设计越来越高密度的集成电路芯片的看似棘手的问题。也就是说,萨瑟兰将注意力转向保持摩尔定律的活力和良好。今天,他仍在俄勒冈州波特兰的办公室里解决问题的一个困难方面。107
Sutherland himself moved on to a very hard problem in a completely different sphere. He paired up with Carver Mead (who coined the term Moore’s Law) to solve the seemingly intractable problems of designing integrated circuit chips of higher and higher density. That is, Sutherland turned his attention to keeping Moore’s Law alive and well. He’s still working on a difficult aspect of the problem today from his office in Portland, Oregon.107
我通过描述我在 1970 年代初向 Ravi Shankar 演示的演示来开始本章。我的目的是通过使用二维情况来推动基于几何的模型的概念,并通过在样条概念中反向显示采样定理来完善采样定理的重要性。最后,样条曲线作为点的插值或近似导致补丁作为插值或曲线的近似(实际上是样条曲线)。这引入了计算机图形学的三维世界。
I started this chapter by describing a demonstration I presented to Ravi Shankar in the early 1970s. My purpose was to drive home the notion of a model based on geometry by using a two-dimensional case and to round out the importance of the Sampling Theorem by showing it in reverse in the concept of spline. Finally, the spline as an interpolation or approximation of points led to the patch as an interpolation or approximation of curves (of splines, in fact). That introduced the three-dimensional world of computer graphics.
然后我回到旋风时代的末期,在这一章的剩余部分中,我们在纳粹和苏联的威胁以及美国对它们的大规模技术反应所催生的环境中度过了 1950 年代和 1960 年代。美国政府,尤其是 ARPA 和 NASA 提供了一个受保护和控制的世界,让计算机创新者茁壮成长。他们在受保护的环境中获得了慷慨的支持,没有通常的盈利和行业竞争负担。
I then returned to the end of the Whirlwind era and spent the rest of the chapter taking us through the 1950s and 1960s in a milieu spawned by the Nazi and Soviet threats and the massive American technological responses to them. The US government and especially ARPA and NASA provided the protected and controlled world that let the computer innovators thrive. They were given their heads in protected environments with generous support and without the usual burdens of profitability and industrial competition.
因为带有彩色笔触的 Ravi Shankar 演示来自 1970 年代,所以您可能会误以为本章的其余部分(大约 1950 年代和 1960 年代)有彩色图形。但它没有。我们只是现在,在 1960 年代末期,色彩即将开花,摩尔定律发电机已准备好驱动它。
Because the Ravi Shankar demonstration with its colored brushstrokes was from the 1970s, you might have been lulled into thinking that the rest of the chapter, about the 1950s and 1960s, had color graphics. But it didn’t. We are only now, at the end of the 1960s, at the point where color is about to flower, and the Moore’s Law dynamo is poised to drive it.
从本章中的形状和灰度图片开始,我们将在接下来的章节中学习颜色、阴影、透明度、纹理、光线、阴影等,一般归类为阴影图像。我们学习如何渲染单一颜色的阴影三角形区域,然后将其放大到完整的计算机图形荣耀。
From shapes and grayscale pictures in this chapter, we graduate in the next chapters to color, shades, transparency, texture, light, shadow, and so forth, generically classed as shaded images. We learn how to render a single colored, shaded triangle-shaped area and then Amplify it to full computer graphics glory.
我进一步将我们的注意力限制在计算机图形的计算机动画部分,我们最终将了解电影是如何从机器的内脏中产生的。
I further restrict our focus there to just the part of computer graphics that is computer animation, and we’ll finally learn how a movie springs from the guts of a machine.
图 7.1
Figure 7.1
第一个彩色像素,1967 年,用于渲染阿波罗月球计划模拟器 NASA-2 中的登月舱。
First color pixels, 1967, used to render the Lunar Module in NASA-2, the Apollo Moon Project simulator.
时期 1 是灰色的。时代 2 是彩色的。1965 年戈登·摩尔 (Gordon Moore) 发表了他著名的“法则”后不久,Digital Light 中的色彩就出现了,这一事件拉开了第二纪元的序幕。这绝非巧合。每一个彩色像素显示器(而且有很多)都是一面飘扬的旗帜,以庆祝——不仅是为了庆祝这一事件,也是为了计算机历史的 Epoch 2 以及它给我们带来的爆炸性放大。像素在迷幻的 60 年代获得了色彩——也就是 1967 年的爱之夏和人类存在的那一年。但这只是巧合。数字色彩并不是反文化的成就。它是主流冲向月球或远离地球的结果,这取决于你如何看待它。直到写完这一章,我才发现完整的故事。1
Epoch 1 was gray. Epoch 2 is color. Color dawned in Digital Light soon after Gordon Moore stated his famous “Law” in 1965, the event that kicked off Epoch 2. It was no coincidence. Every color pixel display (and there are very many) is a flag flying in celebration—not only of that event but also of computer history’s Epoch 2 and the explosive Amplification it brought us. Pixels acquired color in the psychedelic Sixties—in the very year, 1967, of the Summer of Love and the Human Be-In. But that was just coincidence. Digital color wasn’t a countercultural achievement. It resulted from the mainstream rush to the Moon—or away from Earth, depending on how you look at it. I didn’t discover the full story until I wrote this chapter.1
在本章和下一章中,我将简要解释颜色的来源,然后追踪从最初的彩色像素到第一部数字电影的路径,并解释如何计算它们。令人震惊的是,这一切都发生在大约 35 年之内。但这就是摩尔定律和由此产生的放大的含义:每 5 年增加 10 倍。在那些年里,驱动数字光的发电机撕裂了七数量级的能量浪涌——一颗散发着光芒的超新星,今天的每一个屏幕以及本章和下一章的每一页都充满了光芒。第一部数字电影的创作者在这种新浪潮中冲浪,因为它在我们文明的海岸上坠毁。然而,这些电影只是世界上更大的力量在起作用的微小的彩色指标。
In this and the next chapter I’ll briefly explain where color came from, then trace the path from those first colored pixels to the first digital movies and explain how to compute them. The shocker is that it all happened in about 35 years. But that’s what Moore’s Law and the resulting Amplification means: a factor of 10 every 5 years. During those years the dynamo that drove Digital Light ripped through a seven-order-of-magnitude power surge—a supernova with a glow that suffuses every screen today and every page of this chapter and the next. The creators of the first digital movies surfed this new kind of wave as it crashed on the shores of our civilization. Yet those movies were only tiny colorful indicators of a much larger force at work in the world.
这本像素传记从采样的发明开始,到下一章的大数字融合结束。在这些端点之间,我打算涵盖所有数字光,但摩尔定律的本质表明,对于这样一个爆炸性大的领域,以及它的子领域数量不断增加,这本书的空间非常小。如果章节要恰当地代表整体,摩尔定律超新星将迫使更多和(指数)更多的技术进入每个连续的页面。
This biography of the pixel begins with the invention of sampling and ends, in the next chapter, with the Great Digital Convergence. Between those endpoints I intend to cover all Digital Light, but the very nature of Moore’s Law suggests that this book has vanishingly small space for such an explosively large field, with its ever-increasing number of subfields. The Moore’s Law supernova would force more and (exponentially) more technology into each successive page if chapters were to properly represent the whole.
我的解决方案是让面向图片的计算机图形学成为整个广阔领域的最终典范。在面向图片的计算机图形学中,数字电影将代表所有其他内容。由于此处面向图片的计算机图形学代表了更大的数字光领域,因此数字电影代表了从大数字融合中出现的所有其他类型的计算机图形学——包括电子游戏、计算机辅助设计、飞行模拟器、应用程序界面,和虚拟现实。
My solution is to let picture-oriented computer graphics be the final exemplar of the whole vast field. And within picture-oriented computer graphics, digital movies will stand for all the rest. As picture-oriented computer graphics here represents the much larger field of Digital Light, so digital movies represent all the many other kinds of computer graphics that emerged from the Great Digital Convergence—including electronic games, computer-aided design, flight simulators, app interfaces, and virtual reality.
下面是我们将如何进行。从 1965 年开始,我们开始以令人费解的数量级迈出摩尔定律的浪潮,朝着千禧年的数字大融合迈进。我们采取了五个大步骤来实现这一目标——数字电影的缩影。这些步骤被转换为两章彩色像素传记的五个子章。这两章以指数级的速度展开。子章节由摩尔定律在相应时间内起作用的因素:X1、10、100、1,000和 10,000 X—X即以五年为增量。因此,每个子章节的步骤都提醒我们摩尔定律工程奇迹的重要贡献,它赋予了一切力量。XX
Here’s how we’ll proceed. Starting in 1965, we begin to mount the Moore’s Law wave in mind-stretching order-of-magnitude steps, toward the Great Digital Convergence at the millennium. We take five large steps to get there—to the digital movie epitome. These steps are cast as five subchapters of a two-chapter biography of the color pixel. These two chapters unwind at exponential speed. The subchapters are labeled by the Moore’s Law factor at work during the corresponding time: 1X, 10X, 100X, 1,000X, and 10,000X—that is, in five-year increments. Thus each subchapter step reminds us of the essential contribution of the Moore’s Law engineering marvel which empowered it all.
我们从数字光的黎明一章中知道,像素是视野的样本。此外——这是至关重要的——它是一个已被数字化为比特的样本。在本章中,我们使用像素来采样彩色视野。自然,我们称它们为彩色像素。
We know from the Dawn of Digital Light chapter that a pixel is a sample of a visual field. Furthermore—and this is crucial—it’s a sample that has been digitized into bits. In this chapter we use pixels to sample colorful visual fields. Naturally, we call them color pixels.
我们也知道我们看不到彩色像素。它没有形状。这是一个单一点的视野样本。它在位置的数学网格上具有一个位置,并具有与之相关的单一颜色。要看到一个不可见的像素,它必须由显示设备上的显示元素扩展并添加到那里的其他扩展像素。扩展和添加重新引入了原始视野在采样之前具有的无限颜色。这只是重述了最重要的采样定理的魔力。
We also know that we can’t see a color pixel. It has no shape. It’s a sample of a visual field at a single point. It has a location on a mathematical grid of locations and a single color associated with it. To see an invisible pixel, it must be spread by a display element on a display device and added to the other spread pixels there. The spreading and adding reintroduces the infinity of colors that the original visual field had before it was sampled. That’s just a restatement of the magic of the all-important Sampling Theorem.
但是颜色是如何与像素“关联”的呢?每个显示元素都是现实世界中发出彩色光的一块物质,它必须发出数百万种不同颜色的光才能在现代世界中发挥作用。因此,必须有一个输入控件来告诉显示元素要发出多种颜色中的哪一种。
But how is a color “associated” with a pixel? Each display element is a piece of matter in the real world that glows with colored light, and it must emit light of millions of different colors to be useful in the modern world. So there must be an input control to tell a display element which of its many colors to emit.
关键是像素不包含颜色。它拥有颜色控件。彩色显示元素因制造商而异,因此让我们考虑一个典型的。它由三个相邻的微小发光部分组成,每个部分都贡献三种原色成分中的一种——红色、绿色或蓝色(用于发射光)。在正常观看距离下,我们的眼睛将这些微小的独立发光部分融合在一起,形成单一的发光颜色。这样的彩色显示元件需要三个输入控件,例如电压,以改变三个发光的小部件。电压越高,主成分发光越亮。
The point is that a pixel doesn’t hold a color. It holds color controls. Color display elements vary from manufacturer to manufacturer, so let’s consider a typical one. It’s composed of three tiny light-emitting parts in proximity, each contributing one of the three primary color components—red, green, or blue (for emitted light). At normal viewing distances our eyes fuse these tiny separate glowing parts together into a single glowing color. Such a color display element needs three input controls, voltages say, to vary the three small glowing parts. The higher the voltage, the brighter that primary component glows.
我们对彩色像素的定义要求它必须在数字控制下显示。彩色像素中的位驱动彩色显示元件的三个数字控件。说像素存储颜色非常方便,我们有时会使用该术语。但像素实际上并不存储颜色——就像位实际上并不保存 0 和 1 一样。在下一节中,我会小心地说像素控制而不是存储颜色。
Our definition of a color pixel requires that it must be displayed under digital control. The bits in a color pixel drive the three digital controls of a color display element. It’s so convenient to say that a pixel stores a color that we sometimes use that terminology. But pixels don’t actually store colors—just as bits don’t actually hold 0s and 1s. In the next section, I’m careful to say that a pixel controls, rather than stores, a color.
让我们回顾一下如何进行数字计数——尤其是颜色。我们之前曾使用过弱电灯开关作为隐喻。开关可以打开或关闭,类似于表示 1 或 0 的位(如果我们坚持使用数字作为名称)。所以一个1位像素只能控制两种不同颜色的显示。通常,这两种颜色是黑色和白色,但它们可以是任何两种固定颜色——比如淡紫色和黄绿色。
Let’s review how to count digitally—colors in particular. We’ve used the lowly light switch before as a metaphor for a bit. A switch can be on or off, analogous to a bit representing 1 or 0 (if we insist on numbers as names). So a 1-bit pixel can control the display of only two different colors. Typically, the two colors are black and white, but they could be any two fixed colors—say, mauve and chartreuse.
两个电灯开关可以处于四个不同的位置:都打开、都关闭,或者以两种不同的方式一个打开另一个关闭。因此,一个 2 位像素可以将显示元素驱动为四种可能颜色中的一种。随着像素中的位数增加一,它可以控制的可能颜色的数量增加一倍。三个电灯开关可以在八个位置,当新的第三个开关打开时,两个电灯开关的所有四种可能性,加上新开关关闭的两个电灯开关的所有四种可能性。因此,一个 3 位像素可以驱动或控制八种可能的颜色。等等。为方便起见,在提到像素大小(以位为单位)后,我经常将等量的可能颜色控制在括号中。
Two light switches can be in four different positions: both on, both off, or one on and the other off in two different ways. So a 2-bit pixel can drive a display element into one of four possible colors. As the number of bits in a pixel increases by one, the number of possible colors it can control doubles. Three light switches can be in eight positions, all four possibilities for two light switches with the new third switch on, plus all four possibilities for two light switches with the new switch off. So a 3-bit pixel can drive or control eight possible colors. And so forth. For convenience, I will often put the equivalent number of possible colors controlled in parentheses after mentioning the size of a pixel in bits.
当位数达到六位及以上时,彩色像素变得严重。存储像素颜色控件的明显位置就在这些位中。事实上,这种直接存储是当今最常用的方法——这就是为什么像素存储颜色的概念看起来如此自然的原因。
Color pixels became serious when the number of bits reached six and above. The obvious place to store pixel color controls is in those bits. Such direct storage is, in fact, the method most often used today—and that’s why the notion of a pixel storing a color seems so natural.
但是在内存非常昂贵的早期,存储颜色控件的间接方式很流行。它使用所谓的颜色图或颜色查找表。像素中的位被解释为存储在计算机内存中其他位置的颜色控制表中的行号。那行内存位(不是像素位)控制颜色。这个想法是保持每像素的位数很小——因为有这么多的像素——同时使每像素可能的颜色选择的数量很大。
But during the early days of very expensive memory, an indirect way of storing the color controls was popular. It used what was called a colormap, or a color lookup table. The bits in a pixel were interpreted as a row number in a table of color controls stored somewhere else in computer memory. That row of memory bits (not the pixel’s bits) controlled the color. The idea was to keep the bits per pixel small—since there were so many pixels—while making the number of possible color choices per pixel large.
考虑已经提到的 1 位像素。一位可以直接打开或关闭显示元素。就这样。因此,1 位像素可以直接控制的唯一可能颜色是黑色表示关闭 (0),白色表示开启 (1)。但间接地,一位可以指向内存中其他地方的颜色图的两行之一——第 0 行或第 1 行。假设每个颜色图行有 24 位。这足以控制超过 1600 万种不同颜色的显示可能性。只有两行,因此任何时候只有两种可能的颜色可用,但它们可能像淡紫色和黄绿色一样微妙。由于一级间接以电子速度发生,因此就狡猾的人类而言,它会立即发生。使用颜色图技巧,像素不会控制显示元素。它选择控制显示元素的颜色映射表的行。
Consider the 1-bit pixel already mentioned. One bit can directly turn on or off a display element. That’s all. So the only possible colors that a 1-bit pixel can control directly are black for off (0) and white for on (1). But indirectly that one bit can point to one of two rows—row 0 or row 1—of a colormap elsewhere in memory. Suppose each colormap row has 24 bits. That’s enough bits to control over 16 million different color display possibilities. There are only two rows, so only two possible colors are available at any one time, but they could be as subtle as mauve and chartreuse. Since the one level of indirection happens at electronic speeds, it occurs instantaneously so far as pokey humans are concerned. With the colormap trick, a pixel doesn’t control a display element. It selects the row of a colormap table that controls a display element.
一个 8 位像素是一个更典型的例子。一个 8 位像素可以指向颜色映射表中的 256 行之一。同样,让我们假设每个颜色图行都有 24 位。因此,取而代之的是在 256 种可能的颜色(价值 8 位)中直接可用,颜色图技巧使超过 1600 万种颜色(价值 24 位)间接成为可能。在这两种情况下,可以控制的颜色数量保持不变 (256),但在间接情况下,这些颜色的选择数量会大大增加。
An 8-bit pixel is a more typical example. An 8-bit pixel can point at one of 256 rows in a colormap table. Again, let’s assume each colormap row has 24 bits. Thus, instead of 256 possible colors (8 bits’ worth) available directly, the colormap trick makes over 16 million colors (24 bits’ worth) possible indirectly. The number of colors that can be controlled remains the same (256) in both cases, but the number of choices for those colors is immensely increased in the indirect case.
在本章中,我们遇到了 6 位像素(64 色)和 8 位像素(256 色),然后我们跃升至 24 位像素(超过 1600 万色)。一个人最多可以识别大约 1600 万种颜色,因此在一般情况下几乎没有理由使用超过 24 位的像素。24 像素位数在千禧年变得普遍,从而实现了大数字融合。所以 24 位像素(我们说的正好是 16兆色)是当今的标准——在数字电影或手机中。
In this chapter we encounter 6-bit pixels (64 colors) and 8-bit pixels (256 colors), then we leap to 24-bit pixels (over 16 million colors). A human can discern up to about 16 million colors, so there is little reason in ordinary circumstances to use pixels with more than 24 bits. A pixel bit count of 24 became common at the millennium—thus enabling the Great Digital Convergence. So 24-bit pixels (with exactly 16 megacolors we say) are the norm today—in a digital movie or a cellphone.
摆脱过去制约的一种方法是通过数字计算机的故障安全功能模拟替代未来。这是人类所知道的最高水平的“艺术”,实际上是在不知不觉中创造一个新世界。. . . 纯粹审美探索的可能性是革命性的,尚未尝试。City-Scape是迈向未来的第一步。
One way to be free of past conditioning is to simulate alternative futures through the fail-safe power of the digital computer. This is “art” at the highest level ever known to man, quite literally the creation of a new world imperceptibly gaining on reality. . . . The possibilities for purely aesthetic exploration are revolutionary and have yet to be attempted. City-Scape is the first step toward that future time.
——Gene Youngblood,扩展电影,1970 2
—Gene Youngblood, Expanded Cinema, 19702
Gene Youngblood 是 1960 年代洛杉矶报纸的影评人和专栏作家。1970 年,也就是数字大融合前的 30 年,他思考了即将到来的变化,并在《扩展电影》中发表了他的想法。它是媒体艺术领域的权威书籍,这是一个将实验电影、视频——甚至是新生的计算机图形学——作为新兴艺术形式推广的新领域。这是对充满活力的六十年代的总结和庆祝——这是反文化革命的明显成就。令人惊讶的是,这本书告诉我们很多关于数码光的历史。
Gene Youngblood was a film critic and columnist for Los Angeles newspapers in the 1960s. In 1970, three decades before the Great Digital Convergence, he pondered the coming changes and published his thoughts in Expanded Cinema. It was a definitive book in media arts, a new field that promoted experimental film, video—and even nascent computer graphics—as emerging artforms. It was a summation and celebration of the vibrant Sixties in many ways—a clear achievement of the countercultural revolution. Surprisingly, the book turns out to tell us a lot about the history of Digital Light.
我们在第 2 章中了解到像素这个词在 1965 年首次使用。Youngblood 在Expanded Cinema中只提到过一次“PIXELS” ——就这样,全部大写。仅仅五年后,这对他来说仍然是一个陌生的词。摩尔定律也存在于 1965 年,但尚未引起公众的注意,正如 Youngblood 的观察所证明的那样:
We learned back in chapter 2 that the word pixel was first used in 1965. Youngblood mentioned “PIXELS” in Expanded Cinema only once—just like that, all uppercase. It was still a strange word to him only five years later. Moore’s Law existed, also since 1965, but hadn’t yet caught the public’s attention, as evidenced by Youngblood’s observation:
计算机生成运动中的实时逼真图像所需的比特要求远远超出了目前的技术水平。3
The bit requirements necessary for computer generation of real-time realistic images in motion are as yet far beyond the present state of the art.3
Youngblood 并不知道,但他在数码色彩到来的那一刻拍下了珍贵的快照。他没有定义像素,但他的例子让我们专注于定义。他书中的提示引导我找到了第一个有色人种。
Youngblood didn’t know it, but he had taken a precious snapshot of the moment when digital color arrived. He didn’t define pixels, but his examples focus us on a definition. And hints in his book guided me to the first colored ones.
如果Expanded Cinema是对的,那么太空竞赛就是彩色像素的孵化器。正如我们在第 6 章中了解到的那样,军事组织 ARPA 资助了预彩色计算机图形学。它的姊妹机构 NASA 大约在同一时间成立,将计算机图形学推向了彩色。
If Expanded Cinema was right, the space race promised to be the color-pixel incubator. The military organization ARPA funded pre-color computer graphics, as we learned in chapter 6. Its sister institution NASA, founded about the same time, pushed computer graphics into color.
在题为“控制电影和计算机电影”的一章中,Youngblood 讨论了 NASA 与加州帕萨迪纳加州理工学院喷气推进实验室 (JPL) 在水手航天器计划中的合作。从 1962 年到 1973 年,NASA 与 JPL 合作完成了七次成功的火星、金星和水星无人飞行任务。JPL 为该项目建立了一个成像系统。Youngblood 有这样的说法:
In a chapter titled “Cybernetic Cinema and Computer Films,” Youngblood discussed NASA’s involvement with the Jet Propulsion Laboratory (JPL) at Caltech in Pasadena, California, on the Mariner spacecraft program. From 1962 to 1973, NASA teamed up with JPL for seven successful unmanned missions to Mars, Venus, and Mercury. JPL built an imaging system for the project. Youngblood had this to say about it:
这个奇妙的系统将实时电视信号转换为存储在特殊数据光盘上的数字图像元素。图片本身不存储;只有它的数字翻译。4
This fantastic system transforms the real-time TV signal into digital picture elements that are stored on special data-discs. The picture itself is not stored; only its digital translation.4
也就是说,它存储的是离散像素,而不是连续的模拟电视信号。
That is, it stored discrete pixels, not continuous analog television signals.
本部分的题词来自 Youngblood 对City-Scape的讨论,这是一部由 Peter Kamnitzer 拍摄的简化城市景观的彩色电影。Youngblood 在 1970 年还观察到这部电影是在通用电气为 NASA 制造的模拟器上制作的:
The epigraph for this section comes from Youngblood’s discussion of City-Scape, a color film of a simplified urban vista by Peter Kamnitzer. Youngblood also observed in 1970 that the film had been made on a simulator that General Electric built for NASA:
它已被用于模拟登月条件已有十多年了。5
It has been used for more than ten years to simulate conditions of lunar landings.5
NASA 的承包商 GE 和 JPL 早在 1960 年或 1962 年就已经显示彩色像素了吗?请记住,计算机图形学的三驾马车和中心法则——应使用文艺复兴时期的视角在二维中观察三维欧几里得几何——如目前使用的那样,于 1963 年在麻省理工学院首次亮相。如果颜色出现在前面,那将是相当令人惊讶的那个黑白地标。让我们探索一下颜色对 NASA 的意义。
Could NASA contractors GE and JPL have been displaying color pixels as early as 1960 or 1962? Keep in mind that the Triumvirate and the Central Dogma of computer graphics—that three-dimensional Euclidean geometry shall be viewed in two dimensions using Renaissance perspective—debuted, as currently used, at MIT in 1963. It would be quite a surprise if color preceded that black-and-white landmark. Let’s explore what color meant to NASA.
Youngblood 描述了用于以每像素 6 位(64 色)描绘数字彩色图像的 JPL 系统。最终系统是这样工作的:图片被发送到地球并存储在一个磁性旋转磁盘上,然后重新组合成 512 行,每行 480 像素,用于彩色电视显示。但是 JPL 的第一张图像(图 7.2)并没有那么复杂:它只有 200 x 200 像素存储在内存中,而且它的显示是在纸上手绘的!
Youngblood described the JPL system for portraying digital color images at 6 bits per pixel (64 colors). Ultimately the system worked like this: Pictures were sent to Earth and stored on a magnetic spinning disk, then reassembled into 512 rows of 480 pixels each for color television display. But JPL’s very first image (figure 7.2) wasn’t quite so sophisticated: it had only 200 by 200 pixels stored in memory, and its display was hand-drawn on paper!
用于存储像素的数字存储器有一个特殊的词。之所以称为帧缓冲区,是因为它可以缓冲(或存储)一帧(或数字图片)。这只是普通的记忆——除了你可以看到里面有什么。帧缓冲区与显示设备密切相关,显示设备每 30 秒扫描一次帧缓冲区内存,并使用那里的像素来控制例如电视显示器上的颜色。对于第一张太空图片,JPL 使用了机械帧缓冲区——磁性旋转磁盘——由 6 位像素组成,代表 200 行,每行 200 像素。6
There’s a special word for a digital memory that’s used to store pixels. It’s called a framebuffer because it can buffer (or store) one frame (or digital picture). It’s just ordinary memory—except that you can see what’s in it. A framebuffer is intimately associated with a display device, which sweeps through the framebuffer memory every thirtieth of a second and uses the pixels there to control the colors on, say, a television display. For its first space picture, JPL used a mechanical framebuffer—that magnetic spinning disk—composed from 6-bit pixels, representing 200 rows of 200 pixels each.6
图 7.2
Figure 7.2
水手 4 号在 1965 年 7 月的一次飞行中从火星传回了它的第一个图像数据。航天器通过交替的红色和绿色滤镜向地球传递了 21 张照片。由于这些照片是从一艘移动的航天器上拍摄的,因此没有记录连续的图像。但是在它们确实重叠的地方,可以进行粗略的颜色重建——只有红色和绿色成分,但没有蓝色。工程师们渴望看到火星,他们不想等待计算机处理和显示数据。相反,他们从一家美术用品商店购买彩色蜡笔,并将显示元素手绘到原始像素值的数字打印输出上。这不是电子显示“设备”,因此这不是我们定义的第一幅数字彩色图像。7
Mariner 4 sent its first image data back from Mars on a July 1965 flyby. The spacecraft relayed 21 photographs to Earth, taken through alternating red and green filters. Since the photos were taken from a moving spacecraft, successive images weren’t in register. But where they did overlap, a crude color reconstruction was possible—with just the red and green components, but no blue. The engineers were eager to see Mars, and they didn’t want to wait for the computer to process and display the data. Instead they bought colored pastel sticks from an art supplies store and hand-painted the display elements onto a numerical printout of the raw pixel values. This wasn’t an electronic display “device,” so this wasn’t the first digital color image by our definition.7
仔细检查发现这些不是来自火星的颜色。官方报告中明确指出,“虽然得到的数据大致相当于一张双色照片,但并不是要把两张照片组合成一张彩色照片,很多因素结合在一起,阻碍了数码照片的直接解读。”数据作为任何特定颜色的指示。” 兴奋的工程师所做的是为 6 位像素分配颜色,将较亮的颜色分配给较亮的像素,将较暗的颜色分配给较暗的像素。由此产生的颜色表明火星的颜色是他们选择粉彩棒的意外。那些工程师还不知道火星的实际颜色。8
Close inspection reveals that these were not colors from Mars. The official report states clearly, “Although the data obtained are roughly equivalent to a two-color photograph, it was not intended that the two pictures should be combined to form a color picture, and many factors combine to prevent the direct interpretation of the digital data as indicative of any specific color.” What the excited engineers did was assign colors to the 6-bit pixels, with lighter colors assigned to brighter pixels and darker colors to dimmer ones. That the resulting colors suggest the colors of Mars was an accident of their choice of pastel sticks. Those engineers didn’t yet know the actual colors of Mars.8
Mariner 工程师使用的技术类似于将颜色间接存储在像素中的颜色图方式。他们设置了一个颜色键或图例,将棕色分配给 45 到 50 的像素值,将黄色分配给 20 到 25 的像素值,依此类推。他们只使用了六种不同的颜色,而不是技术允许的 64 种颜色(因为 6 位可以存储那么多)。另一种说法是,他们的颜色表将所有 64 个像素值编码为六种颜色。例如,表的第 45 行到第 50 行,对应于从 45 到 50 的像素值,都存储了相同的颜色,棕色。9
The Mariner engineers used a technique that resembles the colormap way of storing a color indirectly in a pixel. They set up a color key, or legend, that assigned brown to pixel values from 45 to 50 and yellow to values from 20 to 25, and so forth. They used only six different colors, rather than the 64 that the technique permitted (because 6 bits can store that many). Another way to put it is that their color table coded all 64 pixel values into just six colors. For instance, rows 45 through 50 of the table, corresponding to pixel values from 45 to 50, all stored the same color, a brown.9
彩色映射图像有时称为伪彩色或假彩色图像。颜色是任意分配给像素值的,没有特定的顺序——与 Mariner 工程师所做的没有什么不同。不要求颜色图中的颜色代表现实。早期的计算机艺术家如此频繁地使用伪色——光谱颜色按彩虹顺序排列——以至于它很快变得像扎染的 T 恤一样陈旧。
A colormapped image is sometimes called a pseudocolor, or false-color, image. The colors are arbitrarily assigned to the pixel values, in no particular order—not unlike what the Mariner engineers did. There’s no requirement that colors in a colormap represent reality. Early computer artists used pseudocolor so often—with spectral colors in rainbow order—that it quickly became as trite as tie-dyed T-shirts.
尽管这是太空计划中的一项重大成就——一张来自火星的彩色照片!——但有两件事让我不能称它为第一个彩色数码灯。首先,正如我们在早期的计算机和电影史中看到的那样,机械磁盘是事件“首次”的一个瑕疵;我们真的在寻找第一个完全电子化的彩色像素实现——使用完全电子化的帧缓冲区。其次,显示元素的手工实现将其置于 Digital Light 之外。但 Mariner 系统是 Digital Light 中引人注目的“几乎首创”。
Although this was a momentous achievement in the space program—a color picture from Mars!—two things keep me from calling it the first colored Digital Light. First, mechanical disks are a blemish on the “firstness” of the event, as we saw in early computer and movie histories; we’re really looking for the first completely electronic implementation of color pixels—using a fully electronic framebuffer. And second, the hand implementation of the display elements puts it outside Digital Light. But the Mariner system was a spectacular “almost first” in Digital Light.
如果 JPL 没有第一个彩色像素,那么来自 Youngblood 的Expanded Cinema的另一个建议是通用电气呢?
If JPL didn’t have the first color pixels, what about General Electric, the other suggestion garnered from Youngblood’s Expanded Cinema?
1964 年 8 月的一份通用电气“最终报告”描述了我认为最早使用计算颜色的方法。为休斯顿的 NASA 载人航天器中心建造的 GE 飞行模拟器的模型仅包含一个无限的地平面,该地平面被覆盖或纹理化,并带有重复的颜色瓷砖。图 7.3 是该模拟器的早期彩色图片,通常称为 NASA-1。它相当粗略地代表了飞行员通过航天器窗口看到的月球表面——红色区域是着陆区,不同的纹理代表陨石坑。10
An August 1964 GE “Final Report” described what I thought might be the earliest use of computed color. A GE flight simulator built for NASA’s Manned Spacecraft Center in Houston featured a model consisting only of an infinite ground plane that was covered, or textured, with repeating tiles of color. Figure 7.3 is an early color picture from that simulator, often called NASA-1. It represents rather crudely the Moon’s surface as seen by a pilot through the spacecraft window—the red area is the landing zone and the different textures represent, say, craters.10
您可以将每个图块视为由较小图块或子图块组成的小光栅有序数组。所以瓦片是一个正方形,由 8 x 8 数组中的 64 个正方形子瓦片组成。这些不是像素!它们实际上是小的几何正方形。NASA-1 计算了一个平铺平面的透视图,一次一个显示元素穿过彩色电视显示器的每个扫描线。它做到这一点非常快,实时。这就是它在 1964 年花费数百万美元的原因。对于每条扫描线上的每个显示元素,NASA-1 计算出飞行员在该点看到纹理平面时会看到哪个图块,以及哪个子图块。这是一个几何计算,使用透视几何。然后它简单地查找那个子图块的颜色并将其发送到彩色显示器。11
You can think of each tile as being a small raster-ordered array of smaller tiles, or subtiles. So a tile is a square consisting of 64 square subtiles in an 8 by 8 array. These are not pixels! They are actually small geometric squares. NASA-1 computed a perspective view of the tiled plane, one display element at a time across each scanline of a color television display. It did this very fast, in real time. That’s why it cost millions of dollars in 1964. For each display element on each scanline, NASA-1 computed which tile a pilot would see at that point looking out into the textured plane, and which subtile. That’s a geometrical calculation, using perspective geometry. Then it simply looked up the color of that subtile and sent it to the color display.11
图 7.3
Figure 7.3
这听起来很像对连续的视觉场景进行采样,然后在显示时从样本中重建场景。但这些样本是模拟的。在这个模拟器中,没有以数字方式存储颜色。每种颜色都是通过旋转电位器来设置的,比如老式收音机上的音量旋钮或天花板灯上的旋转调光器开关。所以 NASA-1 采集了颜色样本,但没有将它们转换为彩色像素。它们不是最早的彩色像素。
That sounds very much like sampling a continuous visual scene and then reconstructing the scene at display time from the samples. But these samples were analog. In this simulator, a color was not stored digitally. Each color was set by rotating a potentiometer, something like the volume knob on an old-fashioned radio or the revolving dimmer switch on your ceiling lights. So NASA-1 took color samples but didn’t convert them to color pixels. They weren’t the earliest color pixels.
这种 NASA-1 着色技术的另一个“几乎首创”是在计算机图形学中使用了一种称为纹理映射的技术。存储在数组中的颜色为原本毫无特色的广阔空间提供了良好的结构。然而,我不称这是纹理映射的第一次使用,因为它不是完全数字化的。首先是等待一个名叫 Ed Catmull 的年轻人的到来,他于 1974 年在犹他大学的一篇非凡的博士论文中首次描述了它。我们将在本章后面听到更多关于他和那篇论文的信息。
Another “almost first” of this NASA-1 coloring technique was the use of a technique called texture mapping in computer graphics. Colors that are stored in an array give fine structure to an otherwise featureless expanse. I don’t call this the first use of texture mapping, however, because it wasn’t fully digital. That first would await the arrival of a young man, named Ed Catmull, who first described it in a remarkable PhD thesis at the University of Utah in 1974. We’ll hear more about him and that thesis later in this chapter.
罗伯特·舒马克(“Shoo mahk er”)是 1960 年代初在纽约州北部通用电气公司 NASA-1 的一名工程师。在从他位于盐湖城的家中发送的一封电子邮件中,他分享了一张自己当时工作的照片,留着平顶发型和一根烟斗。他详细解释了我刚才描述的模拟器图像是如何生成的,尽管那些早期计算机的内存非常有限。最重要的是,他揭示了样本和像素之间的细微差别。12
Robert Schumacker (“Shoo mahk er”) was an engineer on NASA-1 at GE in upstate New York in the early 1960s. In an email sent from his home in Salt Lake City, he shared a photo of himself at work then, with a flattop haircut and a pipe. And he explained in detail how the simulator image I just described was generated despite the very limited memory of those early computers. Most importantly, he revealed that subtle distinction between sample and pixel.12
但后来他告诉我这个项目最奇怪的方面。模拟航天器的滚动——如偏航、俯仰和滚动——必须向飞行员展示。普通电视中的扫描线始终是水平的。但在 NASA-1 中,他们使用阴极射线管的电磁偏转器实时旋转整个电视显示器。舒马克本人已经实施了这种独特的模拟技术。这是一项令人瞠目结舌的工程壮举。但在 1964 年之前的摩尔定律中,即使预算为 100 万美元,它仍然比计算滚动更便宜。13
But then he told me about the most truly bizarre aspect of the project. The roll—as in yaw, pitch, and roll—of a simulated spacecraft had to be displayed to a pilot. Scanlines in normal television are always horizontal. But in NASA-1 they rotated the entire television display using the electromagnetic deflectors of the cathode ray tube—in real time. Schumacker himself had implemented this unique analog technique. It was a jaw-droppingly difficult engineering feat. But it was still cheaper in pre–Moore’s Law 1964 than computing the roll, even with a million-dollar budget.13
Youngblood 在他的书的历史快照中再次暗示了第一个颜色像素。他描述了令人印象深刻的惠特尼家族(加利福尼亚的一个艺术王朝)的美丽集体作品,约翰和詹姆斯兄弟,以及约翰的三个儿子小约翰、迈克尔和马克。惠特尼有第一个彩色像素吗?14
Youngblood dropped another hint about first color pixels in his book’s historical snapshot. He described the beautiful collective work of the impressive Whitney family—an artistic dynasty in California—brothers John and James, and John’s three sons, John Jr., Michael, and Mark. Did the Whitneys have the first color pixels?14
老约翰·惠特尼 (John Whitney Sr.) 令人惊叹的早期“计算机艺术”不是 Digital Light 的一部分,因为它是用模拟设备制作的。他早期的电影作品真的很美,给了我个人灵感,但它们不是数字的。根本没有像素,也没有数字计算机。但在 1968 年,当老约翰创作了一部名为Permutations的电影时,情况发生了变化。它使用了一台数字计算机,但它的图形是书法的,而不是像素的。Permutations中的颜色是事后使用滤色器添加的。这不是计算的。排列很可爱,但不是我们想要的。15
John Whitney Sr.’s stunning early “computer art” isn’t part of Digital Light because it was made with analog devices. His early cinematic works are truly beautiful, and inspired me personally, but they aren’t digital. There were no pixels at all, and no digital computer. But that changed in 1968 when John Sr. created a film called Permutations. It used a digital computer, but its graphics were calligraphic, not pixels. And the color in Permutations was added after the fact, using color filters. It wasn’t computational. Permutations is lovely, but not what we’re looking for.15
他的兄弟詹姆斯惠特尼也创造了美丽的作品,但没有像素。所以我们转向年轻一代。其中两个,小约翰和迈克尔,确实制作了数字计算机艺术电影。迈克尔是第一个使用像素的惠特尼,他的二进制位模式(1969 年)。但他也在光学上添加了颜色——仍然没有颜色像素。稍后,正如我们将看到的,摩尔定律将特别是小约翰推向彩色像素。16
His brother James Whitney also created beautiful work but without pixels. So we turn to the younger generation. Two of them, John Jr. and Michael, did make digital computer art films. Michael was the first Whitney who utilized pixels, with his Binary Bit Patterns (1969). But he too added the color optically—still no color pixels. Later, Moore’s Law would move John Jr., in particular, toward color pixels, as we’ll see.16
我们已经看到 Gene Youngblood 在他的关于 Peter Kamnitzer 的City-Scape的书中写道(如果不是狂赞的话) 。Kamnitzer 是加州大学洛杉矶分校的建筑学教授,他想要一个用于城市规划的图形系统,而不是艺术。为艺术而拍照肯定会被认为是对稀有物品的轻率使用当天的系统,提醒我们在婴儿初生之光的早期也有类似的看法。
We’ve already seen that Gene Youngblood wrote (if not raved) in his book about Peter Kamnitzer’s City-Scape. Kamnitzer, an architecture professor at the University of California at Los Angeles, wanted a graphics system for city planning, not art. Making pictures for art’s sake would surely have been perceived as a frivolous use of the rare systems of the day, reminding us of a similar perception in the early days of Baby’s First Light.
无论 Kamnitzer 的论点是什么,他都成功获得了通用电气为 NASA 位于休斯顿的载人航天中心建造的价值 200 万美元(今天为 1500 万美元)的模拟器。1968 年,他用它创建了City-Scape,这是一个简化的城市景观的实时驾车穿越。模拟是彩色的,但是颜色太原始了,以至于 Youngblood 没有费心在Expanded Cinema中使用它。事实上,图 7.4 来自 Youngblood 的书。
Whatever Kamnitzer’s argument was, he successfully gained access to a $2 million simulator ($15 million today) that General Electric built for NASA’s Manned Spacecraft Center in Houston. In 1968 he used it to create City-Scape, a real-time drive-through of a simplified urban landscape. The simulation was in color, but the color was so primitive that Youngblood didn’t bother to use it in Expanded Cinema. In fact, figure 7.4 is from Youngblood’s book.
图 7.4
Figure 7.4
相反,Youngblood 在提到City-Scape时惊叹于“在计算机生成之前不存在代表性图像”。换句话说,NASA 系统是从零开始制作像素的。Youngblood 对此的惊讶让我们今天感到惊讶。17
Youngblood marveled instead, referring to City-Scape, that “no representational imagery existed before it was produced by the computer.” In other words, the NASA system made pixels from scratch. Youngblood’s astonishment at that amazes us today.17
但让我感兴趣的是这些像素是彩色像素。1968 年,Youngblood 将该系统称为 NASA-2。但它到底是什么,它是什么时候第一次产生颜色的?城市景观讨论是最终刷新我的历史猎物的线索。
But what interested me was that those pixels were color pixels. In 1968. Youngblood called the system NASA-2. But what was it exactly, and when did it first make color? The City-Scape discussion was the clue that finally flushed my historical quarry.
我们的孩子学会了新的技巧,在成熟到成年作为人类进步的工具方面又迈出了一步。当有声电影第一次出现时,人们说世界永远不会一样。半色调 [阴影] 图形已经到来,计算机世界已经永远改变。
Our child has learned a new trick, has taken another step forward in maturing to full adulthood as a tool for the advancement of mankind. When talking movies first appeared, people said the world would never be the same. Half-tone [shaded] graphics has arrived and the computer world has been changed forever.
——W。杰克·布克奈特,1969 18
—W. Jack Bouknight, 196918
NASA-2 是 NASA-1 的儿子。它也是在通用电气为 NASA 航天器模拟——阿波罗月球计划而建造的。相同的工程师创建了这两个系统。以下是 NASA-2 的一些重要的第一次,所有这些都发生在纽约州北部的通用电气公司。它显示:
NASA-2 was son of NASA-1. It too was built at GE for NASA spacecraft simulation—for the Apollo Moon Project. The same engineers created both systems. Here are some important NASA-2 firsts, all of which occurred at General Electric in upstate New York. It displayed:
当我开始了解 NASA-2 拥有第一个彩色像素时,我发现我们在讨论 NASA-1 时遇到的两位关键工程师 Rodney Rougelot(“Roozsh low”)和 Robert Schumacker 都已退休到盐湖城。
As I began to understand that NASA-2 had the first color pixels, I discovered that two of its key engineers, Rodney Rougelot (“Roozsh low”) and Robert Schumacker, who we met in the discussion of NASA-1, had both retired to Salt Lake City.
2018年,我提议去见他们两个。Rougelot 亲切地邀请我到他在犹他大学附近的家中参加这次活动。经过几十年的合作,他和舒马克仍然是最好的朋友。所以他们都在那里,我们聊了七个小时。
In 2018 I proposed a trip to meet the two of them. Rougelot graciously invited me to his home near the University of Utah for the event. He and Schumacker are still best friends after decades of working together. So they both were there, and we chatted for seven delicious hours.
罗德·鲁格洛 (Rod Rougelot) 是一个爱开玩笑、口齿伶俐的大人物。我没有注意到他是两个人中的矮个,直到他笑着指出了这一点。然后他告诉我一个特别有意义的相遇:
Rod Rougelot was a joking, articulate large presence. I didn’t notice that he was the shorter of the two, until he pointed it out—with a grin. Then he told me about an especially meaningful encounter:
1951 年,Rougelot 在开课前四天抵达纽约州北部的康奈尔大学。他很早就参加了在童子军营地举行的新生迎新活动,在那里,他与另一位新生唐纳德·格林伯格(Donald Greenberg)共用一个帐篷,后者将成为另一位计算机图形学先驱。正如我们将看到的,他们的生活将继续交织在一起。21
In 1951 Rougelot arrived at Cornell University in upstate New York four days before classes began. He was early to attend a freshmen orientation held in a Boy Scout camp, where he shared a tent with another entering freshman, Donald Greenberg—who would become another computer graphics pioneer. Their lives would remain intertwined, as we will see.21
Rougelot 于 1956 年毕业于康奈尔大学,获得电气工程学士学位。1960 年 7 月,他开始在通用电气位于康奈尔家乡伊萨卡的工厂工作。
Rougelot graduated from Cornell in 1956 with a bachelor’s degree in electrical engineering. In July 1960 he started work at GE’s facility in Ithaca, also Cornell’s hometown.
同年,两个朋友中个子较高的 Bob Schumacker 从麻省理工学院毕业,获得电气工程硕士学位,也加入了 GE Ithaca。当我在盐湖城 Rougelot 的家中见到他时,他已经丢掉了他年轻时的平顶和烟斗。他现在是一名首席飞行员和一名民间舞者。他说话的时候直视你,这不是胡说八道。当我询问技术细节时,我得到了它们,并根据我的技能水平进行了仔细校准。
That same year Bob Schumacker, the taller of the two friends, graduated from MIT with a master’s in electrical engineering and joined GE Ithaca too. When I met him in Rougelot’s home in Salt Lake City, he had dropped the flattop and pipe of his youth. He’s now a master pilot and a folk dancer. He looks directly at you when he speaks, and it’s no nonsense stuff. When I asked for technical details, I got them, carefully calibrated for my skill level.
他们两人——以及经常被提及的其他团队——为阿波罗计划创建了 NASA-1 和 NASA-2 模拟器。他们在伊萨卡以北约 50 英里的 GE 锡拉丘兹建造了 NASA-1 和 NASA-2。对于 NASA-2,该团队使用了刚刚可用的集成电路。到 1967 年初,这个模拟器已经显示了第一个彩色像素,并使用这些像素显示了第一个 3D 渲染对象。它们是摩尔定律的首批成果之一,就本书而言,它们标志着第二纪元的真正开始。22
The two of them—with an often-mentioned team of others—created the NASA-1 and NASA-2 simulators for the Apollo Project. They built NASA-1 at GE Ithaca and NASA-2 at GE Syracuse, about 50 miles north of Ithaca. For NASA-2 the team used integrated circuits, which were just becoming available. By early 1967, this simulator had displayed the first color pixels and—using those pixels—the first three-dimensional rendered objects. They were among the first fruits of Moore’s Law and, so far as this book is concerned, marked the true start of Epoch 2.22
1972 年,Rougelot 和 Schumacker 加入了盐湖城的 Evans & Sutherland,并在那里创建了一系列令人印象深刻的、日益复杂的飞行模拟器。Ivan Sutherland 在 Skype 对话中告诉我,这些前 GE 工程师对 E&S 随后的成功至关重要。Rougelot 最终成为该公司的首席执行官。23
In 1972 Rougelot and Schumacker joined Evans & Sutherland in Salt Lake City and created there an impressive series of flight simulators of increasing sophistication. Ivan Sutherland told me, in a Skype conversation, that these former GE engineers were most important to the subsequent success of E&S. Rougelot eventually became CEO of the company.23
当图形先驱 Bob Sproull 问我 Rougelot 和 Schumacker 如何制作 NASA-2 项目的原型时,这本书即将完成。他的意思很清楚。第一种颜色可能发生在 1967 年 3 月 31 日之前。Sproull 的直觉是正确的。
I was nearing completion of this book when the graphics pioneer Bob Sproull asked me how Rougelot and Schumacker prototyped the NASA-2 project. His meaning was clear. The first color might have happened earlier than March 31, 1967. Sproull’s intuition was correct.
舒马克记得,为了让 NASA 相信渲染 3D 物体是可行的,他们展示了“一个实时三角形”的演示。我追求领先并击中了薪水。Rougelot 和 Schumacker 然后更详细地记住了这个演示。它是在“1965 年(可能是 1966 年很早)” NASA-1 交付之后提出的。它显示了一个实心红色三角形,实时渲染,在三个维度上令人信服地旋转和平移。他们使用 NASA-1 的可编程部分作为控制运动的计算机,并使用分立组件(尚未集成电路)构建了一个专用设备来进行渲染。24
Schumacker remembered that to convince NASA that rendering three-dimensional objects was feasible, they presented a demo of “one real-time triangle.” I pursued that lead and hit pay dirt. Rougelot and Schumacker then remembered the demo in more detail. It was presented after NASA-1 was delivered “in 1965 (maybe very early 1966).” It displayed a solid red triangle, rendered in real time, that rotated and translated convincingly in three dimensions. They used the programmable part of NASA-1 as the computer that controlled the motions, and they built a special-purpose device from discrete components (not yet integrated circuits) to do the rendering.24
Schumacker 回忆说:“三角形演示让我们相信,即使是只有几个多边形,实现任何有用的系统都会非常庞大和昂贵。幸运的是,在我们竞标合同的时候,第一个实用的真正集成电路问世了。. . . 在我们设计时,摩托罗拉仍在从制造过程中消除错误!” 25
Schumacker recalled, “The triangle demonstration convinced us that implementing any useful systems of even just a few polygons would be prohibitively big and expensive. Fortunately the first practical real integrated circuits came out about the time we bid the contract. . . . Motorola was still getting the bugs out of the fabrication process while we were designing!”25
这个来自 Epoch 2 爆炸最前沿的几乎被遗忘的演示值得特别提及。保守的年代测定表明,第一个彩色像素是在 1966 年初显示的,但日期不详。1967 年的日期捕获了第一个阴影颜色像素渲染。
This almost forgotten demonstration from the bleeding edge of the Epoch 2 explosion deserves special mention. Conservative dating suggests that the first color pixels were displayed in very early 1966, but the date is soft. The 1967 date captures the first shaded color pixel rendering.
Rougelot 和 Schumacker 在 GE 的 NASA-2 上制作了三维阿波罗登月舱的彩色渲染图(返回图 7.1)。他们是如何做到的呢?
Rougelot and Schumacker made colored renderings of the three-dimensional Apollo Lunar Module on GE’s NASA-2 (go back to figure 7.1). How did they do it?
我之前已经注意到,一个复杂的 3D 几何模型几乎总是可以用一个只是三角形的模型来代替。模仿第 6 章,我展示了如何只渲染一个三角形,并理解使用计算机放大的荣耀可以类似地渲染数百万个三角形。
I’ve noted before that a complex three-dimensional geometric model can nearly always be replaced with a model that’s just triangles. Emulating chapter 6, I show how to render only one triangle, with the understanding that millions of triangles are similarly rendered using the glory of computer Amplification.
这里的三角形被认为是由三个线段界定的平面。在平面几何中,三角形是线段,但在这里重要的是它们之间的平坦三角形表面。
A triangle here is considered to be a flat surface bounded by three line segments. In plane geometry, a triangle is the line segments, but here it’s the flat triangular surface between them that matters.
让我们首先看一下这种情况,例如 1967 年的登月舱,其中单个三角形相对于像素间距很大。稍后我们将讨论三角形相对于像素间距较小的情况,这是后千禧年世界的常见情况。图 7.5 显示了这两种情况(仔细查看小三角形)。这些点代表像素位置,即要采集样本的位置。出于我们的目的,假设这些三角形是纯几何。但它们当然不是,它们是对这个页面的显示机制的渲染。让我们假设它们是完美的三角形。
Let’s look first at the case, as in the 1967 Lunar Module, where a single triangle is large with respect to pixel spacing. Later we discuss the case where triangles are small relative to pixel spacing, the usual case in the postmillennial world. Figure 7.5 shows both cases (look carefully for the small triangle). The dots represent pixel locations—that is, where samples are to be taken. For our purposes, imagine that these triangles are pure geometry. But they aren’t, of course, they are renderings into the display mechanism of this page. Let’s just pretend that they are perfect triangles.
将这些三角形渲染成像素的最坏方法如下:如果像素位置落在三角形内,则其像素为三角形的颜色(蓝色),否则为背景颜色(白色)。图 7.6 显示了结果,蓝色的小圆盘代表蓝色像素。请注意,小三角形被完全遗漏了,而大三角形则布满了“锯齿”。
The worst way to render these triangles into pixels is as follows: if a pixel location falls inside a triangle then its pixel is the triangle’s color (blue), otherwise it’s the background color (white). Figure 7.6 shows the result, with little blue disks representing blue pixels. Notice that the little triangle was missed completely, and the big one is ragged with “jaggies.”
但这不是蓝色三角形数字图片的显示,小圆盘也不是像素。(具有讽刺意味的是,插图是一张数码照片。)小圆盘的像素并不比小方块多。我可以用小星星。每个代表一个像素,即一个点位置及其附加颜色。黑点(回到图 7.5)是采样点位置;圆盘是在这些位置采集的彩色样本。请注意,所有图 7.6 中的其他磁盘是白色的,所以在这里你看不到它们。所有这些都必须通过显示设备(屏幕或打印机)进行传播,才能将它们变成我们可以看到的数字图片。
But this isn’t a display of the blue triangle digital picture, and the little disks aren’t pixels. (Ironically, the illustration is a digital picture.) Little disks are no more pixels than little squares. I could have used little stars. Each represents a pixel—that is, a point location and its attached color. The black dots (going back to figure 7.5) are sampling point locations; the disks are colored samples taken at those locations. Notice that all the other disks in figure 7.6 are white, so you can’t see them here. All of these must be spread by a display device (screen or printer) to turn them into a digital picture that we can see.
图 7.5
Figure 7.5
图 7.6
Figure 7.6
虽然这是最糟糕的渲染方式,但它是早期的方式。这是 GE 工程师在 1967 年必须做的事情,以使用第一个彩色像素渲染登月舱。注意图 7.1 中沿 LM 边缘的锯齿。那是幼稚的渲染,很少或没有明确使用采样定理。
Although this is the worst way to render, it’s the way it was done in the early days. It’s what the GE engineers had to do in 1967 to render the Lunar Module with the first color pixels. Notice the jaggies along the edges of the LM in figure 7.1. That was naive rendering, with little or no explicit use of the Sampling Theorem.
接下来我们理想地渲染相同的两个完美三角形,最大限度地利用采样定理。然后我们讨论多年来设计的各种方法来逼近理想的渲染方法。在内存不足和计算能力低下的时代,这些尤其重要。要感受这种不足的深度,请将本节中的 1X到 10X摩尔定律因子与今天(2020 年)的因子(大约 100,000,000,000)进行比较X。那个时候比这差了11个数量级!难以想象——除非你在场。
Next we render the same two perfect triangles ideally, making maximum use of the Sampling Theorem. Then we discuss various methods that have been devised over the years to approximate the ideal rendering method. These were especially important in the days of insufficient memory and low computational power. To feel the depth of that insufficiency, compare the 1X to 10X Moore’s Law factor in this section with today’s (2020) factor, about 100,000,000,000X. It was 11 orders-of-magnitude worse in those days! Unimaginable—unless you were there.
图 7.7
Figure 7.7
采样定理非常清楚。以(略大于)最高频率的两倍采样。但是几何三角形有锋利的边缘。回想一下我们在频率峰值中的经验法则,锐利的边缘具有高频率——非常锐利的边缘具有非常高的频率。事实上,我们不能足够频繁地对完美三角形进行采样。它们的边缘包含太高的频率——无限高。像素和显示元件必须间隔太近,在物理上或经济上都不可行。
The Sampling Theorem is very clear. Take samples at (slightly greater than) twice the highest frequency. But a geometric triangle has sharp edges. Recall our rule of thumb in frequencyspeak that sharp edges have high frequencies—and very sharp edges have very high frequencies. In fact, we can’t sample perfect triangles often enough. Their edges contain frequencies that are too high—infinitely high. The pixels and display elements would have to be too closely spaced to be physically or economically feasible.
在计算机图形学中,我们通常朝另一个方向工作。像素间距是给定的——就像在我们的例子中一样——我们必须让采样定理适应它。这意味着我们必须摆脱它的高频的完美三角形——它的锐利边缘。我们必须确保边缘足够圆润,以使边缘从背景上升的速度不会比像素间距快。图 7.7 显示了两个完美的三角形,它们已经模糊到可以被像素正确采样。小三角已经模糊得几乎不存在了。三角形看起来异常模糊。但想象一下实际间距是那个间距的 1/100,更像是手机上显示元素的间距。在这种情况下,模糊不会很明显。我在这里夸大了。
In computer graphics we typically work in the other direction. The pixel spacing is a given—as it is in our example—and we must fit the Sampling Theorem to it. This means that we must rid a perfect triangle of its high frequencies—its sharp edges. We must ensure that the edges are rounded off enough so that the rise of the edge from the background doesn’t happen faster than the pixel spacing. Figure 7.7 shows the two perfect triangles after they’ve been blurred enough to be properly sampled by the pixels. The small triangle has been blurred almost out of existence. The triangles look exceptionally blurry. But imagine that the actual spacing is say 1/100th that spacing, more like the spacing of display elements on your cellphone. In that case, the blurring wouldn’t be noticeable. I’ve exaggerated it here.
图 7.8 显示了对模糊三角形进行采样得到的像素。同样,我们看不到像素,它们没有形状,所以一个小圆盘只代表一个像素——它的位置和附加的颜色。这次没有错过小三角。
Figure 7.8 shows the pixels that result from sampling the blurred triangles. Again, we can’t see the pixels, and they have no shape, so a little disk only represents a pixel—its location and the color attached. The little triangle isn’t missed this time.
回想一下采样定理告诉我们的内容:当这样表示的像素被显示设备的显示元件扩展和显示时,我们会看到两个模糊的三角形。不是我们模型中完美的几何蓝色三角形。这种锐利的完美是无法用像素来准确表示的。这只是说明采样定理的另一种方式。诀窍在于,在足够高的分辨率下,我们人类对略微模糊的三角形感到满意——因为在正常观看距离下,我们的眼睛看起来并不模糊。
Recall what the Sampling Theorem tells us: when the pixels thus represented are spread and displayed by the display elements of a display device, we see the two blurred triangles. Not the perfect geometric blue triangles in our model. There is no way that such sharp-edged perfection can be represented accurately with pixels. That’s just another way of stating the Sampling Theorem. The trick is that, at sufficiently high resolution, we humans are comfortable with slightly blurred triangles—because they don’t look blurry to our eyes at normal viewing distances.
图 7.8
Figure 7.8
但是我刚刚概述的理想渲染存在问题。从一块硬边几何图形中去除过高的频率意味着什么?什么取代了模型中的三角形?一个三角形应该用一个圆角三角形的计算机描述来代替。或者,如果两个三角形相邻,则必须将连接处修圆并在模型中以某种方式进行描述。这些不是几何概念。实际上,没有人用圆角版本替换计算机图形中的几何模型——去除了过高的频率。那么他们是做什么的呢?他们开发出越来越复杂的对理想场景的近似。事实上,计算机图形学的历史可以被认为是推动更好的近似值来欺骗眼睛。接下来我将讨论其中一个技巧。
But there’s a problem with the ideal rendering I just outlined. What does it mean to remove the too-high frequencies from a piece of hard-edged geometry? What replaces the triangle in the model? A triangle should be replaced with a computer description of a triangle with rounded edges. Or if two triangles abut, then the junction must be rounded off and described somehow in the model. These aren’t geometrical concepts. Nobody actually replaces a geometrical model in computer graphics with a rounded version—with too-high frequencies removed. So what do they do? They develop more and more sophisticated approximations to the ideal scenario. In fact, the history of computer graphics can be thought of as the push for better approximations that trick the eye. I discuss one of these tricks next.
如果我们只是在间隔更近的像素位置进行采样呢?说,两倍的频率?想象一下像素的密度是原来的两倍。图 7.9 显示了左侧的旧像素位置,中间是建议的新像素位置,右侧是两者的叠加。事实上,更密集的采样将使令人不快的混叠伪影(例如锯齿)开始出现的频率(水平和垂直)增加一倍。但问题是我们负担不起四倍像素的帧缓冲区。我们能做什么?
What if we just sampled at more closely spaced pixel locations? Say, twice as often? Imagine that the pixels are twice as dense. Figure 7.9 shows the old pixel locations at the left, the suggested new denser ones in the middle, and superposition of the two at the right. The denser sampling would, in fact, double the frequency (both horizontally and vertically) at which unpleasant aliasing artifacts, such as jaggies, would start to appear. But the problem is that we can’t afford a framebuffer with four times as many pixels. What can we do?
这个想法是在每个实际像素位置(大点)周围的四个位置对模型进行采样,如右图所示。以这种方式为每个实际像素位置获得的四个样本称为其子样本或子像素。四种子样本颜色被平均在一起,形成一个实际像素的颜色——存储并发送到显示元素的像素。您可以在图的右侧看到围绕每个实际像素位置的 2 x 2 子样本位置数组。
The idea is to sample the model at four locations surrounding each actual pixel location (large dots), as shown on the right. The four samples obtained for each actual pixel location in this way are called its subsamples, or subpixels. The four subsample colors are averaged together to form the color of the one actual pixel—the one that is stored and sent to a display element. You can see the 2 by 2 array of subsample locations surrounding each actual pixel location on the right of the figure.
图 7.9
Figure 7.9
图 7.10
Figure 7.10
为了便于说明,我在这里使用了 2 x 2 的子样本数组,但更高的密度也可以。Pixar 使用 4 x 4 的子样本位置数组。图 7.10 显示了两个案例的特写。大点是实际的像素位置,周围的小点是它的子样本位置。在 4 x 4 的情况下,将 16 种子样本颜色平均在一起以形成存储在实际像素中的一种颜色——该颜色最终发送到显示元件以进行扩展和显示。
I’ve used a 2 by 2 array of subsamples here for ease of illustration, but higher densities also work. Pixar uses a 4 by 4 array of subsample locations. Figure 7.10 shows closeups of the two cases. The large dot is the actual pixel location, and the surrounding small dots are its subsample locations. In the 4 by 4 case, the 16 subsample colors are averaged together to form the one color stored in the actual pixel—the color eventually sent to a display element for spreading and display.
二次采样技巧有效地提高了最终图像的分辨率,但它并不能完全避免由于采样非常高的频率(例如三角形的边缘)而导致的伪影,因为频率太低而无法满足采样定理。使用 2 x 2 阵列进行二次采样会使离散样本能够充分处理的最高频率翻倍,而 4 x 4 阵列的最高频率则翻了两番。但是在两种情况下都遗漏的尖锐边缘中仍然存在更高的频率。一个令人惊讶的有效的技巧缓解了这个剩余的问题。当摩尔定律提供三个数量级的计算能力时,我们将回到它。
The subsampling trick effectively increases the resolution of the final image, but it doesn’t completely avoid the artifacts due to sampling very high frequencies—edges of triangles, say—at too low a frequency to satisfy the Sampling Theorem. Subsampling with a 2 by 2 array doubles the highest frequency that can be adequately handled with discrete samples, and the 4 by 4 case quadruples the highest frequency. But there remain even higher frequencies in sharp edges that both cases miss. A surprisingly effective trick alleviates this remaining problem. We’ll return to it when Moore’s Law delivers three more orders of magnitude of computational power.
“你的目标是模拟现实吗?” 是我在计算机图形学早期进行的演讲中一直存在的问题。“不!” 我会回答这个问题,因为我们想创造艺术,而不是模拟现实。我终于在上面的题词中精心设计了反驳,这在当时似乎让提问者和我都满意。我试图说明的一点是,如果动画的世界足够丰富——比如说,接近现实——那么观众就会对它感到满意,并会关注角色。现实不是我们想要的。是人物和他们虚构的世界——或者是所有那些“外面”的图片,完全没有与我们所知道的人物或世界绑定。
“Is your goal to simulate reality?” was a persistent question at talks I gave in the early days of computer graphics. “No!” I would reply, annoyed by the question because we wanted to create art, not simulate reality. I finally crafted the rejoinder in the epigraph above, which seemed to satisfy both the questioners and me—at the time. The point I was trying to make was that if the world of an animation was rich enough—say, approaching reality—then audiences would be comfortable with it and pay attention instead to the characters. Reality wasn’t what we were about. It was the characters and their fictitious worlds—or it was all those pictures “out there” not bound at all to characters or the world as we know it.
然而,模拟现实一直是计算机图形学家的心头好。带路的美国宇航局工程师想向阿波罗宇航员展示月球和登月舱的现实。Digital Light 的计算机辅助设计分支旨在为现实世界展示它们实际出现的物体。
Simulating reality, though, has always been dear to the hearts of computer graphicists. The NASA engineers who led the way wanted to show the reality of the Moon and the Lunar Module to the Apollo astronauts. And the computer-aided design branch of Digital Light aims to display objects for the real world as they would actually appear.
但现实似乎与第一部数字电影的奇幻内容——以及在它们之前电影中的早期视觉效果——存在明显的矛盾。它通过将中心法则扩展到欧几里得几何和文艺复兴视角之外来解决。此后,我们将牛顿物理学纳入中心法则——尤其是光学、运动和重力物理学。计算机当然不受中心法则的约束,无论是否扩展,Digital Light 也不受约束。
But reality seems to be a blatant contradiction to the fantastical content of the first digital movies—and before them the early visual effects in movies. It’s resolved by extending the Central Dogma beyond just Euclidean geometry and Renaissance perspective. We henceforth include Newtonian physics in the Central Dogma—especially the physics of optics, motion, and gravity. Computers certainly aren’t bound by the Central Dogma, extended or not, nor is Digital Light.
将中心法则视为计算机图形学的“交响乐”形式。虽受形式束缚,但创意无限。以中心教条形式打造的奇幻世界尊重现实世界的物理、几何和透视。《玩具总动员》的伍迪和巴斯光年在地球引力中行走,灯光和颜色与他们在现实世界中的工作方式一样。或者至少他们看起来如此。
Think of the Central Dogma as a “symphonic” form for computer graphics. Though bound by the form, creativity is unbounded. The fanciful worlds crafted within the Central Dogmatic form honor real-world physics, geometry, and perspective. Toy Story’s Woody and Buzz Lightyear walk in Earth’s gravity, with lights and colors that work the way they do in the real world. Or at least they appear to.
奇怪的是,以前没有人阐明过中心教条。那可能是因为它太明显了。它当然适用于 CAD 人员,我们已经看到面向图片的计算机图形学和 CAD 有着共同的起源。此外,现代视觉效果工作需要遵守中心法则,以将计算机图形与真人镜头无缝集成。这提醒我们拉里·罗伯茨Triumvirate 中心法则的创始人,为了将 3D 计算机图形线条与现实世界棱镜的照片无缝集成,提出了他的解决方案。
Oddly, nobody has ever articulated the Central Dogma before. That’s probably because it’s just so obvious. It certainly is for CAD people, and we’ve seen that picture-oriented computer graphics and CAD share common origins. Furthermore, modern visual effects work requires adherence to the Central Dogma to seamlessly integrate computer graphics with live-action footage. This reminds us that Larry Roberts, the Triumvirate originator of Central Dogma perspective, came to his solution in an effort to seamlessly integrate three-dimensional computer graphics lines with photographs of real-world prisms.
动画师挤压和拉伸形式,但他们工作的世界是默认的中心法则的“正常”。各地的计算机图形学家都致力于——而且仍然如此——模拟现实,一次只用一种技术。
Animators squash and stretch the form, but the world they work in is the “normal” of the tacitly assumed Central Dogma. Computer graphicists everywhere devoted themselves—and still do—to simulating reality, one technique at a time.
但他们都只是黑客。实际上,模拟肥皂、气泡、空气、水等的物理特性非常昂贵,而且在他的有生之年永远也无法实现。. . . 这不仅不是挫折的根源,反而让他感到安慰,让他感到高兴——甚至可能有点沾沾自喜——他生活在一个复杂性与算法模拟相悖的宇宙中。
But they were all just hacks. Actually simulating the physics of soap, bubbles, air, water, etc., was ludicrously expensive and would never be achieved in his lifetime. . . . Far from being a source of frustration, this comforted him, and made him happy—perhaps even a little smug—that he lived in a universe whose complexity defied algorithmic simulation.
——尼尔·斯蒂芬森,秋季;或者,躲避地狱,2019 27
—Neal Stephenson, Fall; or, Dodge in Hell, 201927
串行数字计算机无法通过为具有有限分辨率的显示器创建图片来实现现实。模拟现实是我们所能追求的。现实是模拟的——至少在我们感兴趣的分辨率上,比现实世界在夸克和量子水平上的精细粒度要粗几个数量级。现实并行运作。来自太阳和其他光源的光线同时在任何地方撞击我们的现实世界。尽管我的题词很圆滑——现实只是复杂性的一种方便度量——现实世界的分辨率非常高。
Reality is unreachable by serial digital computers creating pictures for displays with finite resolutions. Simulating reality is all we can aspire to. Reality is analog—at least at the resolutions that interest us, orders of magnitude coarser than the fine granularity of the real world at the level of quarks and quanta. Reality operates in parallel. Rays from the sun and other light sources impinge on our real world everywhere at the same time. And despite the glibness of my epigraph—Reality is just a convenient measure of complexity—the resolution of the real world is extremely high.
这本书不是计算机图形学教科书,所以我不会描述计算机图形学家为模拟现实而设计的每一种技术。相反,我将概述一些早期的突破以及如何超越它们进行思考。值得一提的是,这些技术广泛应用于 Digital Light 的其他几个方面,例如视频游戏、CAD、飞行模拟器以及虚拟和增强现实。它们不仅限于数字电影这一分支,它构成了我展示所有数字光的骨架。
This book isn’t a computer graphics textbook, so I won’t describe every technique computer graphicists have devised for simulating reality. Rather I’ll sketch several of the early breakthroughs and how to think beyond them. This is a good place to mention that these techniques apply broadly to several other aspects of Digital Light—such as videogames, CAD, flight simulators, and virtual and augmented reality. They aren’t confined to just the one branch, digital movies, that forms the armature for my presentation of all Digital Light.
为了支持这个更大的愿景,我在本章和下一章中的目标涉及第一部数字电影——电影——代表了伟大的数字融合。我强调用于制作第一部电影的技术。但这不是唯一可能的途径。当我们第一次在 NYIT 构思 The Movie 时,我们很乐意通过一个插值中间程序在两个维度上制作它——在中心法则之外。毕竟,多年来,世界对迪士尼的灰姑娘和白雪公主这样的人感到满意。故事和人物引领了这一天——我们并没有忘记这一信息。
My goal in this chapter and the next, in support of that larger vision, concerns the first digital movie—The Movie—representing the Great Digital Convergence. I emphasize the techniques that were used to make that first movie. But that wasn’t the only possible path. When we first conceived The Movie at NYIT, we would have been happy to make it in two dimensions with an interpolating inbetweening program—outside the Central Dogma. After all, the world was satisfied with the likes of Cinderella and Snow White from Disney for years. Story and character carried the day—a message that was not lost on us.
但就像摩尔定律驱动的一切一样,随着计算机图形学社区掌握了每次硬件进步所带来的额外功能,电影的最终 3D 中心法则形式逐渐出现。这或许可以解释为什么迪士尼花了这么长时间才全心全意地采用这种新形式。迪士尼一直等到票房要求提供表格,而不仅仅是电影制作人想要的。
But like everything driven by Moore’s Law, the final three-dimensional Central Dogma form of The Movie emerged piecemeal as the computer graphics community mastered the additional capabilities enabled by each hardware advance. This probably explains why it took Disney so long to wholeheartedly adopt the new form. Disney waited until the form was demanded by the box office, not just desired by the filmmakers.
我已经讨论过渲染,所以现在让我们转向着色,这是本章标题所建议的另一种技术。着色具有选择每个渲染像素的最终颜色的一般含义。上面示例中三角形的阴影很简单:每个像素都是蓝色(或白色)。阴影这个词随着章节的展开而具有更宏大的含义,摩尔定律提供了更多的动力。(太糟糕了,“Moorespower”并没有轻而易举地从舌头上跳下来。)在彩色像素的早期,对表面进行着色具有传统的中心法则的含义 - 直接增加或减少整个表面的颜色亮度,同时保持其色调常数。在这种情况下,变亮意味着增加亮度,变暗意味着降低亮度。
I’ve already discussed rendering, so now let’s turn to shading, the other technology suggested by the chapter title. Shading has the general meaning of choosing the final color of each rendered pixel. The shading of the triangles in the examples above is trivial: every pixel is blue (or white). Shading is a word that takes on grander meaning as the chapter unfolds and Moore’s Law provides more horsepower. (Too bad that “Moorespower” doesn’t trip lightly off the tongue.) In the early days of color pixels, shading a surface had a traditional Central Dogma meaning—the straightforward increase or decrease of color brightness across a surface, while holding its hue constant. In this context, to lighten means to increase brightness, and to darken means to decrease it.
图 7.1 中的阿波罗登月舱渲染说明了这种简单的阴影。单个光源放置在方便的位置,例如该图的观察者的右上方和后面。随着三角形更充分地面对光源,它会变亮。随着它越来越远离它,它变得越来越暗。这被称为平面着色,并且与早期摩尔定律所能适应的一样简单:每个三角形都以一种颜色呈现。
The Apollo Lunar Module rendering in figure 7.1 illustrates such a simple shading. A single light source is placed in a convenient location, such as above right and behind the viewer of that figure. As a triangle more fully faces the light source, it lightens. And it darkens as it increasingly turns away. This is called flat shading and is as simple as early Moore’s Law could accommodate: each triangle is rendered in exactly one color.
对于平面阴影,请考虑在每个三角形的中心升起的旗杆,如图 7.11(左)所示。旗杆顶端朝上,方向垂直于三角形。“向上”与光源之间的角度对计算至关重要。如果三角形面向光源——即角度为零度——那么它的色度就尽可能亮。随着角度的增加,阴影变暗(中)。当三角形与光源成直角时,表面阴影尽可能暗。除此之外,三角形背对光源并且不被照亮(右)。由于此着色计算使用三角法(希腊语表示三角形测量),因此我不会详细介绍。可以说,平面着色的三角计算与几何计算一样精确和明确。计算机可以被告知如何执行一次,然后 Amplification 将它们重复数百万或数十亿次,而无需进一步的人工操作。
For flat shading, think of a flagpole raised at the center of each triangle, as shown in figure 7.11 (left). The top of the flagpole points up, the direction perpendicular to the triangle. The angle between “up” and the light source is crucial to the calculation. If the triangle faces the light source—that is, the angle is zero degrees—then its color shade is as bright as possible. As the angle increases, the shade darkens (middle). When the triangle faces at a right angle to the light source, the surface shade is as dark as possible. Beyond that the triangle faces away from the light source and is unilluminated (right). Since this shading calculation uses trigonometry (Greek for triangle measurement), I won’t present the details. Suffice it to say that the trigonometric computations of flat shading are as precise and well-defined as those of geometry. Computers can be told how to do them once, and then Amplification repeats them millions or billions of times with no further human effort.
图 7.11
Figure 7.11
在本章中,我开始将前几章中的几个线程或流程编织在一起,以提供 Digital Light 的下一阶段——专门用于计算机动画电影的部分。图 7.12 中的流程图旨在捕获这些线程并将它们绑成新的股线。
In this chapter I begin to weave together several threads, or flows, from previous chapters to deliver the next stage of Digital Light—the part devoted to computer-animated movies. The flow chart in figure 7.12 is meant to capture these threads and tie them into new strands.
这张图表的注意事项很熟悉:没有简单的叙述,也没有一个人。为了使大量的名字易于管理,许多人被省略了——在本章和下一章中尤其痛苦——但他们经常在注释中描述。这只是一个草图,而不是完整的学术历史,甚至是专门用于数字电影的计算机图形的受限子集。最后,本章和下一章的散文是对该图的扩展说明。
The caveats for this chart are familiar: There is no simple narrative, and there is no single one person. To keep the flood of names manageable, many persons are omitted—especially painful in this chapter and the next—but they are often described in the annotations. This is only a sketch, not a complete scholarly history, of even the restricted subset of computer graphics devoted to digital movies. Finally, the prose of this chapter and the next is an extended caption to this figure.
我添加了源自 NASA 和通用电气的新链,这导致了第一个彩色像素。它还让位于盐湖城的 Evans & Sutherland 公司走上了一条与前一章面向 ARPA 的方法不同的 E&S 途径。然后,其中三股——犹他大学、E&S 和施乐 PARC——编织在一起,流入纽约理工学院,卢卡斯影业和皮克斯都是从那里衍生出来的。另一条支流从新的(到本章的)通用电气分支流入康奈尔大学,然后从那里流入卢卡斯影业,然后是皮克斯。
I add the new strand originating with NASA and General Electric that led to the first color pixels. It also led to Evans & Sutherland, the company in Salt Lake City, a different pathway to E&S than the ARPA-oriented approach of the preceding chapter. Then three of the strands—University of Utah, E&S, and Xerox PARC—braid together and flow into the New York Institute of Technology, from which Lucasfilm then Pixar derive. Another tributary flows in from the new (to this chapter) GE strand to Cornell University, and from there into Lucasfilm, then Pixar.
为了帮助解决太多的名字,我在这个流程图中引入了一个新设备:一个包围一群人的矩形,通过一些单一的特征将他们联合成一个“集团”。例如,最大的矩形包含 8 个人,他们可以说是由犹他大学捐赠给 NYIT 的。如果箭头触及封闭矩形,则它适用于其中的所有人员。如果它只涉及一个封闭的人,那么它只适用于那个人。例如,犹他州集团的所有八人都在纽约理工大学,但只有吉姆·布林是伯特伦·赫尔佐格(Bertram Herzog)的学生,他是第 6 章中提到的先驱。左下集团的所有五人都是卢卡斯影业计算机图形学非常重要的早期成员(而不是纽约理工学院),但只有罗布·库克是唐·格林伯格在康奈尔大学的学生。等等。
To help with still too many names, I introduce a new device in this flow chart: A rectangle that encloses a group of people unites them into a “bloc” by some single feature. For example, the largest rectangle encloses eight persons who were contributed, so to speak, by the University of Utah to NYIT. If an arrow touches the enclosing rectangle then it applies to all persons inside it. If it touches only one person enclosed, then it applies to that person only. For example, all eight in the Utah bloc were at NYIT, but only Jim Blinn was a student of Bertram Herzog, the pioneer mentioned in chapter 6. All five people in the lower-left bloc were extremely important early members of Lucasfilm computer graphics (and not NYIT), but only Rob Cook was Don Greenberg’s student at Cornell. And so forth.
从前一章重新加入的前两个线程或流是来自 Bob Taylor 和 Herb Freeman 的那些。然后我选择了前一章中的 Ivan Sutherland 和 Dave Evans 主题,本章中新的 Rod Rougelot 和 Bob Schumacker 主题,以及新的 Don Greenberg 主题。我将所有这些结合在一起,形成了纽约理工学院,然后在下一章,去了卢卡斯影业,然后是皮克斯。
The first two threads, or flows, rejoining from the preceding chapter are those descending from Bob Taylor and Herb Freeman. Then I pick up the Ivan Sutherland and Dave Evans thread from the preceding chapter and the new Rod Rougelot and Bob Schumacker thread from this chapter, and also the new Don Greenberg thread. I braid all these together to lead to NYIT, and then in the following chapter, to Lucasfilm, and then Pixar.
DreamWorks Animation 和 Blue Sky Studios 也采用了类似的思路。数字电影的历史上还有很多公司,但这三家具有代表性。他们是千禧年最早在电脑上制作长篇电影的前三人:皮克斯的《玩具总动员》(1995)、梦工厂的《安兹》 (1998)和蓝天的《冰河世纪》(2002)。由于篇幅原因和我个人的专业知识,我主要关注皮克斯的线程。
Similar strands combine for DreamWorks Animation and Blue Sky Studios. There were many more companies in the history of digital movies, but these three are representative. They were the first three to produce feature-length movies completely on computers at the millennium: Pixar’s Toy Story (1995), DreamWorks’s Antz (1998), and Blue Sky’s Ice Age (2002). For space reasons, and my personal expertise, I concentrate mostly on the Pixar threads.
现在,在下一个小节中,让我们朝着这些成就迈出另一个巨大的摩尔定律数量级。
Now, in the next subchapter, let’s take another giant Moore’s Law order-of-magnitude step toward those accomplishments.
X(1970–1975)X (1970–1975)Rod Rougelot 和 Bob Schumacker 在位于伊萨卡的通用电气工厂开发了 NASA-1,该工厂也是康奈尔大学的所在地。他们在北约 50 英里的锡拉丘兹的 GE 开发了 NASA-2——具有第一个彩色像素和第一个实时彩色 3D 渲染。他们在 GE Syracuse 的最后一项成就是 1968 年的非实时(缩写为“non-RT”)系统,旨在进一步开发不受实时限制的三维计算机图形。28
Rod Rougelot and Bob Schumacker developed NASA-1 at the General Electric facility in Ithaca, also hometown to Cornell University. They developed NASA-2—with the first color pixels and first real-time color three-dimensional renderings—at GE in Syracuse, about 50 miles north. Their last accomplishment at GE Syracuse was a non-real-time (abbreviated “non-RT”) system in 1968, designed to further develop three-dimensional computer graphics, unrestricted by the real-time limitation.28
1968 年,Don Greenberg 在康奈尔大学攻读建筑学博士学位,同年,Rougelot 和 SchumackerSyracuse 的非 RT 系统在线。就上下文而言,萨瑟兰的头戴式显示器大约在同一时间在哈佛开发。
During those years, Don Greenberg had proceeded along a separate path to a PhD in architecture at Cornell in 1968, the same year that Rougelot and Schumacker brought the non-RT system online in Syracuse. For context, Sutherland’s head-mounted display was under development at Harvard at about the same time.
图 7.12
Figure 7.12
在“你认识谁”的关键时刻之一,鲁格洛特让格林伯格——他在新生童子军帐篷日时的康奈尔老朋友——访问了新的通用电气系统,即非 RT 系统。然而,有一个问题。格林伯格只能在晚上使用它,名义上是从下午 5 点到早上 8 点,每周三个晚上。它在锡拉丘兹,离伊萨卡大约一个小时的路程。
In one of those crucial “who you know” moments, Rougelot gave Greenberg—his old Cornell buddy from the freshman Boy Scout tent days—access to the new GE system, the non-RT system. There was a catch, however. Greenberg could use it only at night, from 5 p.m. to 8 a.m. nominally, three nights per week. And it was in Syracuse, about an hour away from Ithaca.
几个月来,格林伯格在每一个空闲的日子里,都会开车把他的一群学生从伊萨卡带到锡拉丘兹上夜班。1972 年的“康奈尔电影”由此诞生,这是一部 15 分钟的计算机动画之旅,穿越康奈尔大学校园,展示了一座拟议中的新建筑将如何融入其中。电影中的彩色图像发表在格林伯格关于计算机图形学的文章中1974 年 5 月的美国人,并在其封面上。29
For months, on every available day, Greenberg would drive a crew of his students from Ithaca to Syracuse for the overnight shift. From this slog came the “Cornell movie” of 1972, a 15-minute computer-animated trip through the Cornell campus showing how a proposed new building would fit in. Color images from the movie were published in Greenberg’s article about computer graphics in the Scientific American of May 1974, and on its cover.29
唐·格林伯格是计算机图形学中笑容最灿烂、最热情的人,他的特点是关心他的学生和关心他自己。他指导他的年轻团队在计算机图形学方面取得成功。也许他是一名运动员并不奇怪——而且在他 80 多岁时仍然是网球冠军。从第一部电影开始,他建立了康奈尔著名的计算机图形系,该系与犹他大学的影响力一样大。
Don Greenberg, the man with the readiest, warmest grin in computer graphics, was characteristically as concerned about his students as himself. He coached his young team to computer graphics success. Perhaps it’s no surprise that he’s an athlete—and still a tennis champ in his 80s. Starting with that first movie, he built Cornell’s renowned computer graphics department, which became as influential as the University of Utah’s.
Rougelot 和 Schumacker 在 1967 年就已经有了实时 3D 渲染图形。但他们的系统依赖于 NASA 的无底资源,并且使用了专用硬件。我区分了实时动画和电影动画,每帧的计算都需要尽可能长的时间。康奈尔大学的电影属于大学里的个人可以在通用计算机上完成的范围之内。它是第一个 3D 渲染的计算机动画吗?
Rougelot and Schumacker already had real-time three-dimensional rendered graphics in 1967. But their system depended on NASA’s bottomless resources and used special-purpose hardware. I draw a distinction between real-time animation and film animations where the computation of each frame takes as long as necessary. The Cornell movie fell within the boundaries of what single individuals at universities could accomplish on general-purpose computers. Was it the first three-dimensional rendered computer animation?
该荣誉的知名竞争者是 1971 年由犹他大学研究生 Ed Catmull 报道的一张脸变成蝙蝠的一秒钟动画。或者是 Ed 的同学 Fred Parke 在 1971 年制作的动画面孔。或者据说 Ed 在 1972 年 1 月计算并在 1972 年 8 月演示的动画手(图 7.13,左)。或者是 Ed 的同学 Fred Parke 在 1972 年创作的动画人脸(图 7.13,中间)。或者唐·格林伯格的学生马克·莱沃伊所说的康奈尔大学电影于 1972 年中秋完成(图 7.13,右)。其中,只有康奈尔的电影是彩色的。Ed 于 1971 年末或 1972 年 1 月初完成的面对面着色图形动画,显然是同时为同一班级制作的 Fred 的动画脸,是这次特殊比赛的获胜者。让我们称之为领带。但1972 年这一年再次出现了显着的技术融合,就像电影的 1895 年一样。30
Known contenders for the honor are a one-second animation of a face becoming a bat in 1971 reported by Ed Catmull, then a graduate student at the University of Utah. Or an animated face by Ed’s classmate Fred Parke also in 1971. Or the animated hand Ed reportedly computed in January 1972 and demonstrated in August 1972 (figure 7.13, left). Or an animated human face by Ed’s classmate, Fred Parke, in 1972 (figure 7.13, middle). Or the Cornell movie that Marc Levoy, Don Greenberg’s student, says was completed in mid-autumn 1972 (figure 7.13, right). Of these, only the Cornell movie was in color. Ed’s face-to-bat shaded graphics animation, completed in late 1971 or perhaps early January 1972, and Fred’s animated face made apparently at the same time, for the same class, are the winners of this particular contest. Let’s call it a tie. But once again there was a remarkable technological convergence in a single year, 1972, like 1895 for movies.30
图 7.13
Figure 7.13
最有趣的模型包含大量三角形——通常是数百万个。考虑第 6 章中的线框茶壶,它有数百个三角形。或者康奈尔电影中康奈尔校区的建筑。从选定的角度看,这些三角形经常相互重叠。如果它们充满纯色,那么它们往往会相互隐藏。也许早期研究最多的计算机图形学问题被称为可见表面问题或隐藏表面问题,它相当于同一件事:在场景中的所有三角形中,哪些三角形对虚拟相机可见中央教条?
Most interesting models contain a multitude of triangles—often millions of them. Consider the wireframe teapots in chapter 6, with hundreds of triangles. Or the buildings on the Cornell campus in the Cornell movie. These triangles often overlap one another as seen from a chosen viewpoint. And if they are full of solid color then they tend to hide one another. Perhaps the most studied computer graphics problem in the early days was called the visible-surface problem, or the hidden-surface problem, which amounts to the same thing: Of all the triangles in a scene, which ones are visible to the virtual camera of the Central Dogma?
几何学的真正概念是,在我们可以计算的意义上,我们确切地知道三角形的每个点的位置——在它的表面上的任何地方。我们确切地知道虚拟相机的视点在哪里以及它的外观。
The very notion of geometry is that we know exactly where every point of a triangle is located—anywhere on its surface—in the sense that we can calculate it. We know exactly where the viewpoint of the virtual camera is located and which way it’s looking.
特别是,可以计算从视点到三角形上任意点的距离。我们称该距离为点的深度。因此,离观察者的眼睛更远的点——离虚拟相机——更深入到场景中。我们可以计算三角形上像素位置的点的深度。这就是几何数学的全部意义所在。我不是要你理解如何进行这样的计算。我只要求你明白,当计算机被指示做一次这样的计算时,它可以一次又一次地无限次地做,而不再需要人类。
In particular, the distance from the viewpoint to any point on a triangle can be calculated. Let’s call that distance the point’s depth. Thus a point farther away from the viewer’s eye—from the virtual camera—is deeper into the scene. We can calculate the depths of points on a triangle at pixel locations. That’s what the math of geometry is all about. I’m not asking that you understand how to do such calculations. I ask only that you understand that when a computer has been instructed to do such a calculation once, it can do it again and again ad infinitum with no further need of humans.
只考虑两个三角形,一个蓝色的和一个红色的,如图 7.14 所示。一种在另一个之前渲染一个的简单方法,即使它们相交,如下所示:
Consider just two triangles, a blue one and a red one, as shown in figure 7.14. An easy way to render one in front of the other, even if they intersect, follows:
图 7.14
Figure 7.14
顺便说一句,深度缓冲是 Ed Catmull 1974 年著名的博士论文的主要贡献。Ed 实际上在深度缓冲方面位居第二,Wolfgang Strasser 在他1974 年的博士论文中几乎没有抢到。但是施特拉瑟的论文是德文的,所以他们彼此并不了解。31
Depthbuffering, by the way, was a major contribution of Ed Catmull’s famous 1974 PhD thesis. Ed was actually second with depthbuffering, barely scooped by Wolfgang Strasser in his 1974 PhD thesis. But Strasser’s thesis was in German, so they didn’t know about each other.31
深度缓冲很容易描述,但它有一个问题:你必须渲染所有的三角形,甚至是那些完全隐藏的三角形。可见表面的一些方法解决方案建议按深度顺序对三角形进行排序,然后仅渲染可见或部分可见的三角形。这通常可以节省很多渲染时间。
Depthbuffering is easy to describe, but it has a problem: you have to render all the triangles, even those that are completely hidden. Some approaches to visible-surface solutions suggest ordering the triangles in depth order and then rendering only those that are visible or partially visible. This can often save much rendering time.
图 7.15
Figure 7.15
但是相交的三角形不能按深度顺序排列。一个三角形的一部分比另一个三角形更深,而它的另一部分则更浅。但是您总是可以将相交的三角形细分为不相交的较小三角形,如图 7.15 所示。
But intersecting triangles can’t be put in depth order. Part of one triangle is deeper than the other triangle, while its other part is shallower. But you can always subdivide intersecting triangles into smaller triangles that don’t intersect, as shown in figure 7.15.
无论您将深度缓冲用于可见表面解决方案还是深度排序的(不相交的)三角形,放大的魔力都可以重复数百万个三角形的计算。不应将大量计算与难度相混淆,尤其是当它们中的每一个都像深度缓冲一样容易理解时。
Whether you use depthbuffering for visible-surface solution or a depth-ordered sort of (non-intersecting) triangles, it’s the magic of Amplification that repeats the computation for millions of triangles. Vast numbers of computations shouldn’t be confused with difficulty, especially when each one of them is as easy to understand as depthbuffering.
中心法则规定数字对象会像现实世界的对象一样投射阴影。计算机图形模型最初只包含对象描述和虚拟相机的位置。但是模型的概念很快扩展到包括光源,例如灯。在早期,光源非常简单。它在一个点上有一个位置,并向各个方向发射白光。这是一个点光源。随着摩尔定律力量的增长,光源变得更加精美,并且更仔细地模拟了真实世界的光源。它们有范围——也就是说,它们占据了一个区域,而不仅仅是一个点——并且有颜色,以及真正的灯、光和太阳的其他属性。
The Central Dogma dictates that digital objects cast shadows just as real-world objects do. A computer graphics model initially contained only object descriptions and the location of the virtual camera. But the notion of a model quickly expanded to include light sources, such as lamps. In the early days, a light source was very simple. It had a location at a single point and emitted white light in all directions. It was a point light source. As Moore’s Law power grew, the light sources got fancier and more carefully simulated real-world light sources. They had extent—that is, they occupied an area, not just a point—and had color, and other properties of real lamps, lights, and the sun.
图 7.16
Figure 7.16
确定阴影本质上与隐藏表面问题相同。如果您只考虑一个简单的点光源,这一点尤其明显。想象一下,虚拟摄像机从光源位置查看场景。从这个视点看不到的任何表面都必须在阴影中。
Determining shadows is essentially the same problem as the hidden-surface problem. This is particularly obvious if you consider only a single simple point light source. Imagine that the virtual camera views the scene from the location of the light source. Any surface that cannot be seen from this viewpoint must be in shadow.
因此,计算阴影是一个定义明确但乏味的计算。只要说我们知道所有物体的几何形状以及光源的几何位置就足够了。因此,计算哪些表面处于阴影中很简单。然后我们可以在以后使用这个事实来确定当我们从所需的视点看到它时最终应该将什么颜色渲染到显示器上,这将与光源本身不同。摩尔定律的改进后来允许具有范围和颜色的多个光源。而且,像往常一样,放大意味着程序员只需要设计一种算法。我们的计算机会忠实地重新执行它数百万次。32
Calculating shadows therefore is a well-defined, if tedious, computation. Suffice it to say we know the geometry of all the objects, and the geometrical location of the light source. So it’s straightforward to calculate which surfaces are in shadow. Then we can use that fact later to determine what color should finally be rendered to the display when we see it from the desired viewpoint, which will be different from the light source itself. Improvements in Moore’s Law would later allow multiple light sources, with extent and color. And, as usual, Amplification means that a programmer had to devise only one algorithm. Our computers would faithfully re-execute it millions and billions of times.32
到目前为止,我们看到渲染的三角形具有简单的纯色——最简单的着色模型——如果它们处于阴影中或远离光源,它们可能会变暗。早期的计算机图形学家很快学会了如何以更奇特的方式进行渲染,因为摩尔定律赋予了他们更多的力量。例如,随着与虚拟相机的距离(深度)增加,或者与已知光源的接近度减少(图 7.16,左),颜色可以被着色。三角形可能是部分透明的(左起第二个)。三角形可以用另一张图片的像素进行纹理处理,比如草或牛仔布(第三张)。这本质上是我在之前对 NASA-1 模拟器的讨论中简要解释的纹理映射技术。或者可以使用这些技术的组合(图 7.16,右)。这些只是无穷无尽的几个例子。
The triangles we’ve seen rendered so far had a simple solid color—the simplest of shading models—perhaps darkened if they were in shadow or aimed away from the light source. Early computer graphicists quickly learned how to render in fancier ways as Moore’s Law gave them more power. For example, the color could be shaded as distance (depth) from the virtual camera increased, or as nearness to a known light source decreased (figure 7.16, left). And triangles could be partially transparent (second from left). A triangle could be textured with pixels from another picture, of say grass or denim (third). This is essentially the texture mapping technique I explained briefly in the earlier discussion of the NASA-1 simulator. Or combinations of the techniques could be used (figure 7.16, right). These are just a few examples from an infinite variety.
纹理映射是基于一个从根本上强大的想法。这是基于像素的数字光与基于几何的数字光结合的一个典型例子。强大的想法是一个数字图像可以控制另一个图像的外观。纹理映射是基于这个想法的几种技术中的第一种。
Texture mapping is based on a fundamentally powerful idea. And it’s a prime example of pixel-based Digital Light married to geometry-based Digital Light. The powerful idea is that one digital image can control what another looks like. Texture mapping was the first of several techniques that were based on this idea.
图 7.17
Figure 7.17
我们已经看到 Rod Rougelot 和 Bob Schumacker 在阿波罗计划的 NASA-1 模拟器中提出了这个想法的模拟版本。当通过几何三角形的扫描线在电视显示器上被渲染成颜色时,颜色是从访问彩色几何子图块的光栅阵列的几何计算中获得的。一旦计算出适当的子图块,它的(模拟)颜色就会发送到显示器。
We’ve already seen that Rod Rougelot and Bob Schumacker had the analog version of the idea in the NASA-1 simulator for the Apollo Project. As a scanline through a geometric triangle was being rendered into color on a television display, the color was obtained from a geometric computation that accessed a raster array of colored geometric subtiles. Once the appropriate subtile had been computed, then its (analog) color was sent to the display.
由 Ed Catmull 在 1974 年的博士论文中介绍的数字等价物,用像素的光栅阵列代替了几何子块的光栅阵列——也就是说,它用数字化样本代替了几何。
The digital equivalent, introduced by Ed Catmull in that 1974 PhD thesis, replaces the raster array of geometric subtiles with a raster array of pixels—that is, it replaces geometry with digitized samples.
在图 7.17 中,一个三角形显示在左上角。存储在计算机内部模型中的三角形没有颜色。相反,它的颜色间接存储在右侧表示的纹理图中——来自黄玫瑰的数码照片。
In figure 7.17, a triangle is represented at top left. There is no color for the triangle stored in the computer’s internal model. Instead its colors are stored indirectly in the texture map represented at the right—from a digital photograph of a yellow rose.
三角形实际上是不可见的。它以数学方式存储在计算机模型中,作为几何上完美的欧几里得三角形。你看不到它。您看到的三角形是将抽象三角形渲染到此页面的显示中。
The triangle isn’t actually visible. It’s stored mathematically in a computer model as a geometrically perfect Euclidean triangle. You can’t see it. The triangle you do see is a rendering of the abstract triangle into the display of this page.
同样,纹理贴图是像素数组,您看不到它们。玫瑰是纹理贴图的显示,而不是纹理贴图本身。这提醒了本书的主要观点之一:像素的显示与像素本身是分开的。要查看像素,它们必须由所选显示介质的显示元素(在本例中为打印页面)散布。下面的解释要求您不要将尖尖的像素与其平滑显示混为一谈。
Similarly, a texture map is an array of pixels, and you can’t see them. The rose is a display of the texture map, not the texture map itself. This is a reminder of one of the principal points of this book: The display of pixels is separate from the pixels themselves. To see pixels, they must be spread by the display elements of the chosen display medium—the printed page in this case. The explanation that follows asks that you not conflate spiky pixels with their smooth display.
所以玫瑰是用来控制另一个颜色的采样图片。您可以将纹理映射视为将贴花应用于三角形。或者将三角形想象成饼干切割器,将纹理图想象成面团。以您希望的任何角度贴上贴花或切出饼干,例如此处使用的 10 o。但是贴花和饼干面团是光滑连续的东西。为了理解这些隐喻,您必须记住,纹理贴图总是可以通过扩展和添加采样定理所教导的像素来重建为平滑的连续图片。
So the rose is a sampled picture that’s used to control the colors of another. You can think of texture mapping as applying a decal to a triangle. Or think of the triangle as a cookie cutter and the texture map as the dough. Apply the decal, or cut out a cookie, at any angle you wish—such as the 10o used here. But decals and cookie dough are smooth continuous things. To make sense of these metaphors you must remember that a texture map can always be reconstructed into a smooth continuous picture by spreading and adding the pixels as taught by the Sampling Theorem.
这个想法是将三角形逐个扫描线渲染为显示设备的像素。在图中,中间的三角形表示过程中游。上面的扫描线已经被渲染。这些点(粗略地)表示沿着当前扫描线的像素位置,接下来要渲染。那里的像素颜色取自玫瑰纹理贴图。玫瑰上的圆点表示要对颜色进行采样的位置。简单的几何计算计算纹理中与要显示的像素位置相对应的点。在玫瑰上如此计算的点线倾斜 10度,以考虑贴花或饼干切割器的旋转。
The idea is to render the triangle, scanline by scanline, into pixels for a display device. In the figure, the middle triangle shows the process midstream. The upper scanlines have already been rendered. The dots indicate (crudely) the pixel locations along the current scanline to be rendered next. The pixel colors there are to be taken from the rose texture map. The dots on the rose show the locations to be sampled for colors. A straightforward geometric calculation computes the point in the texture that corresponds to a pixel location to be displayed. The line of dots so calculated on the rose is tilted 10o to take rotation of the decal or cookie cutter into account.
但是有一个问题。纹理贴图是像素。就计算机而言,这是一个尖尖的钉床。您在纹理贴图中采样的点,基于几何,几乎可以肯定不对应于纹理贴图的像素之一。一般来说,直接的几何计算会产生一个位于纹理图像素位置之间的点。早期,从业者使用纹理图中距离计算点最近的像素的颜色,将一个像素渲染到显示器上。这是一个很差的近似值,但当时没有足够的能力进行更高级的计算。下一个想法是找到离计算点最近的四个像素,并将它们的颜色平均为最终显示颜色。
But there’s a problem. A texture map is pixels. It’s a spiky bed of nails so far as the computer is concerned. The point that you sample in the texture map, based on the geometry, almost certainly doesn’t correspond to one of the texture map’s pixels. In general, the straightforward geometric calculation results in a point that lies between the pixel locations of the texture map. In the early days, practitioners used the color of the pixel in the texture map nearest to the calculated point to render a pixel to the display. That’s a poor approximation, but there wasn’t enough power then for fancier computations. The next idea was to find the four nearest pixels to the calculated point and average their colors for the final display color.
但是有一种正确的方法来进行纹理映射,这是采样定理的直接结果:在纹理映射中扩展和添加像素以获得连续光滑的表面——贴花或饼干面团——正是从无到有引入的东西的魔力在科捷利尼科夫一章中。那么计算的点必须落在这个重建的光滑表面上的某个地方。重建表面上那个确切点的颜色是要发送到显示设备的颜色。已经设计了许多年的技巧来避免进行这种完整的计算,但它是随时待命。所缺少的只是一个足够高的摩尔定律因子。
But there is a right way to do texture mapping that is a direct consequence of the Sampling Theorem: Spread and add the pixels in the texture map to get a continuous smooth surface—the decal or cookie dough—exactly the magic of something from nothing introduced in the Kotelnikov chapter. Then the calculated point must fall somewhere on this reconstructed smooth surface. The color at that exact point on the reconstructed surface is the color to send to the display device. Many years’ worth of tricks have been devised to avoid doing this full computation, but it was always there for the taking. All that was missing was a sufficiently high Moore’s Law factor.
纹理映射的更大理念值得重复:一张图像可以用来控制另一张图像。纹理映射使用控制图像来确定其他图像的颜色。在一般意义上,纹理映射是一种流行的着色形式,着色提供渲染像素的颜色。但是还有另一个含义,颜色的阴影取决于物理牛顿光学的模拟。
Texture mapping’s larger idea bears repeating: one image can be used to control another. Texture mapping uses the control image to determine the color of the other image. Texture mapping is a popular form of shading in the general sense that shading supplies the color of a rendered pixel. But there’s another meaning too, where the shading of a color depends on simulation of physical, Newtonian optics.
计算机图形学家很快发现,随着摩尔定律力量的增强,如何颠覆几何真相以获得更令人愉悦的阴影。1971 年在犹他大学的法国人 Henri Gouraud 有一个聪明的想法,即在三角形的每个角上放置一个不同的“向上”。他没有在三角形的中心放置一根旗杆,而是在每个角落放置了旗杆——然后将它们向不同的方向倾斜。他计算了每个角落的颜色,根据前面解释的那个角落的“向上”进行着色。然后在这些角落阴影之间插入三角形上每个点的阴影。Gouraud 使用的这种插值是所谓的线性插值:如果一个角的阴影是 A,另一个角的阴影是 B,那么两个角中间的点就有 A 和 B 中间的阴影。图 7。33
Computer graphicists quickly discovered, with increased Moore’s Law power, how to subvert the geometrical truth to get more pleasing shading. The Frenchman Henri Gouraud, at the University of Utah in 1971, had the clever idea of putting a different “up” at each corner of a triangle. Instead of one flagpole at the center of the triangle, he placed flagpoles at each corner—and then tilted them in different directions. He computed the color at each corner, shaded according to the “up” at that corner as explained earlier. Then the shade at each point on the triangle was interpolated between these corner shades. The kind of interpolation Gouraud used is so-called linear interpolation: if the shade at one corner is A and at another corner is B, then a point halfway between the two corners has the shade halfway between A and B. Figure 7.18 (right) shows that careful choice of the ups at the corners yields a shaded image that’s superior to simple flat shading.33
图 7.18
Figure 7.18
图 7.19
Figure 7.19
但是Gouraud 阴影有些地方不太对劲。正如我们在现实世界中的实际物体上经常看到的那样,没有适当的亮点,至少没有令人信服的亮点。1973 年,一名越南学生 Bui Tuong Phong 来到犹他州解决这个问题。他指出,Gouraud 阴影假定了一种不自然的光源,其强度随着远离它而呈线性或成比例地变化。没有光源实际上是这样工作的。没有一个是线性的。Phong 在他的光源模型中添加了一个真实的非线性(图 7.19,右)。这意味着当向上接近光源时,其三角形的颜色会显着快速变亮。您会在该附近获得更逼真的亮点。34
But something wasn’t quite right about Gouraud shading. There was no proper highlight as we often see on actual objects in the real world, at least not a convincing one. A Vietnamese student, Bui Tuong Phong, stepped forward at Utah in 1973 to take care of that problem. He noted that Gouraud shading assumes an unnatural light source, one whose intensity varies linearly, or proportionally, as up veers away from it. No light source actually works that way. None are linear. Phong added a realistic nonlinearity to his light source model (figure 7.19, right). That means as up approaches the light source, the color shade of its triangle brightens dramatically fast. You get a more realistic highlight in that vicinity.34
Phong 还使用了一种更复杂的方法来计算阴影,这需要更多的马力,但效果更好。像 Gouraud 一样,他在每个角落都放置了旗杆,然后将它们倾斜到不同的方向。在它们之间插入了一个平滑的 ups 表面,从而在三角形的任何点上定义了“up”。Phong 使用的插值类型也是线性插值:如果一个角的上倾斜角度 A,而另一个角的上倾斜角度 B,则两个角中间的点在 A 和B. 一般来说,它几乎总是不是一个旗杆在中心的方向。
Phong also used a more sophisticated way to calculate the shading, which required more horsepower but gave better results. Like Gouraud, he placed flagpoles at each corner and then tilted them in different directions. A smooth surface of ups was interpolated between them, thus defining “up” at any point on the triangle. The kind of interpolation Phong used was also linear interpolation: if the up at one corner is tilted at angle A and the up at another corner is tilted at angle B, then a point halfway between the two corners has an up angle halfway between A and B. In general, it’s almost always not the one-flagpole-at-the-center direction.
回想一下第 6 章对样条线和补丁的讨论,插值只是“颠倒”的采样。因此,Phong 着色本质上是采样数学与几何数学的另一种结合。将其视为定义其光学形状的表面,而无需实际更改模型的几何形状。可以说,它是一个起伏的表面,漂浮在底层几何模型之上——这是一个巧妙的技巧,可以在没有真正去除平面的情况下去除平面,如图 7.19 所示(右图,忽略轮廓)。这是一种新型好莱坞的另一种假面技术。
Recall from the discussion of splines and patches in chapter 6 that interpolation is just sampling “upside down.” So Phong shading is essentially another marriage of the math of sampling with the math of geometry. Think of it as a surface that defines its optical shape without actually changing the geometrical shape of the model. It’s a surface of ups, so to speak, floating above the underlying geometric model—a neat trick that gets rid of flat facets without really getting rid of them, as the result shown in figure 7.19 (right, ignoring the silhouette). It’s another false-front technique for a new kind of Hollywood.
这个技巧可以概括。Phong 在拐角处使用简单的比例或线性插值。通过使用分布在曲面上的更多 ups,您可以进行双三次插值,以创建一个平滑的起伏曲面,例如 Bézier 补丁。我将展示如何在下一个数量级上将这个想法发挥到极致。
And the trick generalizes. Phong used simple proportional, or linear, interpolation between the ups at the corners. By using more ups distributed over a surface, you could interpolate bicubically to create a smooth undulating surface of ups from, say, Bézier patches. I’ll show how to take that idea to an extreme at the next order of magnitude.
Phong 将光照模型的概念添加到计算机图形建模中。换句话说,阴影也具有照明的附加意义。阴影概念开始推广到更复杂的物理光学模拟。
Phong added the notion of a lighting model to computer graphics modeling. To put it another way, shading took on the added meaning of lighting as well. The shading notion began to generalize to more sophisticated simulations of physical optics.
与此同时,Digital Light 的另一个分支正在加利福尼亚州推进,靠近斯坦福大学,该地区很快就会被称为硅谷。它也是关于彩色像素的,但它在中心法则之外。
Meanwhile another branch of Digital Light was advancing in California, near Stanford University, in an area soon to be known as Silicon Valley. It was also about color pixels, but it was outside the Central Dogma.
Richard “Dick” Shoup 于 1943 年出生在匹兹堡,在吉布森尼亚以北几英里的地方长大,一头红发,脸上满是雀斑。他是一个拥有 50 英亩肘部空间的农场孩子,后来成为一名出色的爵士长号手和电子高手。在 1950 年代后期,迪克的叔叔给了他一些关于无线电和电子的小册子,这些小册子是科幻杂志《神奇故事》的创作者雨果·格恩斯巴克 (Hugo Gernsback) 写的,这些小册子启发了他未来的职业生涯。35
Richard “Dick” Shoup was born in Pittsburgh in 1943 and grew up red-haired and freckled-faced a few miles north in Gibsonia. He was a farm kid with 50 acres of elbow room, who would become an accomplished jazz trombonist and electronics whiz. In the late 1950s, Dick’s uncle gave him some pamphlets on radio and electronics written by Hugo Gernsback, creator of Amazing Stories, the science fiction magazine, and they inspired his future career.35
迪克于 1970 年在戈登·贝尔(Gordon Bell)手下的卡内基梅隆大学(Carnegie Mellon University)获得博士学位,后者后来成为 Digital Equipment Corporation 的首席架构师。贝尔在那里帮助设计了 PDP-1,这是Spacewar出名的计算机。迪克的论文是关于可编程计算机逻辑的,该方案采用逻辑“单元”的许多副本,可以对其功能和与相邻单元的连接进行编程。我们成为了好朋友,因为我 1969 年的博士论文是关于元胞自动机的。我的主题大致相当于他的硬件研究的数学等价物。
Dick got his PhD in 1970 from Carnegie Mellon University under Gordon Bell, who would become chief architect at Digital Equipment Corporation. Bell helped design the PDP-1 there, the computer that Spacewar made famous. Dick’s dissertation was about programmable computer logic, a scheme that employs many copies of a logic “cell” that can be programmed for function and connectivity to neighboring cells. We became fast friends because my 1969 PhD dissertation had been about cellular automata. My topic was roughly the mathematical equivalent of his hardware research.
完成那篇论文的第二天,迪克向西去了加利福尼亚,加入了伯克利计算机公司,打算建造一台大型分时机器。但是时机不对。就在那时,分时度假市场跌入谷底,让他和他的高级同事担心到 1970 年 11 月的薪水。幸运的是,鲍勃·泰勒刚刚从伯克利进入旧金山湾对面的施乐帕洛阿尔托研究中心 (PARC)。他迅速找到了这家倒闭公司的几个关键人物,包括迪克舒普。
The day after he finished that dissertation, Dick went west to California to join the Berkeley Computer Corporation intent on building a massive timesharing machine. But the timing was wrong. The bottom fell out of the timesharing market just then, leaving him and his high-powered colleagues worried about a paycheck by November 1970. Fortunately, Bob Taylor had just joined Xerox Palo Alto Research Center (PARC) across San Francisco Bay from Berkeley. He quickly scooped up several of the key folks at the failing company, including Dick Shoup.
迪克对 PARC 的主要贡献是他的彩色视频系统。他设计并建造了它的硬件并编写了它的第一个软件,包括SuperPaint。该系统具有每像素 8 位(256 色)和一个完全数字的帧缓冲区。迪克并不是第一个使用彩色像素的人——六年前的 NASA-2 图片证明了这一点——但他的系统认真而充分地利用了它们。他的像素可供任何人使用,像我一样,会编程或绘画。可以这么说,它们是通用的彩色像素。
Dick’s main contribution to PARC was his Color Video System. He designed and built its hardware and wrote its first software, including SuperPaint. The system had 8 bits per pixel (256 colors) and a completely digital framebuffer. Dick wasn’t the first with color pixels—the NASA-2 picture from six years earlier proves that—but his system made serious and full use of them. His pixels were available to anyone, like me, who could program or paint. They were general-purpose color pixels, so to speak.
正如我们在第 6 章中了解到的那样,阿尔伯特·爱因斯坦在 1938 年写信从纳粹手中拯救孩子赫伯·弗里曼。三十年后,当时是计算机图形学的先驱,弗里曼聘请我刚从斯坦福研究生院毕业,担任新的助理教授。约克大学,他在那里担任系主任。我是一名计算机科学家,爱好绘画,用油和丙烯酸树脂,所以我一定看起来很适合计算机图形学。他很快就敦促我从高塔跳到臭气熏天——放弃我的博士工作,即计算机科学的定理证明部分,转而从事图片制作。但我的回答是,“当你得到颜色时,赫伯,我会做的。” 事实上,我不得不被猛地从我的脚上拉下来并停止寒冷才能做出改变。
Albert Einstein wrote letters to save the child Herb Freeman from the Nazis in 1938, as we learned in chapter 6. Three decades later, by then a computer graphics pioneer, Freeman hired me fresh out of Stanford graduate school as a new assistant professor at New York University, where he was department chair. I was a computer scientist who painted as a hobby, with oils and acrylics, so I must have seemed like a natural fit for computer graphics. He soon urged me to make the leap from tower to stinks—to forsake my PhD work, the theorem-proving part of computer science, for the picture-making part. But my response was, “When you get color, Herb, then I’ll do it.” In fact, I had to be jerked off my feet and stopped cold to make the change.
1972 年末,当我在冰冷的新罕布什尔州滑雪场上滑雪时,警钟敲响了。我的长袜帽滑落,让我失明。另一位完全失控的滑雪者在碰撞路线上向我冲过来。我全速穿过他。我可能已经刺穿或去脑了他,但绊脚石却毫发无伤地溜走了。我没有。我的右股骨严重的螺旋形骨折使我在全身石膏中躺了三个月,从乳头到脚趾——一个完全依赖他人的无助、不动的病人。
The wake-up call came while I was schussing an icy New Hampshire ski slope in late 1972. My stocking cap slipped and blinded me. Another skier, completely out of control, was barreling toward me on a collision course. I ripped through him at full speed. I might have impaled or debrained him, but the stumblebum skied away unharmed. I didn’t. A nasty spiral fracture of my right femur put me down for three months in a full body cast, nipples to toes—a helpless, immobile invalid completely dependent on others.
但我在那张石膏婴儿床上并不痛苦。离得很远。这是一个广阔的精神游乐场。似乎当你把你的大脑从移动你的身体的苦差事中解脱出来时,它就可以自由地做其他事情了。为了消磨那些时间,我想了又想。终于清楚地意识到我的生活和那个绊脚石一样偏离了轨道。
But I wasn’t miserable in that plaster crib. Far from it. It was a vast mental playground. It seems that when you relieve your brain from the chore of moving your body around, it becomes free for everything else. To while away those hours, I thought and thought and thought. And finally realized with harsh clarity that my life was as off course as that stumblebum.
出事了。在学术上我进展顺利,但我没有为我的艺术做任何事情。无奈之下,我做出了决定。当我从演员阵容中脱颖而出时,我会辞去教授的职务并返回加利福尼亚,那里“会有好事发生”。现在回想起来,这是一个令人惊叹的无内容计划。但我还是执行了它——好事确实发生了。在那里,我与我的蜂窝逻辑朋友 Dick Shoup 重新建立了联系。在他的催促下,我于 1974 年加入了他在全盛时期的施乐 PARC,并找到了彩色像素和绘画程序。艺术和计算机。36
Something was wrong. Academically I was well under way, but I wasn’t doing anything about my art. Inexorably, I reached a decision. When I emerged from the cast, I would resign my professorship and return to California where “something good would happen.” As I look back now, it was a breathtakingly content-free plan. But I executed it anyway—and the something good did happen. There I reconnected with my cellular logic friend, Dick Shoup. At his urging, I joined him in 1974 at Xerox PARC—in its heyday—and found color pixels and a paint program. Art and computers.36
迪克很清楚他不是第一个拥有彩色像素的人,但他不知道是谁。事实上,我们已经看到,Rougelot 和 Schumacker 及其团队比迪克早 6 年,也就是 1967 年获得了第一个彩色像素。他们的 6 位像素(64 色)在NASA-2 航天器模拟器。我在注释中列出了 1968 年和 1969 年每像素 2 位和 3 位的几个系统,包括贝尔实验室的琼·米勒 (Joan Miller) 的第一个 3 位像素(8 色)的绘画程序。所有这些发展,除了米勒的,都使用机械磁盘作为记忆,她的系统使用模拟色彩控制,所以它不是全数字的。37
Dick was clear that he wasn’t the first with color pixels, but he didn’t know who was. In fact, we’ve seen that Rougelot and Schumacker and their team had the first color pixels six years earlier than Dick, in 1967. Their 6-bit pixels (64 colors) were implemented in the NASA-2 spacecraft simulator. I list in the annotation several systems with 2 and 3 bits per pixel in 1968 and 1969, including the first paint program, with 3-bit pixels (8 colors), by Joan Miller at Bell Labs. All these developments, except Miller’s, used mechanical disks for memory, and her system used analog color control, so it wasn’t fully digital.37
迪克也不愿声称他是第一个使用 8 位像素(256 色)的人。谁知道,他会问,那些秘密政府机构在 1960 年代和 1970 年代都在做什么?我听说过 1973 年在 PARC 早于迪克的 8 位像素(256 色)的轶事,但没有找到任何文件证据。38
Dick was also reluctant to make the claim that he was first with 8-bit pixels (256 colors). Who knew, he’d ask, what those secret government agencies had been up to in the 1960s and 1970s? I’ve heard anecdotes, but found no documentary evidence, of 8-bit pixels (256 colors) predating Dick’s at PARC in 1973.38
尽管如此,SuperPaint 在几个方面表现出色:它有一个颜色映射,将 256 个像素值中的每一个映射到 1600 万种颜色中的一种——即 8 位输入,24 位输出。它是符合美国 NTSC 标准的完整视频,具有摄像机输入、NTSC 兼容视频输出和 NTSC 编码器,可在标准电视演播室监视器上显示。最重要的是,每个像素都在通用计算机的计算机程序控制之下。它可能是第一个完全数字化的 8 位帧缓冲系统——目前还没有定论。39
Nevertheless, there were several ways in which SuperPaint excelled: It had a colormap that mapped each of the 256 pixel values to one of 16 million colors—that is, 8 bits in, 24 bits out. It was video complete to the American NTSC standard, with a video camera in, NTSC-compatible video out, and an NTSC encoder for it to display on a standard television studio monitor. Most importantly, every pixel was under computer program control with a general-purpose computer. And it might have been the first completely digital 8-bit framebuffer system—the jury’s still out on that.39
图 7.20 显示了 1974 年在 PARC 上 SuperPaint 的菜单显示。顶部的 HSB 颜色选择器滑块——用于色调、饱和度和亮度——代表了我对 Digital Light 的第一个算法贡献。他们替换了 Shoup 最初在那里编程的 RGB 滑块(用于红色、绿色和蓝色)。我曾尝试将粉红色与 RGB 滑块混合,但无法做到。我让迪克添加一个艺术家友好的机制。我解释说,粉红色很容易混合,如果你可以从色环中选择一种色调——在这种情况下为红色——然后添加白色以使其变亮。或者选择橙色并添加黑色使其变暗为棕色。“从来没有人这样做过,”他说。所以我做到了,一夜之间实现了这个低调的水果概念。使用新的滑块,增加白色降低的饱和度。添加黑色减少值或亮度。40
Figure 7.20 shows SuperPaint’s menu display at PARC in 1974. The HSB color selector sliders at the top—for hue, saturation, and brightness—represent my first algorithmic contribution to Digital Light. They replaced the RGB sliders—for red, green, and blue—that Shoup originally programmed there. I had tried to mix pink with the RGB sliders and couldn’t do it. I asked Dick to add an artist-friendly mechanism. Pink is easy to mix, I explained, if you can choose a hue from the color circle—red in this case—then add white to lighten it. Or choose an orange hue and add black to darken it to a brown. “Nobody’s ever done that,” he said. So I did, implementing this low-hanging fruit concept overnight. With the new sliders, adding white reduced saturation. Adding black decreased value, or brightness. The hue chosen in this figure is a fully saturated and fully bright magenta.40
SuperPaint 不是计算机图形,尽管我花了数年时间才理解到足以做出这样的声明。中心教条没有生效。在上一章中,我将计算机图形定义为将几何模型渲染为像素。但迪克舒普的像素并没有为几何服务。SuperPaint(几乎)没有几何图形。
SuperPaint wasn’t computer graphics, although it took me years to understand enough to make that statement. The Central Dogma was not in effect. In the preceding chapter I defined computer graphics to be the rendering of geometric models into pixels. But Dick Shoup’s pixels weren’t in the service of geometry. SuperPaint had (almost) no geometry in it.
迪克当然知道如何将几何图形渲染成像素。正如我们在黎明一章中讨论的那样,他在 1973 年在 PARC,但不是在 SuperPaint 中渲染的没有锯齿的直线和车轮就是证明。SuperPaint 的菜单上有几个基于几何的工具。例如,单击最上面一行图标(图 7.20)中从左数第四个图标会调用画线工具。SuperPaint 然后会在用户选择的任意两点之间渲染一条锯齿状的线段。它可以渲染一个矩形。那是几何上的。
Dick certainly knew how to render geometry into pixels. The straight lines and wagon wheels he rendered without jaggies in 1973—at PARC, but not in SuperPaint—are witness to that, as we discussed in the Dawn chapter. And there were a couple of geometry-based tools available on the menu of SuperPaint. For instance, a click on the fourth icon from the left in the top row of icons (figure 7.20) invoked a line-drawing tool. SuperPaint would then render a jagged line segment between any two points the user selected. And it could render a rectangle. That was about it geometrically.
图 7.20
Figure 7.20
使用手持设备(在这种情况下是平板电脑上的触控笔)在显示器上移动光标是当时的一个新概念。迪克必须向每个新用户解释在平板电脑上单击并拖动“向下”的交互技术,同时跟随显示屏上的“向上”光标。从 1973 年的 SuperPaint 开始,彩色的菜单、图标、光标和滑块开始逐渐普及。
Moving a cursor on a display with a handheld device—a stylus on a tablet in this case—was a new concept then. Dick had to explain the interaction technique of clicking and dragging “down there” on the tablet, while following a cursor “up here” on the display to each new user. Menus, icons, cursors, and sliders—in color—began their climb to the commonplace starting with SuperPaint in 1973.
那么,什么是 SuperPaint?它是一种图片创作工具,但不是计算机图形学。它是基于像素的,但不是图像处理系统。它是互动的,但不是电子游戏。然而,它绝对是数码光,因为它是通过像素来调节的。
So, what was SuperPaint? It was a picture creation tool, but not computer graphics. It was pixel-based, but not an image processing system. It was interactive but not a videogame. It was definitely Digital Light, however, because it was mediated via pixels.
我以前使用的一些术语对于描述 SuperPaint 或一般的绘画程序特别有价值。关键的区别在于创意空间和展示空间。计算机图形学的创造力发生在一个看不见的创意空间中。它驻留在计算机内存中的几何模型中。它成为了当它通过像素渲染到显示空间时可见。绘画程序中的创造力直接发生在显示空间中。绘画程序是不区分创意空间和显示空间的图像创建系统。像素(通常)不是几何图形的渲染,也不是模拟现实。它们是由用户艺术家从头开始创建的。他们不尊重采样定理,因为他们不采样连续体。他们只是。这是一种冗长的说法,他们不尊重中央教条。典型的计算机图形程序就像摄影。您以完美的方式排列 3D 对象,然后从特定的角度拍摄它们。绘画程序就像绘画一样。他们让你从头开始制作你想要的任何图像。
Some of the terms I’ve used previously become especially valuable for describing SuperPaint, or paint programs in general. The crucial distinction is between Creative Space and Display Space. Creativity in computer graphics occurs in a Creative Space that’s invisible. It resides in a geometric model held in computer memory. It becomes visible when it’s rendered into Display Space via pixels. Creativity in a paint program occurs directly in Display Space. Paint programs are image creation systems that do not distinguish Creative Space from Display Space. The pixels (usually) aren’t renderings of geometry, nor do they simulate reality. They are created from scratch by the user-artist. They don’t honor the Sampling Theorem because they don’t sample a continuum. They just are. Which is a long-winded way of saying they don’t honor the Central Dogma. The typical computer graphics program is like photography. You arrange three-dimensional objects in the perfect way, and then take a picture of them from a particular viewpoint. Paint programs are like, well, painting. They let you make whatever image you want from scratch.
但是绘画程序绝对是合成计算机图形的一部分,而不是分析图像处理。图像处理没有创意空间。现代世界已经把绘画和图像处理混为一谈,所以原来的区别是模糊的。Adobe Photoshop 最初设计用于处理摄影图像,但现代版本包括各种风格的绘画和几何定义元素的结合。
But paint programs are definitely part of synthetic computer graphics and not analytic image processing. There is no Creative Space in image processing. The modern world has conflated painting and image processing, so the original distinctions are blurred. Adobe Photoshop was designed originally to process photographic images, but the modern version includes painting in a variety of styles and the incorporation of geometrically defined elements.
绘画程序背后有一个模型。但这只是一个比喻,不是几何学,也不是物理学。这是用画笔在画布上绘画的行为。像 SuperPaint 这样的绘画程序用计算机程序模拟了这个比喻。画笔只是一组像素。在图 7.20 中,当前选择的画笔(用红色箭头表示)是一个中等大小的圆盘。画笔的“手柄”是在其平板电脑上与 SuperPaint 一起使用的物理触控笔。它可能是一只老鼠,已经在 PARC 的其他地方使用,但 Shoup 发现这只老鼠很笨拙——“就像用一块肥皂画画。”
There is a model of sorts behind a paint program. But it’s just a metaphor, not geometry and not physics. It’s the act of painting with a brush on a canvas. A paint program like SuperPaint simulates this metaphor with a computer program. The brush is simply a cluster of pixels. In figure 7.20 the currently selected brush (indicated by a red arrow) is a medium-sized disk. The “handle” of the brush is the physical stylus used with SuperPaint on its tablet. It could have been a mouse, already in use elsewhere at PARC, but Shoup found the mouse clumsy—“like painting with a bar of soap.”
在 SuperPaint 中,当用户在平板电脑上滑动(无压力)触控笔时,显示屏上的光标会跟踪移动。所以光标总是显示当前位置。当用户在触控笔上施加压力,关闭笔尖上的一个小开关时,当前画笔的副本将写入该位置的帧缓冲区,并立即以当前颜色显示。只要您对触控笔保持压力,副本就会被写入帧缓冲区并因此显示出来,速度与可以从数位板读取触控笔位置一样快。这是当今与计算机交互的一种显而易见的方式,但当时并非如此。
In SuperPaint, as a user slides (without pressure) a stylus across a tablet, a cursor on the display tracks the movement. So the cursor always shows the current location. The moment the user applies pressure on the stylus, closing a tiny switch in its tip, a copy of the current brush is written into the framebuffer at that location, and it’s instantly displayed in the current color. So long as you keep pressure on the stylus, copies are written into the framebuffer—and hence displayed—as fast as the stylus location can be read from the tablet. This is an obvious way to interact with a computer today, but it wasn’t then.
究竟是什么被复制或绘制到帧缓冲区中?它是一组具有当前画笔形状、当前颜色并以当前位置为中心的像素。笔画由用户使用触控笔所走的路径定义,由用户的移动指示的一系列分离点。如果这些点足够接近,则连续绘制到帧缓冲区中的画笔副本会重叠并看起来形成一个连续的笔划。但中风实际上并不是连续的。在那些糟糕的过去,很容易将数位板划得太快以至于计算机跟不上,留下一个“划”的分开的笔刷副本。
What exactly gets copied, or painted, into the framebuffer? It’s a set of pixels with the shape of the current brush, in the current color, and centered on the current location. A paint stroke is defined by the path the user takes with the stylus, a sequence of separated points that are indicated by the user’s movements. If the points are close enough then the copies of the brush that are consecutively painted into the framebuffer overlap and appear to form a continuous stroke. But the stroke isn’t actually continuous. In those bad old days, it was easy to stroke the tablet so fast that the computer couldn’t keep up, leaving a “stroke” of separated brush copies.
最终,随着摩尔定律使计算机变得更快,编写的绘画程序可以沿着几何定义的路径呈现连续的笔触。但这需要多年的发展。一开始,渲染连续笔画的速度慢得令人尴尬。我们已经在这些页面中遇到过这个概念。第 6 章中 Ravi Shankar 的样条演示是一个几何定义的笔画。正是缓慢的渲染——我在平板电脑上的手势和笔画渲染到帧缓冲区之间的暂停——在那个演示中引起了惊喜和惊奇。
Eventually, as Moore’s Law made computers faster, paint programs were written that could render a continuous brush stroke along a geometrically defined path. But that took many years to develop. Rendering a continuous stroke was awkwardly slow at first. We have already encountered the notion in these pages. The spline demo for Ravi Shankar in chapter 6 was a geometrically defined paint stroke. It was the slow rendering—the pause between my gesture on the tablet and the rendering of the stroke into the framebuffer—that evoked the surprise and amazement in that demo.
Adobe Photoshop 是这一系列图片创建工具的主要产物,尽管它最初被设计为一个图像处理程序,用于交互式地按摩用相机拍摄的像素,而不是用画笔制作的。绘画隐喻是一个强有力的隐喻。SuperPaint 或更高版本的 Photoshop 等计算机程序将其重新解释为使用由用户控制的画笔定义的本地操作以交互方式创建或修改图片。
Adobe Photoshop is the dominant outgrowth of this line of picture-creation tools, although it was originally designed as an image processing program for interactively massaging pixels that were taken with a camera, not made with a brush. The painting metaphor is a powerful one. A computer program like SuperPaint or later Photoshop reinterprets it to mean interactively creating or modifying a picture with local operations that are defined by a brush that the user controls.
在我第一次接触 SuperPaint 和彩色视频系统后,我给 PARC 写了一封信,其中包含以下观察结果(与许多人一样,系统及其主要程序令人困惑):“我看到这台机器的第一个直觉是它会成为制作动画电影的好工具。” 为了准备正式加入他们,我从普雷斯顿·布莱尔(Preston Blair)的一本著名的操作手册中自学了角色动画的基础知识,这位伟大的动画师在迪斯尼的幻想曲(1940)中制作了风信子河马舞蹈。图 7.21 显示了反弹和走动的封面和页面。41
After my first encounters with SuperPaint and the Color Video System, I wrote a letter to PARC with this observation (confusing, as many do, the system with its principal program): “One of my first intuitions on seeing the machine was that it would be a fine instrument for making animated films.” In preparation for officially joining them, I taught myself the basics of character animation from a famous how-to book by Preston Blair, the great animator who made Hyacinth Hippo dance in Disney’s Fantasia (1940). Figure 7.21 shows the cover and the pages for bounces and walks.41
当我在 1974 年到达 PARC 时,早期 Genesys 动画程序的创始人 Ron Baecker 正在那里进行长期逗留。哈佛动画师埃里克·马丁也是如此。他们和我一样被 Dick Shoup 的 SuperPaint 系统所吸引。当然,Eric 很快就绘制并录制了一个可爱的弹跳球动画,The Ever-Popular Bouncing Ball (1974),该动画可在线获取。42
When I arrived at PARC in 1974, Ron Baecker, the dashiki-clad creator of the early Genesys animation program, was visiting there for an extended stay. And so was Harvard animator Eric Martin. They were as attracted to Dick Shoup’s SuperPaint system as I was. And, naturally, Eric soon painted and recorded a lovely bouncing ball animation, The Ever-Popular Bouncing Ball (1974), which is available online.42
在我的第一个动画中,有一个来自 Blair 书中的步行循环。然后我开始走一个海盗的头、一个泡菜、一把锤子和一个西红柿——以及大卫·迪弗朗西斯科(David DiFrancesco)头部的数字扫描。虽然我们不知道,但我们正在迈出最终通往皮克斯和第一部数字电影的道路上的一些第一步。
Among my first animations there was a walk cycle right out of Blair’s book. Then I proceeded to walk a pirate’s head, a pickle, a hammer, and a tomato—and a digital scan of David DiFrancesco’s head. Although we didn’t know it, we were taking some of the first steps on the road that would lead eventually to Pixar and the first digital movie.
当我遇到艺术家 David DiFrancesco 时,他已经在全球范围内寻找融合计算机和艺术的方法。允许获得国家艺术基金会的资助他在 1970 年代初与 Computer Image Corporation 的 Lee Harrison III 一起工作。大卫去东京是为了接触哈里森的一个作品,叫做 Scanimate,一种模拟动画机器,1974 年他刚刚回来,当时他看到迪克舒普在旧金山进行了 SuperPaint 演示。大卫从观众那里问迪克 SuperPaint 与哈里森的 Scanimate 有什么共同点。这是一个很好的问题,因为迪克和李哈里森是好朋友,迪克很了解 Scanimate。他鼓励大卫给 PARC 打电话。43
When I met the artist David DiFrancesco, he’d already been on a worldwide quest for ways to meld computers and art. A National Endowment for the Arts grant allowed him to work with Lee Harrison III of Computer Image Corporation in the early 1970s. David had gone to Tokyo for access to one of Harrison’s creations, called Scanimate, an analog animation machine, and had just returned in 1974 when he saw Dick Shoup give a SuperPaint demo in San Francisco. From the audience David asked Dick what SuperPaint had in common with Harrison’s Scanimate. It was a well-placed question because Dick and Lee Harrison were good friends, and Dick knew Scanimate well. He encouraged David to call PARC.43
图 7.21
Figure 7.21
但是当他的许多电话开始打来时,迪克让我处理这些电话。大卫不停的恳求,加上他不同寻常的幽默,对我施了魔法。我终于心软了,建议我们在 SuperPaint 上分享一个晚上的“干扰”。这意味着时间顺序的干扰——只有一个手写笔——一个艺术家会画一段时间,然后另一个会添加到画中,然后第一个艺术家会修改第二个的作品,等等。
But when his many calls started to come, Dick asked me to handle them. David’s nonstop entreaties, enlivened with his unusual humor, worked their magic on me. I finally relented and suggested that we share an evening “jamming” on SuperPaint. That meant time-sequential jamming—there was only one stylus—where one artist would paint for a while, then the other would add to the painting, then the first artist would modify the work of the second, and so forth.
大卫喜欢机器就像他喜欢艺术一样。他喜欢任何类型的机器——相机、汽车、飞机,尤其是摩托车。他是个摩托车狂——品味高雅。他的收藏品以 1938 年的 Brough Superior 和 1951 年的 Vincent Black Shadow 为特色。因为他喜欢所有的机器,所以他忍受了使用早期数字机器的固有折磨。他可以通过痛苦来获得结果。这都是冒险的一部分!
David loved machines as much as he loved art. He loved any kind of machine—cameras, cars, planes, and especially motorcycles. He was a motorcycle maniac—with refined taste. His collection featured a 1938 vintage Brough Superior and a 1951 Vincent Black Shadow. Because he liked all machines, he put up with the inherent torture of working with the early digital ones. He could drive right through the pain for the results. It was all part of the adventure!
这种对困难的漠不关心是早期计算机艺术家的特征。另一位大卫,大卫米勒,将在 PARC 与我们同在,并以 David Em 的身份继续加入帕萨迪纳喷气推进实验室的未来同事吉姆·布林。Em 将在 JPL 的荧光灯、咆哮和结冰的空调以及机构绿墙中受苦多年,以创作他的日落美丽的数字绘画和奇怪的瓷砖 3D 风景。您必须在他们的童年时期爱上这些机器并设想它们的成长。你必须渴望发现的过程,并相信这项技术会在“几年内”变得不那么苛刻。我们还没有学会援引摩尔定律,但这就是我们正在做的事情。
This indifference to hardship was characteristic of early computer artists. Another David, David Miller, would jam with us at PARC and proceed—as David Em—to join future colleague Jim Blinn at Pasadena’s Jet Propulsion Lab. Em would suffer for years in the fluorescent lights, roaring and freezing air conditioners, and institutional green walls at JPL to create his sunset-beautiful digital paintings and strangely tiled three-dimensional landscapes. You had to love the machines in their childhood and envision their growth. You had to crave the process of discovery and believe that the technology would become less harsh “in a couple of years.” We hadn’t yet learned to invoke Moore’s Law, but that’s what we were doing.
David DiFrancesco 熟悉他所说的“艺术商业”,他很快建议我们向 NEA 申请拨款,以利用 SuperPaint 提供的新艺术媒介——彩色光栅图形。他需要这笔钱,因为他只是非正式地在 PARC 工作,而我想做艺术并称之为艺术。作为纽约大学教授,我获得了几项国家科学基金会的资助。NSF 拨款提案有 40 页厚,一式 20 份提交,所以当大卫告诉我 NEA 是如何运作的时,我松了一口气。您只需要提交一个页面!他知道,因为他目前靠第二次 NEA 资助生活。伴随单页的艺术家作品是主要考虑因素。我们使用 Dick Shoup 的系统制作了一段视频,并提交了一份一页的赠款提案,巩固了我们的关系并共同投票。44
David DiFrancesco, familiar with “art biz” as he called it, soon suggested that we ask the NEA for a grant to exploit the new artistic medium that was offered by SuperPaint—color raster graphics. He needed the money since he was only at PARC unofficially, and I wanted to make art and call it that. I’d gotten several National Science Foundation grants as an NYU professor. NSF grant proposals were 40 pages thick and submitted in 20-plicate, so I listened in relieved surprise as David told me how the NEA worked. You only had to submit a single page! He knew because he was currently living on his second NEA grant. The artists’ work that accompanied the single page was the principal consideration. We made a video using Dick Shoup’s system and submitted it with a one-page grant proposal, cementing our relationship and casting our lots together.44
现在还不算太快。不久之后,我在 1975 年 1 月 16 日被解雇了。当我问我为什么被解雇时,鲍勃·泰勒的老板杰里·埃尔金德告诉我,施乐决定不做彩色。45
And it was not a moment too soon. I was fired soon afterward, on January 16, 1975. When I asked why I was being let go, Jerry Elkind, Bob Taylor’s boss, told me that Xerox had decided not to do color.45
“但是,”我难以置信地争辩道,“颜色就是未来,而你完全拥有它。”
“But,” I argued in disbelief, “color is the future, and you own it completely.”
“这可能是真的,但非黑即白是公司的决定。”
“That may be true, but it’s a corporate decision to go black and white.”
我不应该感到惊讶。鲍勃泰勒早些时候开了一枪警告。有一天他找我问:“你不觉得Shoup的系统很难用吗?纽曼的方法不是更好吗?” 他指的是威廉·纽曼,他和 SuperPaint 在同一个房间的一个角落里工作。威廉就是我们在计算章节中遇到的那个人,他是艾伦·图灵的导师马克斯·纽曼的儿子,曾与图灵本人玩过某种形式的大富翁。威廉当时正在 PARC 的 Alto 计算机上设计具有 1 位像素的黑白图形。“不!” 我在里面尖叫,而在外面悄悄地反对。泰勒显然不明白。
I shouldn’t have been surprised. Bob Taylor had fired a warning shot earlier. He had approached me one day and asked, “Don’t you think Shoup’s system is difficult to use? Isn’t Newman’s approach better?” He meant William Newman, who was working in a corner of the same room as SuperPaint. William was the very fellow we met in the computation chapter who was the son of Alan Turing’s mentor Max Newman and had played a form of Monopoly with Turing himself. William was designing black-and-white graphics with 1-bit pixels on PARC’s Alto computer. “No!” I had screamed inside, while disagreeing quietly on the outside. Taylor obviously didn’t get it.
所以施乐吹掉了彩色图形,就像他们在大约一年后错过了个人电脑一样。46
So Xerox blew off color graphics, just as they missed the personal computer about a year later.46
无论我们离开 PARC 的原因是什么,David DiFrancesco 和我都需要找到“下一个帧缓冲区”来满足我们希望获得的 NEA 拨款。随着摩尔定律的无情改进,帧缓冲区的大小将从几年后,PARC 的大型微波炉变成了单个图形卡,然后变成了现在图形芯片的一小部分。但在当时,帧缓冲区是一种稀有且昂贵的野兽。
Whatever the reasons for our departure from PARC, David DiFrancesco and I needed to find “the next framebuffer” to satisfy the NEA grant we hoped to land. With inexorable Moore’s Law improvements, a framebuffer would shrink from the size of a large microwave oven at PARC to a single graphics card a few years later, and then to a vanishingly small part of a graphics chip now. But at the time a framebuffer was a rare and expensive beast.
我们听说盐湖城的 Evans & Sutherland 正在建造下一个,所以那是我们的第一个目的地。纯属巧合,当我们驶入 E&S 的停车场时,一辆黄色和黑色的莲花在我们身边飞驰而过。Jim Kajiya 跳了出来,头发垂到腰间,甚至比我的还要长。Kajiya 是一位杰出的工程师和理论家——后来成为加州理工学院的教授——正在 E&S 构建下一个帧缓冲区。几十年来,他将是一位重要的同事。47
We heard that Evans & Sutherland in Salt Lake City was building the next one, so that was our first destination. By sheer coincidence, as we pulled into the parking lot at E&S, a yellow and black Lotus zipped in beside us. Out hopped Jim Kajiya, with hair down to his waist, even longer than mine. Kajiya, a brilliant engineer and theoretician—and later a professor at Caltech—was building the next framebuffer at E&S. He would be an important colleague for decades.47
我们希望能够访问这个新生的帧缓冲区的希望很快就破灭了。虽然我们从来没有提到“艺术”这个词,但很明显,艺术是我们的目的。这在政治上与犹他州与国防相关的资金来源——美国计算机图形的军事暴君——并不相符。我们正要失望地离开时,有人提到一位名叫亚历山大·舒尔(Alexander Schure)博士的来自长岛的“疯狂的富人”最近经过并“买下了眼前的一切”。“他买了帧缓冲吗?” 我急忙问道。是的!他想拍动画电影!以茶壶着称的马丁·纽厄尔(Martin Newell)第二天就要启程前往富人所在的纽约理工学院咨询。他答应给我打电话报告。
Our hopes that we would get access to this nascent framebuffer were quickly dashed. Although we never mentioned the word “art,” it was clear that art was our purpose. This didn’t mesh politically with Utah’s defense-related funding sources—the US military tyrant for computer graphics. We were about to depart disappointed when someone mentioned that a “crazy rich man” named Dr. Alexander Schure from Long Island had passed through recently and “bought one of everything in sight.” “Did he buy a framebuffer?” I asked hurriedly. Yes! And he wanted to make animated movies! Martin Newell, of teapot fame, was departing the next day to consult at the rich man’s school, the New York Institute of Technology. He promised to call me with a report.
纽厄尔的建议很快就来了,“如果我是你,我会跳上下一班飞机。” 大卫和我就是这样做的。
Newell’s advice soon came, “If I were you, I’d jump on the next plane.” David and I did just that.
“我们应该找谁?” 我问过另一个犹他州的熟人。
“Who should we ask for?” I had quizzed another Utah acquaintance.
“埃德·卡特莫尔。但要小心,他是虔诚的摩门教徒。”
“Ed Catmull. But be careful, he’s a devout Mormon.”
“这不是问题。”
“That’s not a problem.”
X(1975–1980)X (1975–1980)我们的愿景将加速时间,最终将其删除。
Our vision will speed up time, eventually deleting it.
——亚历山大·舒尔,NYIT 48总裁兼联合创始人
—Alexander Schure, president and cofounder, NYIT48
长岛的富人亚历山大·舒尔(图 7.22)是我们的“亚历克斯叔叔”,因为一个纯粹但惊人的巧合。我在 PARC 附近的加利福尼亚室友是 Richard 和 Sandra Gilbert。理查德告诉我,他在纽约的叔叔正在做我在 PARC 所做的事情,但我解雇了他。在计算机图形的小世界里,我怎么会不知道这样的人呢?理查,经济学家,一定是误会了。但是,当我第一次去纽约理工学院旅行回来时,我对在那里遇到的那个人感到非常兴奋,理查德惊呼道:“Alvy!他就是我一直想告诉你的那个叔叔。” 49
Alexander Schure, the rich man (figure 7.22) on Long Island, was our “Uncle Alex” because of a pure but astonishing coincidence. My California housemates near PARC were Richard and Sandra Gilbert. Richard told me that his uncle in New York was doing what I was doing at PARC, but I dismissed him. How could I not know about such a person in the small world of computer graphics? Surely Richard, an economist, must be mistaken. But when I returned from my first trip to the New York Institute of Technology, tremendously excited about the man I’d met there, Richard exclaimed, “Alvy! He’s the uncle I’ve been trying to tell you about.”49
图 7.22
Figure 7.22
亚历克斯叔叔认为自己是下一个沃尔特迪斯尼。你几乎可以看到错觉是如何形成的。一位家庭朋友 Alexander Nikolaievich Prokofiev de Seversky(图 7.23)、Alex 叔叔的“Sasha”以及纽约理工学院的受托人,曾在一部迪斯尼电影中出现。
Uncle Alex saw himself as the next Walt Disney. You can almost see how the delusion formed. A family friend, Alexander Nikolaievich Prokofiev de Seversky (figure 7.23), “Sasha” to Uncle Alex, and a trustee of the New York Institute of Technology, had featured in a Disney film.
De Seversky 在第一次世界大战中是俄罗斯的王牌海军飞行员。他是 1917 年革命后在俄罗斯不受欢迎的贵族,因此他乘坐西伯利亚大铁路前往符拉迪沃斯托克,然后乘坐日本轮船抵达旧金山,逃离了俄罗斯1918 年 4 月 21 日。50
De Seversky was an ace naval pilot for Russia in World War I. He was an aristocrat unwelcome in Russia after the 1917 Revolution, so he escaped from Russia by taking the Trans-Siberian Railway to Vladivostok and then a Japanese steamship that arrived in San Francisco on April 21, 1918.50
图 7.23
Figure 7.23
De Severksy 在纽约定居,在那里他创办了一家名为 Seversky Aircraft 的飞机公司,后来更名为 Republic Aviation。珍珠港事件发生后不久,他出版了一本颇具影响力的著作《通过空中力量取得胜利》,该书主张建立一支独立的美国空军。1943 年,迪斯尼公司把这本书变成了一部同名的动画宣传片,沃尔特热心支持这个项目。De Seversky 本人在影片中出现了大约 10 分钟。当胜利在纽约开业时,迪斯尼一家和他一起在长岛呆了几天。51
De Severksy settled in New York, where he started an aircraft company, Seversky Aircraft, later renamed Republic Aviation. Shortly after Pearl Harbor he published an influential book, Victory Through Air Power, which argued for the creation of an independent US air force. In 1943 the Disney company turned the book into an animated propaganda movie of the same name, a project that Walt supported enthusiastically. De Seversky himself appears in the film for about 10 minutes. The Disney family stayed with him on Long Island for several days when Victory opened in New York.51
1964 年,de Seversky 帮助 NYIT 购买了校园内最令人印象深刻的建筑(图 7.24),最初是为 Alfred I. du Pont 家族建造的。它最终将在几部电影中扮演角色,秃鹰的三天(1975)和亚瑟(1981)。舒尔为他的朋友和恩人将这座建筑改名为 de Seversky 豪宅。它将成为 1970 年代 NYIT 视频工作室未来的家,通过树林直接连接到“隔壁”的计算机图形实验室。de Seversky 的豪宅也将成为我和大卫·迪弗朗西斯科与亚历克斯叔叔第一次见面的戏剧性场景,由 Ed Catmull 和 Malcolm Blanchard 引导他到场。52
In 1964 de Seversky helped NYIT purchase the most impressive building on campus (figure 7.24), built originally for the Alfred I. du Pont family. It would eventually play roles in a couple of movies, Three Days of the Condor (1975) and Arthur (1981). Schure renamed the building the de Seversky mansion for his friend and benefactor. It would become the future home of the NYIT video studio in the 1970s, with a direct link to the computer graphics lab “next door” through the woods. The de Seversky mansion would also be the dramatic setting for the first meeting David DiFrancesco and I had with Uncle Alex, ushered into his presence by Ed Catmull and Malcolm Blanchard.52
在 Schure 听说过计算机图形学之前,他已经在校园里建立了一个 100 人的动画工作室来制作一部长篇动画电影Tubby the Tuba。它使用了我在有关电影和动画的章节中描述的相同的老式 cel 动画技术,迪士尼用来制作Victory Through Air Power的技术。
Before Schure ever heard of computer graphics, he had established a 100-person animation studio on the campus to work on a feature-length animated film, Tubby the Tuba. It used the same old-fashioned cel animation technology I described in the chapter about movies and animation, the technology Disney used to produce Victory Through Air Power.
但后来一位旅行推销员向 Alex Schure 推销计算机图形学。Pete Ferentinos 是 Evans & Sutherland 的东海岸销售代表。费伦蒂诺斯对 NYIT 打了一个冷电话,很快 Schure 就对计算机图形设备可以为Tubby the Tuba节省的成本表示热情。作为推销的一部分,Ferentinos 安排 Schure 参观盐湖城的 E&S,并会见 Dave Evans 和 Ivan Sutherland。53
But then a traveling salesman sold Alex Schure on computer graphics. Pete Ferentinos was the East Coast sales representative of Evans & Sutherland. Ferentinos made a cold call on NYIT and soon had Schure enthused about the cost savings that computer graphics equipment could make for Tubby the Tuba. As part of his sales pitch, Ferentinos arranged for Schure to visit E&S in Salt Lake City and meet Dave Evans and Ivan Sutherland.53
图 7.24
Figure 7.24
这一强大的攻势将舒尔推到了边缘。他为 NYIT 购买了几款 E&S 产品。然后埃文斯问他谁来运行这些设备,并补充说:“你只是错过了合适的人。” 他指的是刚毕业的 Ed Catmull。那是 1974 年,大约在我被带出 PARC 的同一时间。
This strong offensive pushed Schure over the edge. He bought several E&S products for NYIT. Then Evans asked him who would run the devices, adding, “You just missed the right man.” He meant recent graduate Ed Catmull. This was 1974, about the same time that I was being ushered out of PARC.
当 Ed 于 1974 年从犹他大学获得博士学位时,他的一位顾问 Ivan Sutherland 正在好莱坞创建一家使用计算机的公司。埃德希望这家公司能成为他进入电影制作,尤其是动画制作的门票。在 2017 年 5 月的 Skype 对话中,我向 Sutherland 询问了该公司的情况。
When Ed graduated from the University of Utah with his PhD in 1974, one of his advisers, Ivan Sutherland, was in the process of creating a company that would use computers in Hollywood. Ed hoped that this company would be his ticket into moviemaking, animation in particular. I asked Sutherland about the company in a May 2017 Skype conversation.
“我们早了 10 年,”萨瑟兰谈到他 1974 年的尝试时说,他和联合创始人格伦弗莱克计划将其称为图片/设计集团。萨瑟兰和弗莱克当时做了几项设计工作,但从来没有足够的工作来支持一家公司。它从未离开地面。54
“We were 10 years too early,” Sutherland said of his 1974 foray, which he and cofounder Glen Fleck planned to call The Picture/Design Group. Sutherland and Fleck did several design jobs at the time but could never get enough of them to support a company. It never got off the ground.54
埃德不能再等了。他有一个妻子和一个年幼的孩子要抚养。因此,他在波士顿的一家计算机辅助设计公司 Applicon 找到了一份工作。1974 年,纽约理工学院的 Alex Schure 打来电话时,他就在那儿。尽管 Ed 在 Applicon 只工作了一个月左右,但他抓住了 Schure 提供的机会——在纽约理工大学运行 E&S 设备并制作动画电影。Ed 的未来在于面向图片的计算机图形学,而不是 CAD。
Ed could wait no longer. He had a wife and a young child to support. So he took a job at a computer-aided design company, Applicon, in Boston. That’s where he was when the 1974 call came from Alex Schure at the New York Institute of Technology. Although Ed had been at Applicon for only a month or so, he leapt at the opportunity Schure offered—something about running E&S equipment at NYIT and making an animated movie. Ed’s future lay in picture-oriented computer graphics, not CAD.
Malcolm Blanchard 是犹他州计算机科学系的另一位毕业生,也是 Ed 在 Applicon 的同事,他于 1974 年底与他一起来到纽约理工大学。55
Malcolm Blanchard, another graduate of the Utah computer science department and Ed’s officemate at Applicon, came with him to NYIT in late 1974.55
几个月后,即 1975 年初,“实验室”的后两名成员加入了,当时所有新机器都已交付。他们是大卫·迪弗朗西斯科和我,来自施乐 PARC,鲍勃·泰勒创立的实验室。所以两个 ARPA 线程,Sutherland 和 Taylor 的,在 NYIT 交织在一起。
The second two members of “the Lab” joined just a few months later, in early 1975, before all the new machines had been delivered. They were David DiFrancesco and me, from Xerox PARC, the laboratory Bob Taylor had founded. So two ARPA threads, Sutherland’s and Taylor’s, entwined at NYIT.
1975 年,犹他州的基于几何的计算机图形学与 PARC 的基于像素的图形学结合,为该组织播下了种子,最终被称为皮克斯。这是艺术和技术的有力结合。另一种说法是,中心法则内部(犹他州)和中心法则外部(PARC)联手。纽约理工学院的四位最初的实验室成员——Ed、Malcolm、David 和我——将在 1980 年的卢卡斯影业和 1986 年的皮克斯集团的后期表现中保持在一起。
The geometry-based computer graphics at Utah married the pixel-based graphics at PARC in 1975 to seed the group to be known eventually as Pixar. It was a potent mixing of art and technology. Another way to put it is that inside the Central Dogma (Utah) and outside the Central Dogma (PARC) joined forces. The four original Lab members at NYIT—Ed, Malcolm, David, and I—would stay together through the later manifestations of the group as Lucasfilm in 1980 and Pixar in 1986.
埃德和马尔科姆是已婚男人,埃德很快有了第二个孩子。他们基本上在工作日保持朝九晚五的日程安排,周末不工作。但大卫和我仍然单身,日以继夜地工作,周末也是如此,创作艺术——尤其是在帧缓冲区到达之后。我们只在必要时才睡觉。
Ed and Malcolm were married men, and Ed soon had a second child. They essentially kept a 9-to-5 schedule on weekdays and didn’t work weekends. But David and I were still single and worked around the clock, on weekends too, making art—particularly after the framebuffer arrived. We slept only when we had to.
大卫靠他的 NEA 拨款过活,但它已经用完了。我们还没有听说我们一起提出的赠款的命运。大卫检查了一下,发现 NEA 失去了我们的艺术提交,这让他很生气,也让我很沮丧。为了弥补,他们同意实地考察。但这正是我们想要的!很难解释我们在做什么,但很容易展示。
David was living off his NEA grant, but it was running out. We hadn’t heard yet about the fate of the grant we’d proposed together. David checked and discovered to his anger and my dismay that the NEA had lost our art submission, the crucial part. To make amends they agreed to a site visit. But that’s exactly what we wanted! It was hard to explain what we were doing, but easy to show.
NEA 派出了艺术家 Stan Vanderbeek 和一位名叫 Nancy Rains 的官员。范德贝克很有名,在控制论的偶然性(在第 6 章中提到)和扩展电影(在这一章中)都有特色。事实上,范德贝克创造了“扩展电影”一词。56
The NEA sent out the artist Stan Vanderbeek and an official named Nancy Rains. Vanderbeek was famous, featured in both Cybernetic Serendipity (mentioned in chapter 6) and Expanded Cinema (in this one). In fact, Vanderbeek had coined the term “expanded cinema.”56
下午 4 点,我和大卫在长岛曼哈塞特火车站接了团队,这是现场访问的最后一天的最后一个小时。他们正在履行 NEA 的职责,但只是勉强而已。“我们需要赶上五点钟的火车,”雷恩斯命令道。这意味着我们只有三十分钟的时间参观。“好吧,但我们认为你不会想要。”
David and I picked up the team at the Manhasset, Long Island, train station at 4 p.m., the last possible hour of the last possible day for site visits. They were doing their NEA duty, but just barely. “We need to catch the 5 o’clock train,” Rains ordered. That meant we would have only thirty minutes for the visit. “OK, but we don’t think you’ll want to.”
他们没有。从我们在 PARC 的日子开始,David 和我就习惯于一看到彩色像素和光栅图形就张大嘴巴。NEA 对也不例外。我们聊了几个小时,看着照片,还拍了照片。最后,大约凌晨 4 点,他们建议是时候返回曼哈顿著名的阿冈昆酒店了。我们把他们赶了进来,我们四个人都洋溢着幸福和友情。在旅馆里,范德贝克把手伸进车窗,最后摇了摇,说:“好吧,你们这些孩子拿到了补助金!”
And they didn’t. From our days at PARC, David and I were accustomed to mouths agape at first sight of color pixels and raster graphics. The NEA pair were no different. We talked and looked at pictures—and made pictures—for hours. Finally, about 4 a.m., they suggested that it was time they returned to the renowned Algonquin Hotel in Manhattan. We drove them in, all four of us high with happiness and camaraderie. At the hotel, Vanderbeek thrust his hand through the car window for a final shake and said, “Well, you boys got your grant!”
在纽约理工学院以西约 10 英里的长岛北岸有一台不同寻常的实时计算机图形机。它模拟了一艘通过纽约市港口的大型油轮。现在很难相信,但是在阿拉斯加埃克森瓦尔迪兹石油泄漏灾难发生之前,有一个计划允许巨型油轮进入那个重要的港口。由于大型油轮需要一英里的转弯半径才能进行右转或左转,而且按照这个标准,纽约港是一个狭小的空间,船长必须先在模拟器上练习。这个想法很疯狂,从未发生过,但模拟器是真实的。后来,当噩梦终于在 1989 年发生在广阔的威廉王子湾时,它被用来重现和研究埃克森瓦尔迪兹的事故。57
There was an unusual real-time computer graphics machine on the North Shore of Long Island about 10 miles west of NYIT. It simulated a massive oil tanker negotiating New York City’s harbor. It’s hard to believe now, but there was a plan afoot to allow giant tankers in that important harbor—before the Exxon Valdez oil-spill disaster in Alaska, that is. Since a large tanker needs a mile turning radius to make a right or left turn, and since the New York harbor is a tight space by that measure, a skipper had to practice on a simulator first. The idea was crazy and never happened, but the simulator was real. And it was used later to recreate and study the Exxon Valdez mishap when that nightmare did finally happen in 1989—in vast Prince William Sound.57
盐湖城的 Evans & Sutherland 创建了海港模拟器,名称很笨拙,即计算机辅助运筹学设施或 CAORF(发音为“Kay orf”)。它于 1975 年 7 月安装在长岛金斯角的美国商船学院。你进入了一座砖房——船头!——通过舷窗通往“桥”。马桶是一个“头”。在里面,你发现自己在船桥上,配有导向轮、扫描雷达、速度控制杆和雾喇叭控制装置。所有这些都是真实的,而不是计算机模拟。
Evans & Sutherland in Salt Lake City created the harbor simulator, with the ungainly name Computer Aided Operations Research Facility, or CAORF (pronounced “Kay orf”). It was installed in July 1975 at the US Merchant Marine Academy in Kings Point, Long Island. You entered a brick building—with a prow!—through portholed doors to “the bridge.” The toilet was a “head.” Inside you found yourself on a ship’s bridge, complete with pilot wheel, sweeping radar, speed control lever, and foghorn control. All of these were real, not computer simulations.
(无玻璃)窗户的景色令人惊讶。它完全是计算机生成的,充满了你的视觉空间。桥上的真实设备是虚幻计算机模拟的人机界面。飞行员看到了简化的纽约港的 240 度展示,其中包括自由女神像、维拉萨诺海峡大桥、帝国大厦和纽约市的其他天际线。当你用轮子驾驶时,“油轮”穿过这个计算机生成的港口。58
The view out the (glassless) windows was the surprise. It was completely computer generated and filled your visual space. The real devices on the bridge were the human interface to the unreal computer simulation. The pilot saw a 240-degree display of a simplified New York Harbor with the Statue of Liberty, the Verrazano-Narrows Bridge, the Empire State Building, and the rest of the New York City skyline. The “tanker” moved through this computer-generated harbor as you piloted with the wheel.58
CAORF 由 NASA-2 的 Rod Rougelot 和 Bob Schumacker 和第一个彩色像素设计。他们于 1972 年 10 月离开 GE 并加入 E&S。Rougelot 自然成为 CAORF 的项目工程师,而 Schumacker 也在他的团队中。“我们把公司押在了这上面,”Rougelot 告诉我。它奏效了。航空业从油轮模拟器中了解到,也可以模拟驾驶飞机。航空公司飞行模拟器使 E&S 取得了成功。59
CAORF was engineered by Rod Rougelot and Bob Schumacker—of NASA-2 and the first color pixels. They had left GE and joined E&S in October 1972. Rougelot became the project engineer for CAORF, with Schumacker on his team, naturally. “We bet the company on it,” Rougelot told me. And it worked. The airline industry understood from the tanker simulator that piloting airplanes could be simulated too. Airline flight simulators made E&S successful.59
油轮模拟器的软件由 John Warnock 管理。他后来在 PARC,甚至后来共同创立了 Adobe。但与此同时,他的 E&S 商店在加利福尼亚。一位名叫克里斯汀·巴顿 (Christine Barton) 的年轻女性在 CAORF 的软件上工作,然后来到长岛,将其安装在这座令人敬畏的建筑中。
Software for the tanker simulator was managed by John Warnock. He was later at PARC and even later cofounded Adobe. But meanwhile his E&S shop was in California. A young woman, Christine Barton, worked there on CAORF’s software and came to Long Island for its installation in the prowed building.
Schumacker 于 1974 年参加了 Ed Catmull 在犹他大学的论文答辩。因此,在 CAORF 装置上,他邀请 Ed 到附近的纽约理工学院访问。这可能就是克里斯汀认识埃德的方式。她的说法是,她得知 NYIT 就在附近,并且最近购买了 E&S 设备,所以她打电话给 Ed 并在那里拜访了他。无论如何,在 Ed 描述了他在做什么之后,Christine 向他要了一份工作,他雇用了她。1975 年,她成为 NYIT 小组的第一位女性计算机科学家,也是该小组的第五位成员。她是早期以男性为主的计算机图形学领域为数不多的女性之一。60
Schumacker had attended Ed Catmull’s thesis defense at the University of Utah in 1974. So at the CAORF installation, he invited Ed over for a visit from nearby NYIT. That may have been how Christine met Ed. Her version is that she learned NYIT was nearby and had recently bought E&S equipment, so she called Ed and visited him there. In any event, after Ed described what he was doing, Christine asked him for a job, and he hired her. She was the first woman computer scientist with the NYIT group and its fifth member, in 1975. She was one of the few women anywhere in male-heavy early computer graphics.60
Christine 拥有网络专业知识。她曾与互联网的早期 ARPAnet 前身合作。在 LAN 成为通用术语之前,她会将我们在 NYIT 的多台计算机连接到局域网中。她的网络服务器还将帧缓冲区分配给竞争用户,这是当时世界上没有其他人遇到的问题。大多数地方都幸运地拥有一个能够以 512 x 512 像素分辨率保存一个 8 位视频图像(256 色)的帧缓冲区。NYIT 在其鼎盛时期拥有18个这样的帧缓冲区。可以使用 Christine 的系统以各种方式配置它们。例如,可以将其中的三个组合在一起形成 24 位全彩色视频图像(1600 万色)。61
Christine had network expertise. She had worked with the early ARPAnet precursor to the internet. She would connect our many computers together at NYIT into a local area network before LAN was a common term. Her network server also allocated framebuffers to competing users, a problem nobody else in the world had at the time. Most places were lucky to have one framebuffer capable of holding one 8-bit video image (256 colors) at 512 by 512 pixel resolution. NYIT, at its height, had 18 of these framebuffers. They could be configured in various ways using Christine’s system. For example, three of them could be ganged together for a 24-bit full-color video image (16 million colors).61
克里斯汀创造了艺术。和我们一样,她在 NYIT 的新生系统上制作了动画。她住在霍洛威学院,这是另一座与纽约理工学院有关的豪宅,离校园一英里左右。
And Christine made art. She created animations on the nascent system at NYIT, as we all did. She lived in Holloway House, yet another mansion associated with NYIT, this one a mile or so distant from the campus.
“克里斯蒂”,正如我们当时所说的,她带我们参观了新的 CAORF 模拟器,从而赢得了大卫·迪弗朗西斯科和我的喜爱。她有一个熟人,一名现场员工,晚上让我们进入设施。那是乐趣开始的时候。我们驾驶油轮,将模拟器发挥到极致。我们把天空染成了红色。我们以每小时 200 英里的速度驾驶油轮,低于水位 40 英尺,高于 40 英尺。我们全速飞过自由女神像,看看会发生什么,飞过帝国大厦。当然,什么也没发生——它是只是一个模拟。E&S 程序员没有在这些结构中放入任何信息,因为不应该有人在那里。用来模拟它们的多边形在被击中时就消失了——锐利的边缘从屏幕上退去——露出黑色的虚无,就像把彩色玻璃窗打碎到黑暗中一样。
“Christie,” as we called her then, endeared herself to David DiFrancesco and me by taking us to visit the new CAORF simulator. She had an acquaintance, an on-site employee, who let us into the facility at night. That’s when the fun began. We joyrode the tanker, taking the simulator to its limits. We turned the sky red. We flew the tanker at 200 miles per hour, 40 feet below the water level and 40 feet above. We flew it through the Statue of Liberty at full speed to see what would happen, and through the Empire State Building. Nothing happened, of course—it was just a simulation. The E&S programmers hadn’t put any information inside those structures, because no one was supposed to be there. The polygons that were used to simulate them simply went away when they were struck—sharp edges receding offscreen—revealing black nothingness, like shattering a stained-glass window into the dark.
图 7.25
Figure 7.25
以法莲·科恩著,1977 年。
By Ephraim Cohen, 1977.
图 7.25 是 1977 年实验室人员的示意图:(左起)Ephraim、Garland Stern 和 Lance Williams、Tom Duff 和 Christine Barton,Duane Palyka 和 Ed Catmull 隔着很远,而我和 David DiFrancesco 与我们的车辆.
Figure 7.25 is a drawing that shows the Lab personnel in 1977: (from the left) Ephraim, Garland Stern and Lance Williams, Tom Duff and Christine Barton, with Duane Palyka and Ed Catmull distant between them, and me and David DiFrancesco with our vehicles.
1975 年,影响我们图形和电影制作未来的两个人来到了纽约理工大学。来自犹他大学的 Lance Williams 和 Garland Stern 与我们一起度过了第一个夏天。兰斯和加兰是技术组合,身高差不多,都留着金色的长发——加兰扎着马尾辫。他们谈了同样的话,一起制定了计划。他们都在第二年夏天又来了,然后永久地加入了我们。62
Two people who would influence our graphics and moviemaking future arrived at NYIT in 1975. Lance Williams and Garland Stern, from the University of Utah, spent that first summer with us. Lance and Garland were a technological duo, approximately the same height, both with long blonde hair—Garland’s in a ponytail. They talked the same talk and hatched plans together. They both came again the next summer and then joined us permanently.62
多面的 Lance Williams 对我个人来说尤其重要。他和我一直在争吵,但正是这种智力上的较量让我们双方都受益——反正我也是。他向我介绍了威廉·巴勒斯 (William Burroughs) 的《裸体午餐》,这本书对我们这些刚刚离开 60 年代的人来说特别引人入胜,还向我介绍了布鲁斯·斯普林斯汀 (Bruce Springsteen)。
Multifaceted Lance Williams was particularly important to me personally. He and I argued all the time, but it was the kind of intellectual tussling that benefitted us both—me anyway. He introduced me to William Burroughs’s Naked Lunch, a particularly fascinating book for those of us just exiting the Sixties, and to Bruce Springsteen.
更重要的是,Lance 教会了我如何对光栅图像进行抗锯齿处理。他是从我在第 6 章中提到的音频专家 Tom Stockham 那里学到的,他教了一代犹他州学生有关采样的知识。Lance 还向我介绍了孙悟空,这是一个很受欢迎的亚洲文学人物,他将在我们的电影未来出现。63
More importantly, Lance taught me how to antialias raster images. He’d learned it from Tom Stockham, the audio expert I mentioned in chapter 6 who taught a generation of Utah students about sampling. And Lance also introduced me to the Monkey King, a popular Asian literary character who would figure in our cinema future.63
加兰·斯特恩(Garland Stern)一旦永久加入纽约理工学院,就编写了二维动画程序,该程序将告知皮克斯未来与迪士尼的关系。
Garland Stern, once he joined NYIT permanently, wrote the two-dimensional animation program that would inform Pixar’s future relationship with Disney.
摩尔定律还没有为 3D 动画提供足够的动力,因此了解计算机如何最好地帮助 2D 动画师是当时的问题。起初答案并不明显。
Moore’s Law hadn’t yet delivered enough horsepower for three-dimensional animation, so learning how the computer could best help two-dimensional animators was the issue of the day. The answer wasn’t obvious at first.
Ed Catmull 写了我们都认为是 cel 动画的计算机方法。. . 但有一个问题。他的动画程序,称为Tween,是一个出色的二维中间程序。它使用的插值与第 6 章中描述的关键帧动画程序非常相似,Nestor Burtnyk 和 Marceli Wein 于 1970 年在加拿大创建。动画师 Peter Foldes 在Burtnyk-Wein 中间系统上创作了具有里程碑意义的电影饥饿( Le Faim) (1974)。纽约理工学院的动画师最终制作了一部 22 分钟的电视短片,名为Measure for Measure (1980),部分内容是在 Tween 上。但他们遇到了困难。
Ed Catmull wrote what we all thought would be the computer approach to cel animation . . . but there was a problem. His animation program, called Tween, was an excellent two-dimensional inbetweening program. It used interpolation much like the keyframe animation program described in chapter 6 that Nestor Burtnyk and Marceli Wein had created in Canada in 1970. The animator Peter Foldes created the landmark film Hunger (Le Faim) (1974) on the Burtnyk-Wein inbetweening system. And NYIT animators eventually produced a 22-minute television short called Measure for Measure (1980) partly on Tween. But they had difficulties with it.
Ed 解决了他们提出的每一个问题,但他无法解决的内在缺陷是二维计算机动画比三维更难这一不直观的事实。考虑一个人在侧面向左走,摆动他的手臂。我们知道,凭借我们的人类智慧,远(或右)臂出现在男人的后面,消失在后面,然后在他走路时重新出现在他的面前。然后它在男人面前改变方向,消失在背后,然后重新出现在男人的背后。但是计算机不知道这一点。它如何从一个位置插入到另一个位置?“后面”是什么意思?是什么让这六个位置刚刚描述了一个物体的运动?在三个维度上,手臂是一个在空间中平稳移动的物体。
Ed addressed every issue they raised, but the intrinsic flaw he couldn’t address was the unintuitive fact that two-dimensional computer animation is more difficult than three-dimensional. Consider a man walking to the left in profile, swinging his arms. We know, with our human intelligence, that the far (or right) arm appears in back of, disappears behind, and then reappears in front of the man as he walks. Then it changes directions while in front of the man, disappears behind, and then reappears in back of the man. But the computer doesn’t know this. How does it interpolate from one position to the other? What does “behind” mean? What makes the six positions just described the motion of a single thing? In three dimensions, the arm is one object moving smoothly through space. The standard hidden-surface solutions of computer graphics take care of the arm’s disappearing behind the body as it swings.
受过经典训练的 NYIT 动画工作人员发现 Tween 令人生畏。对于习惯用铅笔和纸的人来说,这并不自然。图 7.26 是Measure for Measure中罗马士兵的角色“模型表” ,说明了他们感到沮丧的原因。基于此模型表的关键帧中的每条编号曲线对应于下一个关键帧中的类似曲线,其中士兵处于稍微改变的位置——例如,头部稍微转动,右臂抬起。Tween 通过动画师必须提供的指令将每条曲线插值到其对应的曲线上。如果关键帧比如第 10 帧,下一个关键帧是第 14 帧,然后 Tween 将创建三个由这些插值曲线组成的中间帧。
The classically trained NYIT animation staff found Tween formidable. It wasn’t natural to people who were used to pencil and paper. Figure 7.26, a character “model sheet” for a Roman soldier in Measure for Measure, suggests why they were dismayed. Each numbered curve in a keyframe based on this model sheet corresponds to a similar curve in the next keyframe, which has the soldier in a slightly altered position—head turned a little and right arm raised, say. Each curve was interpolated by Tween to its corresponding curve via instructions that the animators had to provide. If the keyframe was frame number 10, say, and the next keyframe was frame number 14, then Tween would create three inbetween frames composed of those interpolated curves.
图 7.26
Figure 7.26
图 7.27
Figure 7.27
图 7.27 显示了仅移动士兵右臂的困难。在最左边寻找曲线编号 39。图 7.27(左)显示了曲线 39 从其在关键帧 10 中的位置到其在关键帧 14 中的位置沿直线路径(虚线)以相等的时间步长移动。这只是一个愚蠢的插值。计算机不知道这是一只手臂,需要像手臂一样在一个单元中移动。请注意,曲线向运动的中间方向缩短,然后再次变长。所以这个手臂会随着它的移动而改变大小和外观体积。并且中间帧在帧之间移动相同的距离。动画师几乎从不想要一个僵硬和不优雅的动作。
Figure 7.27 shows the difficulties of moving only the soldier’s right arm. Look for curve number 39 on the leftmost edge. Figure 7.27 (left) shows curve 39 moving from its position in keyframe 10 into its position in keyframe 14 along a straight-line path (dotted line) in equal time steps. It’s just a dumb interpolation. The computer has no idea that this is an arm and needs to move in a unit like an arm. Notice that the curves shorten toward the middle of the motion then lengthen again. So this arm would change size and apparent volume as it moved. And the inbetweens move the same distances between frames. Animators hardly ever want a movement that rigid and ungraceful.
为了实现令人愉悦的动作,纽约理工学院的动画师必须告诉 Tween 要遵循的路径以及如何在时间间隔内间隔。在图 7.27(右)中,手臂边缘沿曲线(虚线)移动并保持长度。它在(必然)相等的时间步长中移动不同的距离。它慢慢地移动,然后快速,然后又缓慢地移动。在最坏的情况下,动画师同样必须告诉每一行如何移动——仅此罗马就有一百多行。
To achieve a pleasing movement, the NYIT animators had to tell Tween what path to follow and how to space the inbetweens in time. In figure 7.27 (right), the arm edge moves along a curved arc (dotted) and preserves length. And it moves different distances in the (necessarily) equal time steps. It moves slowly then fast then slowly again. In the worst case, the animators would similarly have to tell every line how to move—for over a hundred lines in this Roman alone.
对于经典动画师来说,补间插值不仅是一种全新的工作方式,而且我们计算机图形学人员也发现它本质上也很困难。这对我们来说是一个重要的教训。由于电影的定义要求它是完全数字化的——不允许手绘——它几乎肯定需要 3D 角色模型。第三个维度,以及它的连接性、对象和深度的概念,将产生巨大的影响。
Not only was Tween interpolation a completely new way of working for the classic animators, but we computer graphics people found it inherently difficult too. It was an important lesson for us. Since the definition of The Movie required that it be completely digital—nothing hand-drawn allowed—it would almost certainly require three-dimensional character models. The third dimension, with its notions of connectedness, objects, and depth, would make all the difference.
与此同时,Garland Stern 创建了一个二维动画程序,纽约理工学院的动画师们可以直观地理解——一个允许手绘的程序。他们使用它(除了 Tween 之外)来生成Measure for Measure。它允许他们在铅笔和纸,一如往常。他们——而不是计算机——做了关键帧插值,就像他们一直做的那样。他们手工制作了所有中间帧。但其他一切都是在计算机上完成的——着墨、不透明、构图和拍摄。原始图纸是模拟的,但其他一切都是数字的。64
Meanwhile Garland Stern created a two-dimensional animation program that the NYIT animators did intuitively understand—one that allowed hand drawing. They used it (in addition to Tween) to produce Measure for Measure. It allowed them to work in pencil and paper, just as they always had. They—not the computer—did the keyframe interpolation, just like they always had. They created all the inbetween frames by hand. But everything else was done on the computer—inking, opaquing, frame composition, and filming. The original drawings were analog, but everything else was digital.64
Garland 的程序,称为SoftCel,是一个“扫描和绘制”系统。动画师用铅笔和纸在标准 cel 动画纸上绘制每一帧,就像他们往常一样。每帧中的单独字符被绘制在单独的纸片上,并分别手工绘制在中间。使用扫描仪,加兰将动画师制作的每幅画都数字化了。也就是说,他通过对其进行采样并将如此获得的灰度像素存储在计算机中的数字文件中来制作每幅图的数字版本。像素是拍摄的,不是制作的。曲线没有锯齿,因为它们不是来自硬边高频几何图形的渲染。扫描仪保留了实际铅笔画的平滑度。65
Garland’s program, called SoftCel, was a “scan-and-paint” system. The animators drew each frame with pencil and paper on standard cel animation paper just as they always had. Separate characters in each frame were drawn on separate pieces of paper and inbetweened, by hand, separately. With a scanner, Garland digitized each drawing the animators produced. That is, he made a digital version of each drawing by sampling it and storing the grayscale pixels so obtained in digital files in the computer. The pixels were taken, not made. The curves didn’t have jaggies because they weren’t renderings from hard-edged, high-frequency geometry. The smoothness of the actual pencil drawings was preserved by the scanner.65
每一帧都被带入帧缓冲区,以便在计算机显示器上看到。通常它是嘈杂的,由灰尘产生的虚假点,例如,在扫描期间在纸张上或扫描仪玻璃上。SoftCel 用户将消除扫描图像的噪声并对其执行其他图像处理任务,例如增亮和对比度增强。一项重要的工作是关闭所有打开的曲线。动画师可能认为他画了一个封闭的椭圆,而事实上,他在其中留下了一个小间隙。对于下一步——用纯色填充一个区域——关闭这些间隙至关重要。您可以将本段中的所有过程视为在传统 cel 动画中使用印度墨水在透明 cel 上上墨的数字版本。
Each frame was brought into a framebuffer so that it could be seen on a computer display. Typically it was noisy, with spurious dots created by dust, say, on the paper or on the scanner’s glass during scanning. A SoftCel user would rid the scanned image of noise and perform other image processing chores on it—such as brightening and contrast enhancement. An important chore was to close all open curves. An animator might have thought he’d drawn a closed oval when, in fact, he’d left a small gap in it. It was crucial to the next step—filling an area with solid color—that such gaps be closed. You can think of all the processes in this paragraph as the digital version of inking on a transparent cel with India ink in traditional cel animation.
然后像素创建阶段接管了扫描和绘画的绘画部分。在纽约理工大学的头几个月,我编写了一个名为TintFill的程序来完成传统 cel 动画中不透明步骤的数字等效。正如我在电影和动画章节中所描述的,经典的遮光剂用印度墨水在 cel 上绘制线条内的区域。就像孩子的图画书一样,重点是保持纯色画在线条内,而不是越过它们。66
The pixel creation stage then took over—the paint part of scan-and-paint. During my first months at NYIT, I wrote a program called TintFill to accomplish the digital equivalent of the opaquing step in traditional cel animation. As I described in the movies and animation chapter, classic opaquers painted the areas inside lines drawn on a cel in India ink. Like with a child’s coloring book, the point was to keep the solid color painted inside the lines, not crossing them.66
同样,TintFill 用单一的纯色填充封闭区域(例如 Roman 的右臂和手指)。用户将选择一种颜色,然后单击要填充它的区域。TintFill 完成了剩下的工作。如果 TintFill 在封闭曲线中发现间隙,则颜色会泄漏并淹没整个绘图,因此需要关闭区域定义曲线中的所有间隙。
Similarly, TintFill filled closed areas—such as the Roman’s right arm and fingers—with a single solid color. A user would select a color then click on an area to be filled with it. TintFill did the rest. If TintFill found a gap in an enclosing curve, then the color leaked out and flooded the entire drawing, hence the need for closing all gaps in area-defining curves.
一个字符的所有区域都以这种方式依次填充。结果被保存到计算机上的数字文件中。此时,最终作品的每一帧都存在多个文件。如果一个场景中有三个动画角色,那么该场景中的每一帧都有三个单独的数字文件,每个角色一个。
All areas of a character were sequentially filled this way. The result was saved to a digital file on the computer. At this point, several files existed for each frame of the final piece. If there were three animated characters in a scene, then there were three separate digital files, one for each character, for every frame in that scene.
同时,一位艺术家使用数字绘画程序将背景场景绘制到帧缓冲区中,并将每个场景保存到数字文件中。由于我在 Xerox PARC 使用 Dick Shoup 的 SuperPaint 时就知道如何编写绘画程序,所以我在 NYIT 早期的另一个主要程序是Paint,这是一个具有 256 种颜色的 8 位绘画程序。还有其他几个 8 位绘图程序,包括 Garland Stern 在犹他州编写并随身携带的一个。因为我想要一个不同的用户界面,所以我自己编写了一个,然后我与专业的 cel 动画背景艺术家 Paul Xander 合作,使这个工具成为他使用的有效工具。67
Meanwhile, an artist painted background scenes into a framebuffer using a digital paint program and saved each into digital files. Since I knew how to write paint programs from my time with Dick Shoup’s SuperPaint at Xerox PARC, my other major program in the early days at NYIT was Paint, an 8-bit paint program with 256 colors. There were several other 8-bit paint programs in existence, including one that Garland Stern had written at Utah and brought with him. I wrote my own since I wanted a different user interface, and then I worked with a professional cel-animation background artist, Paul Xander, to make this an efficient tool for his use.67
最后一步是将一帧的所有数字文件组合或“合成”成最终帧,并将其发送到胶片打印机或录像机。首先将帧的背景场景从数字文件恢复到帧缓冲区。然后每个字符层将在背景上方以适当的顺序恢复。角色图层的透明部分可以让后面的图像显示出来,尤其是背景。Alpha 通道使这种合成成为可能。
The final step was to combine, or “composite,” all the digital files for one frame into a final frame and send it to a film printer or a videotape recorder. First a background scene for the frame would be restored to a framebuffer from a digital file. Then each of the character layers would be restored in proper order above the background. The transparent parts of the character layers would let the images behind show through, the background in particular. The alpha channel made such compositing possible.
我们在纽约理工学院接触的一切都是第一次。我们曾经尝试过列出第一名,但很快就长得离谱。但寿命最长、影响最大的事件几乎是偶然发生的。Ed Catmull 和我发明了alpha 通道。
Everything we touched at NYIT was a first. We tried to make a list of firsts once, but it soon became ridiculously long. But the one that had the longest life and the most ramifications happened almost casually. Ed Catmull and I invented the alpha channel.
在实验室历史的早期和一天傍晚,我们的赞助人 Alex Schure 叔叔拜访并问我:“我们拥有世界上最好的计算机图形,对吗?” 我向他保证我们做到了。“我们如何留在前面?” 当时我们只有一个帧缓冲区,512 x 512 像素,每像素 8 位(256 色)。它花费了舒尔 80,000 美元。我告诉他,如果他再给我们买两个 8 位帧缓冲区,那么我们可以将它们组合在一起并拥有一个 24 位帧缓冲区(超过 1600 万种颜色)。我解释了 256 色和 16 兆色之间的区别,世界上没有人有这种能力。
Early in the Lab’s history and late one evening, our patron Uncle Alex Schure visited and quizzed me: “We have the best computer graphics in the world, right?” I assured him that we did. “How do we stay out in front?” We had only one framebuffer at the time, 512 by 512 pixels, 8 bits per pixel (256 colors). It had cost Schure $80,000. I told him that if he bought us two more 8-bit framebuffers then we could gang them together and have one 24-bit framebuffer (over 16 million colors). I explained the difference between just 256 colors and 16 megacolors, and that nobody in the world had that capability.
我不相信 Schure 理解我,但几周后他宣布他又买了五个8 位的东西,所以我们会有两个24 位的东西!五个新的 8 位帧缓冲区每个花费 60,000 美元。因此,第一个 RGB 或全彩色 24 位帧缓冲区花费了他 200,000 美元——最初购买 8 位的 8 万美元加上购买两个新的 8 位的 12 万美元——但第二个只花费了 180,000 美元。我们不仅拥有世界上第一个全彩色帧缓冲区,而且还拥有其中两个。他在我们身上花了相当于今天的 1,700,000 多美元,就我这么说。回想起来,这种慷慨比当时更让我印象深刻。当时,我们很兴奋。
I wasn’t convinced that Schure understood me, but a few weeks later he announced that he’d bought five more of those 8-bit thingees, so we would have two of those 24-bit thingees! The five new 8-bit framebuffers cost $60,000 each. So the first RGB, or full-color, 24-bit framebuffer cost him $200,000—$80K for the initial 8-bit purchase plus $120K for two new 8-bit ones—but the second one only cost $180,000. Not only did we have the first full-color framebuffers in the world, but we had two of them. And he had spent the equivalent in today’s money of over $1,700,000 on us, just on my say so. This largesse impresses me even more in retrospect than it did then. At the time we were, simply, thrilled.
他很快就会以大约 40,000 美元的价格为我们再购买 12 个 8 位帧缓冲区——摩尔定律在起作用。这总计额外增加了 480,000 美元,或今天约为 1,900,000 美元。大约在 1978 年,我们拥有比地球上任何其他人都多的全彩色像素。我们是计算机图形界羡慕的对象。对于校准,您今天的手机拥有的像素内存容量比实验室所有 18 个帧缓冲区的总和还要多。而且,作为对所有这一切背后的源源不断的驱动力的提醒,摩尔定律从那时起已经提升了八个数量级。68
He would soon buy us 12 more 8-bit framebuffers at about $40,000 each—Moore’s Law at work. That totals to an additional $480,000, or about $1,900,000 today. We easily had more full-color pixels than anybody else on the planet in about 1978. We were the envy of the computer graphics community. For calibration, your cellphone today has more pixel memory capacity than all 18 of the Lab’s framebuffers combined. And, as a reminder of the incessant driving force behind all this, Moore’s Law has cranked through eight orders of magnitude since then.68
我们为全 24 位 RGB 疯狂。我在 1977 年将具有 8 位像素的 Paint 推广到具有 24 位像素的Paint3。我将其称为 Paint3,因为它使用了三个帧缓冲区。它是世界上第一个“全彩”或 24 位绘画程序。它具有 16 种百万色——如此之多,以至于艺术家可以用不会产生锯齿的软边刷子进行绘画。颜色融合在一起,就像它们与真正的油漆一样。“这就像用冰淇淋蛋筒作画,”有人令人难忘地说道。69
We went crazy with full 24-bit RGB. I generalized Paint with 8-bit pixels to Paint3 with 24-bit pixels in 1977. I called it Paint3 because it used three framebuffers. It was the first “full-color,” or 24-bit, paint program in the world. It featured 16 megacolors—so many that an artist could paint with soft-edged brushes that didn’t create jaggies. The colors melded together as they would with real paints. “It’s like painting with an ice-cream cone,” someone said memorably.69
我很快将所有面向像素的程序推广到 24 位版本。有了这么多的记忆,Ed 和我很容易一天就能为每张数码照片添加第四个频道。我们称它为 Alpha 通道。我们创建它是为了解决一个特定问题,没有意识到 alpha 会变得多么重要。现代数字成像世界依赖于它。
I soon generalized all pixel-oriented programs to the 24-bit version. And with so much memory lying around, it was easy for Ed and me to leap one day to the addition of a fourth channel for every digital picture. We called it the alpha channel. We created it to solve one particular problem, not realizing how important alpha would become. The modern digital imaging world depends on it.
Ed 试图解决的问题是一个长期存在的问题,即我之前讨论过的隐藏表面问题——从虚拟相机的角度来看,场景的哪些表面是可见的?不必渲染隐藏的表面,从而节省大量计算时间。已经有几种算法可以解决这个问题。
The problem Ed was trying to solve was the perennial one, the hidden-surface problem that I’ve previously discussed—what surfaces of a scene are visible to a virtual camera from its point of view? Hidden surfaces don’t have to be rendered, saving much computation time. There were already several algorithms available that made stabs at this problem.
Ed 正在开发一个新的,假设虚拟相机看到一个二维世界,它被分成一系列小方块,就像透过一个窗纱一样。(稍后会详细介绍。)请注意,小方块是模型的几何定义区域,而不是像素。
Ed was developing a new one that assumed the virtual camera saw a two-dimensional world divided into an array of little squares, as through a window screen. (More about that later.) Note that the little squares were geometrically defined areas of the model—not pixels.
Ed 的算法计算了他模型中每个几何对象与每个小正方形区域的交集。如果几个对象与一个正方形相交,则它进一步确定每个对象的多少区域对虚拟相机可见。换句话说,他解决了每个小正方形区域的隐藏表面问题,并用一个像素表示结果。每个像素代表其位置周围的方形几何区域。问题是确定最能代表单个正方形区域内所有复杂性的一种颜色。
Ed’s algorithm calculated the intersection of each geometric object in his model with each of the little square areas. If several objects intersected a square, then it further determined how much area of each object was visible to the virtual camera. In other words, he solved the hidden-surface problem in each little square area and represented the result with one pixel. Each pixel represented a square geometric area around its location. The problem was to determine the one color that would best represent all the complexity inside a single square area.
该正方形区域的最终前景像素颜色是贡献对象颜色的平均值,每种颜色均由其占据的正方形区域加权。它的不透明度是被物体遮挡的正方形区域。如果他们完全遮蔽了广场,然后那里的前景像素完全不透明。如果他们完全错过了正方形,那么像素是完全透明的。否则它是部分不透明的。
The final foreground pixel color for that square area was an average of the colors of the contributing objects, each weighted by the area of the square it occupied. Its opacity was the area of the square obscured by the objects. If they completely obscured the square, then the foreground pixel there was completely opaque. If they completely missed the square, then the pixel was completely transparent. Otherwise it was partially opaque.
Ed 想针对任何二维背景渲染三维前景对象。为了测试算法,他从预设的背景图片开始,这样他就可以知道每个小方块背后的最终颜色,以防被前景物体遮挡。但他不想总是有一个“硬连线”的背景。
Ed wanted to render three-dimensional foreground objects against any two-dimensional background. To test the algorithm, he started with a preset background picture so that he would know the ultimate color behind every little square, in case it wasn’t obscured by the foreground objects. But he didn’t want to always have a “hard-wired” background.
他对我说:“我希望有一些简单的方法可以在不同的背景下检查我的算法。” 我们聊了几分钟,很快就看到了解决方案。在他计算每个最终像素的某个时刻,他的算法如上所述计算了结果前景颜色及其部分不透明度。将其与背景颜色相结合是一个可分离的问题。所以我们把它分开了。
He said to me, “I wish there was some easy way to check my algorithm against different backgrounds.” We chatted for a few minutes and quickly saw the solution. At some point in his computation of each final pixel, his algorithm calculated, as described above, the resulting foreground color, and its partial opacity. Combining this with the background color was a separable problem. So we separated it out.
我编写了在 NYIT 使用的程序,用于在计算机文件中保存和恢复数字图像,这些文件通常存储在数字磁盘上。这些是第一个全彩色、24 位保存和恢复程序,因为我们是第一个拥有 24 位像素的程序。我立刻知道如何解决 Ed 的问题。我会简单地为这些程序中的每个像素添加第四个通道。它将保持像素的不透明度。
I had written the programs used at NYIT to save and restore digital images to and from computer files, typically stored on a digital disk. These were the first full-color, 24-bit save and restore programs, because we were the first to have 24-bit pixels. I knew immediately how to solve Ed’s problem. I would simply add a fourth channel to each pixel in these programs. It would hold the pixel’s opacity.
如果一个像素是不透明的,它的 8 位 alpha 通道的值为 255(全为 1)。如果它是透明的,它的 alpha 值为 0(全为 0)。两者之间有 254 种可能的部分不透明度。所以每个图像像素现在有 32 位,红色、绿色、蓝色和 alpha 各 8 位。我们称它们为 RGBA 像素。Christine Barton 的帧缓冲区分配系统让我们从网络上的四个 8 位帧缓冲区中配置一个 32 位帧缓冲区。
If a pixel was opaque, its 8-bit alpha channel had value 255 (all 1s). If it was transparent, its alpha value was 0 (all 0s). There were 254 possible partial opacities available in between. So each image pixel now had 32 bits, 8 each for red, green, blue, and alpha. We called them RGBA pixels. Christine Barton’s framebuffer allocation system let us configure a 32-bit framebuffer from four 8-bit ones on the network.
Ed 将更改他的算法,使其仅计算每个像素的前景色及其不透明度,并将结果保存到计算机文件中,该文件支持新的第四个通道。换句话说,他会忽略背景颜色,直到后面的步骤。我将重写恢复程序,以便它能够识别新的 alpha 通道并使用它来正确地将 Ed 计算的前景色与已经显示在帧缓冲区中的任意背景结合起来。
Ed would change his algorithm so that it computed only the foreground color and its opacity at each pixel and saved the results to a computer file, one that honored the new fourth channel. In other words, he would just ignore the background color until a later step. I would rewrite the restore program so that it would recognize the new alpha channel and use it to correctly combine Ed’s computed foreground color with an arbitrary background that was already displayed in a framebuffer.
为什么我们称它为alpha?因为这是我们在公式中用于组合前景图像和背景图像的术语。简而言之,我将它们称为f和b。Alpha 是希腊字母α,但我们以这种方式发音公式:“alpha f plus one minus alpha b ”。这个想法是 alpha 就像一个控制旋钮,当你转动它时,它会从 0 到 1 平滑地变化。“alpha f ”是指 alpha 乘以f。因此,转动控制旋钮会导致这种对结果的贡献从无前景图像平滑地变化到完整的前景图像。“一减阿尔法b ”表示“一减阿尔法”乘以乙。转动旋钮会导致此贡献从完整背景图像变为无背景图像。
Why did we call it alpha? Because that’s the term we used in the formula for combining a foreground image with a background image. For short I’ll call them f and b. Alpha was the Greek letter α, but we pronounced the formula this way: “alpha f plus one minus alpha b.” The idea was that alpha was like a control knob that varied smoothly from 0 to 1 as you turned it. By “alpha f” we meant alpha times f. So turning the control knob caused this contribution to the result to vary smoothly from no foreground image to full foreground image. And “one minus alpha b” meant the quantity “one minus alpha” times b. Turning the knob caused this contribution to vary from full background image to no background image.
图 7.28
Figure 7.28
图 7.29
Figure 7.29
这个想法是只转动一个控制旋钮,并将两个贡献加在一起。所以旋钮在一个极端(alpha 为 0)会导致没有前景图像加上完整的背景图像——只有背景。在另一个旋钮极端(alpha 为 1)处,结果是完整的前景图像加上没有背景图像——只有前景。Alpha 的值直接反映了前景图像的不透明度。
The idea is that only one control knob is turned, and the two contributions are added together. So the knob at one extreme (alpha is 0) results in no foreground image plus full background image—only background. At the other knob extreme (alpha is 1), the result is full foreground image plus no background image—only foreground. Alpha’s value directly reflects the opacity of the foreground image.
旋钮处于中间位置(alpha 为 0.5)会产生一半前景和一半背景的图像。在其四分之一的位置(alpha 为 0.25),生成的图像是四分之一的前景图像加上四分之三的背景图像。如果您将旋钮从一个极端平滑地转动到另一个极端,您将获得从背景图像到前景图像的完整电影交叉溶解。一幅图像平滑地替换了另一幅图像。图 7.28 显示了从蓝色方块上的白色十字到白色方块上的红色圆圈的交叉融合,因为 alpha 从 0 到 1 以 0.25 的步长变化。
The knob at its halfway position (alpha is .5) results in an image that is half foreground and half background. At its one-quarter position (alpha is .25), the resulting image is one-fourth foreground image added to three-fourths background image. If you smoothly turn the knob from one extreme to the other, you get a full movie cross-dissolve from background image to foreground image. One image smoothly replaces the other. Figure 7.28 shows a cross-dissolve from a white cross on a blue square to a red circle on a white square, as alpha varies from 0 to 1 by steps of .25.
我一直在谈论好像整个图像只有一个 alpha 值(不透明度)。事实上,这就是图 7.28 所示的内容。但是通过在每个像素中引入一个 alpha 通道,我们允许每个像素具有不同的不透明度。相同的公式在逐个像素的基础上起作用。一些前景像素可以是透明的,一些是不透明的,还有一些是部分不透明的,这意味着背景像素可以在这些位置部分显示出来。因此,RGBA 像素将其颜色保留在 RGB 通道中,并说明该颜色对 A 或 alpha 通道的重要性。因此 32 位像素成为我们的标准。
I’ve been talking as if there was a single value of alpha (opacity) for an entire image. In fact, that’s what figure 7.28 shows. But by introducing an alpha channel into each pixel, we allow a different opacity at each pixel. The same formula works on a pixel-by-pixel basis. Some foreground pixels can be transparent, some opaque, and others partially opaque, meaning that a background pixel can show through partially at those locations. An RGBA pixel thus holds its color in the RGB channels and states how seriously that color matters with the A, or alpha, channel. Thus 32-bit pixels became our norm.
以逐像素方式使用的 Alpha 如图 7.29 所示。前景物体只是圆形的红色圆盘,没有背景。它外面的所有像素都是透明的(或沿磁盘边缘部分透明)。最右边的图像是合成在最左边的方形图像上的红色圆盘。这是在逐个像素的基础上使用红色圆盘的 alpha 通道完成的。图像序列在其他方面就像上面的那样:全局 alpha 用于将一个图像交叉溶解到另一个图像上——在这种情况下,一个成形的图像在一个矩形图像上。
Alpha used in the pixel-by-pixel way is shown in figure 7.29. The foreground object is just the round red disk, with no background. All pixels outside it are transparent (or partially transparent along the disk edge). The rightmost image is the red disk composited over the leftmost square image. That’s done with the alpha channel of the red disk on a pixel-by-pixel basis. The sequence of images is otherwise just like the one above: a global alpha is used to cross-dissolve one image over the other—in this case a shaped image over a rectangular one.
Alpha 是一个微不足道的开发——至少我们当时是这么认为的。我们第一个到达那里是因为我们是第一个拥有大量像素内存的人。这是一个非常简单的想法,以至于我在第二天早上就完全实现了它,并为我们的编程手册提供了完整的页面,其中将新类型的像素描述为 RGBA 表示红色、绿色、蓝色和 alpha,从而为今天仍在使用的新频道。Ed 也很快完成了他的工作,改变了他的隐藏表面程序,以新的 RGBA 格式存储每个前景像素的第四个值,即其不透明度。
Alpha was a trivial development—or so we thought at the time. We got there first because we were the first to have a wealth of pixel memory. It was so easy an idea that I’d implemented it completely by the next morning, complete with pages for our programming manual that described the new kind of pixels as RGBA for red, green, blue, and alpha, thus establishing the name for the new channel that’s still in use today. And Ed had done his part quickly too, changing his hidden-surface program to store a fourth value with each foreground pixel, its opacity, in the new RGBA format.
为了运行他的测试,Ed 只需执行以下步骤: (1) 使用我的“旧”24 位恢复程序将任何RGB 背景图像b提取到帧缓冲区中。假设它到处都是不透明的。(2) 使用我的新 32 位恢复程序将 RGBA 前景图像f提取到同一帧缓冲区中,这是他的程序以新格式保存的图像。恢复程序在每个像素处执行“alpha f加一减 alpha b ”公式,其中前景图像中每个像素处的 A 保存了 Ed 在那里计算的 alpha 值(不透明度)。背景图像在阿尔法“控制旋钮”将前景图像从不透明变为透明的地方显示出来。
To run his tests, Ed had only to perform these steps: (1) Use my “old” 24-bit restore program to fetch any RGB background image b into a framebuffer. It was assumed to be opaque everywhere. (2) Use my new 32-bit restore program to fetch an RGBA foreground image f into the same framebuffer, an image that his program had saved in the new format. The restore program executed the “alpha f plus one minus alpha b” formula at each pixel, where A at each pixel in the foreground image held the alpha value (opacity) that Ed had computed there. And the background image showed through in places where the alpha “control knob” changed the foreground image from opaque to transparent.
新的 Alpha 通道可以轻松地将前景字符放置在背景图像上。被纯色填充的角色部分是不透明的。描绘彩色区域的扫描曲线具有柔和的边缘,这意味着它们是部分透明的。这让他们与背后的一切优雅地结合在一起。数字 cel 的所有其他部分都是透明的,alpha 为 0。
The new alpha channel made it easy to place foreground characters over a background image. The parts of a character that had been filled with solid color were opaque. The scanned curves delineating colored areas had soft edges, meaning that they were partially transparent. This let them combine gracefully with whatever was behind. All other parts of a digital cel were transparent, with alpha 0.
在扫描和绘画中为铅笔画创建 Alpha 通道很简单。绘图本身就是它自己的 Alpha 通道——嗯,实际上绘图的负片是。一幅画是用黑色铅笔在白色背景上绘制的,因此它的底片将是黑色背景上的白色图画。假设扫描的图形位于 8 位帧缓冲区中,其中 255(所有位为 1)表示白色像素,0(所有位为 0)表示黑色像素。扫描绘图中的灰色将介于 255 和 0 之间。让我们选择其中一个作为示例 - 例如灰度值 100。要获得绘图的 alpha 通道,请从白色 (255) 中减去每个像素。这就是接受否定的意思。因此,白色像素的 alpha 值为 255–255,即 0。它将是透明的。黑色像素的 alpha 值为 255–0 或 255。它将是不透明的。不透明(155/255 或约 61% 不透明)。任何颜色不透明的区域都将完全不透明,当然,使用 alpha 255。
It was straightforward to create an alpha channel for a pencil drawing in scan-and-paint. The drawing itself was its own alpha channel—well, actually the negative of the drawing was. A drawing was made in black pencil on a white background, so its negative would be a white drawing on a black background. Suppose the scanned drawing lies in an 8-bit framebuffer, with 255 (all bits 1) representing a white pixel and 0 (all bits 0) representing a black one. The grays in the scanned drawing would lie between 255 and 0. Let’s choose one of them for an example—say gray value 100. To get the alpha channel for the drawing, subtract each pixel from white (255). That’s what it means to take the negative. So a white pixel would have an alpha value of 255–255, or 0. It would be transparent. A black pixel would have alpha 255–0, or 255. It would be opaque. And a gray value, say 100, would have an alpha of 255–100, or 155, and would be partially opaque (155/255 or about 61 percent opaque). Any areas opaqued with color would be fully opaque, of course, with alpha 255.
阿尔法可能看起来微不足道,但它是深刻的。我花了很多年才意识到它的全部深度。几年后,我们在卢卡斯影业的同事汤姆·波特和汤姆·达夫将想法演变的下一步,他们在新频道中添加了一个“代数”——基本想法的一个重要扩展。他们观察到,如果将颜色“预乘”到一个像素中而不是原始颜色存储在像素中,则每次恢复图片时都可以节省大量乘法。当乘法缓慢且昂贵时,这又回来了。我们四个人因为我们对数字电影制作的共同贡献而获得了技术奥斯卡奖 - 组合数字图像的通用方法。
Alpha may have seemed trivial, but it was profound. It took me many years to perceive its full profundity. The next step in the evolution of the idea would come some years later from our colleagues at Lucasfilm, Tom Porter and Tom Duff, who added an “algebra” to the new channel—a non-trivial extension of the elemental idea. And they observed that if you stored the colors “pre-multiplied” by alpha in a pixel instead of the raw color, you could save a lot of multiplications every time the picture was restored. This was back when multiplications were slow and expensive. The four of us got a technical Academy Award for our combined contribution to digital filmmaking—the universal method for combining digital images.
如果没有 alpha,今天的许多流行程序都不会是现在的样子。Adobe Photoshop 和 Microsoft PowerPoint 浮现在脑海中。但即使是 Windows 和 MacOS 等操作系统也使用 alpha 来做浮动图标、圆角和部分透明的窗口。
Many popular programs today would not be what they are without alpha. Adobe Photoshop and Microsoft PowerPoint spring to mind. But even operating systems such as Windows and MacOS use alpha to do floating icons, rounded corners, and partially transparent windows.
几年后,我将在皮克斯之后创办的公司,名为 Altamira Software,将建立在一个逻辑上和深刻地从增强的 Alpha 通道中产生的想法:数字图像不必是矩形的。预乘 alpha 最终让我们能够推翻矩形的暴政。考虑上面的红色圆盘。其形状由其 Alpha 通道的非零部分定义。具有 alpha 0 的像素并非出于所有实际目的而存在。圆盘是一个圆形的图像对象。它是由像素组成的精灵(或成形图像),而不是几何形状。我和我的同事基于这个概念编写了一个图像合成程序 Altamira Composer ,并在 1995 年将它(和公司)卖给了微软。
The company I would start years later, after Pixar, called Altamira Software, would be built on an idea that sprang logically and profoundly from the enhanced alpha channel: a digital image does not have to be rectangular. Pre-multiplied alpha finally allows us to overthrow the tyranny of the rectangle. Consider the red disk above. Its shape is defined by the non-zero parts of its alpha channel. The pixels with alpha 0 don’t exist for all practical purposes. The disk is a round image object. It’s a sprite (or shaped image) made of pixels, not geometry. My colleagues and I wrote an image compositing program, Altamira Composer, based on this notion and sold it (and the company) to Microsoft in 1995.
阿尔法没有什么需要服从中心法则,尽管阿尔法当然经常用于它的服务。绘图程序及其相关程序(例如 Photoshop)不受中心法则的约束,Composer 也不受约束。
There is nothing about alpha that requires submission to the Central Dogma, although alpha is certainly often used in its service. Paint programs and their relatives, such as Photoshop, aren’t subject to the Central Dogma, and neither was Composer.
拥有如此多受过大学训练的成员,纽约理工学院实验室类似于一个学术部门也就不足为奇了。这个地方是自愿和合议的。出版物和学术荣誉比薪水或头衔更重要。就像在大学里,没有人想当系主任,所以 Ed Catmull 承担了这个吃力不讨好的职责。人们没有被分配任务,尽管 Ed 可能偶尔会提出一项建议。通常,每个人都只是弄清楚需要做什么并自愿去做。但每个人都知道,纽约理工大学是天赐之物,是一个资金雄厚的研究天堂,我们都尽可能地努力工作。这个花园每天都有新发现伊甸园!我们必须为所有新的植物和动物命名——并收集所有低垂的果实。
With so many university-trained members, it’s no surprise that the NYIT Lab resembled an academic department. The place was consensual and collegial. Publications and academic kudos were more important than pay or title. Just as at a university, nobody wanted to be department chairman, so Ed Catmull took on that thankless duty. People weren’t assigned tasks, although Ed might suggest one occasionally. Typically, each person just figured out what needed to be done and volunteered to do it. But everyone was aware that NYIT was a godsend, a well-funded research paradise, and we all worked as hard as we possibly could. There were new discoveries every day in this Garden of Eden! We got to name all the new plants and animals—and gather all the low-hanging fruit.
埃德低调的管理风格很适合当初那一小群任性的人。但这些年来,我们一点一点地开始感受到他作为一名真正的经理在工作。他为实验室和一个小型数字音频小组增加了硬件设计,如果 Ed 不是经理,这两者都不会发生。他利用他在犹他大学的人脉,偶尔为实验室增加人员——或者至少是暑期探访——。Lance Williams 和 Garland Stern 是 1975 年和 1976 年这些夏季访客中的第一批。他们中的许多人像 Lance 和 Garland 一样“卡住”,成为了正式员工。
Ed’s low-key management style was right for the original small group of headstrong individuals. But over the years, little by little, we started to feel him at work as an actual manager. He added hardware design to the Lab and a small digital audio group, neither of which would have happened if Ed hadn’t been the manager. And he exploited his University of Utah connections by making occasional personnel additions—or summer visitations, at least—to the Lab. Lance Williams and Garland Stern were the first of these summer visitors in 1975 and 1976. Many of them “stuck,” like Lance and Garland, and became permanent employees.
没有坚持的人是 Jim Blinn,他在 1976 年夏天从犹他州加入我们。他过去是,现在仍然是一个身材高大、身材瘦长的长发男人,经常穿着一件他母亲织的特别绿色的毛衣。他是一位才华横溢的技术明星,给人一种阴森森的严厉,但这是对慷慨和诙谐幽默的伪装。70
One who didn’t stick was Jim Blinn, who joined us from Utah for that same 1976 summer. He was, and still is, a tall and gangly long-haired man, frequently outfitted in a sweater of a particular green knitted by his mother. He’s a brilliant technical star who affects a saturnine sternness, but it’s a disguise for generosity and a wry humorous streak.70
在那次访问结束之前,Blinn 制作了一个纹理映射的 3D 茶奶精(来自 Martin Newell 著名的茶具)和一个绕圈跑的 3D“人”,他的表面相对于固定的阴影具有逼真的阴影光源。在犹他大学和纽约理工学院之间穿梭时,他还尝试了一种称为凹凸贴图的新着色技术。值得进一步讨论,因为就像纹理映射一样,它是 Digital Light 中样本和几何图形的另一种定义震撼的结合。在这两种情况下,像素都成为几何对象的创意空间模型的一部分。也就是说,在这两种情况下,像素都会从显示空间跃迁到创意空间。
Before that visit was over, Blinn had animated a texture-mapped three-dimensional tea creamer (from Martin Newell’s famous tea service) and a three-dimensional “man” who ran in a circle, with realistic shading of his surfaces relative to a fixed light source. Shuttling between the University of Utah and NYIT, he also experimented with a new shading technique called bump mapping. It’s worth discussing further because, like texture mapping, it’s another definition-shaking marriage of samples and geometry in Digital Light. In both cases, pixels become part of the Creative Space model of a geometric object. That is, in both cases pixels make the leap from Display Space into Creative Space.
与纹理映射一样,一个图像控制另一个图像的外观。也就是说,一个样本数组控制几何表面的外观,因为它被渲染到另一个数组中。在这种情况下,控制图像会影响表面的外观形状。图 7.30 显示了凹凸贴图如何使橙色球体看起来像橙色。这很明显,因为几何形状根本没有改变。查看“橙色”的边缘,注意平滑、无凹凸的轮廓。这是另一个好莱坞的假前技巧,只要明显的颠簸相对于整体几何形状很小,效果就很好。如果我没有指出来,你会注意到那无颠簸的轮廓吗?
As in texture mapping, one image controls the appearance of another. That is, one array of samples controls the look of a geometric surface as it’s rendered into another array. In this case the controlling image affects the apparent shape of a surface. Figure 7.30 shows how bump mapping can make an orange sphere appear to be an orange. It’s only apparent because the geometry doesn’t change at all. Look at the edge of the “orange” and note the smooth, bumpless silhouette. It’s another Hollywood false-front trick that works wonderfully so long as the apparent bumps are small relative the overall geometry. Would you have noticed the bumpless silhouette if I hadn’t pointed it out?
凹凸贴图将早期的着色技术提高了摩尔定律的两个数量级。它将多次上升的概念(还记得那些小旗杆吗?)发挥到了极致。在球体的最终渲染中,控制图像像素(如图 7.30 中所示)在每个像素处改变向上的方向。在最简单的平面着色情况下,up 只是每个三角形中心的旗杆。然后 Gouraud 在每个三角形的角落引入了上升的概念——倾斜的旗杆。他们定义了一个“上升表面”,你可以想象它漂浮在三角形上方。当每个最终像素被渲染到显示器中时,用于对其进行适当着色的 up 取自 ups 浮动表面中的相应位置。
Bump mapping advances the earlier shading techniques by two orders of Moore’s Law magnitude. It takes the notion of multiple ups (remember those little flagpoles?) to the limit. The control image pixels (shown in figure 7.30, center) change the direction of up at each pixel in the final rendering of the sphere. In the simplest case of flat shading, up is just the flagpole at the center of each triangle. Then Gouraud introduced the notion of ups at the corners of each triangle—tilted flagpoles. They defined a “surface of ups” that you can imagine floating above the triangle. As each final pixel is rendered into a display, the up used for shading it properly is taken from the corresponding place in that floating surface of ups.
图 7.30
Figure 7.30
凹凸贴图将三角形上少数几个点(例如角)的上升次数增加到每个点的上升次数。凹凸贴图中的每个像素都可以有不同的向上。使用经典的采样定理重建 - 扩展每个样本并添加 - 从凹凸贴图中的 ups 生成一个 ups 表面,以创建一个浮动在三角形上方的表面,如您所愿。你看不到这个浮动表面,但你可以看到它引起的阴影扰动——凹凸。
Bump mapping increases the number of ups at a handful of points on a triangle, such as its corners, to an up at every point. Each pixel in a bump map can have a different up. Using classic Sampling Theorem reconstruction—spread each sample and add—a surface of ups is generated from the ups in the bump map to create a surface floating above the triangles as complex as you want. You can’t see this floating surface, but you can see the shading perturbations—the bumps—it induces.
无需深入三角杂草,只需说在表面上逐点愚弄 ups 可以用来让我们看到表面上并不真正存在的凸起——从某种意义上说,它们不在几何模型。
Without getting into the trigonometric weeds, suffice it to say that fooling with the ups point by point on a surface can be used to make us see bumps on a surface that aren’t really there—in the sense that they aren’t in the geometric model.
Blinn 于 1976 年在犹他州和 NYIT 的圣诞节访问期间首次提出这个想法,但直到 1978 年他将其转化为在年度计算机图形会议 Siggraph 上发表的论文时才完善它。与此同时,这是他在犹他州的博士论文的一部分。图 7.31 显示了他的第一个动画凹凸贴图球体(具有无凹凸轮廓),按光栅扫描顺序,从 1977 年开始。71
Blinn first worked on the idea in 1976 at Utah and during a Christmas visit to NYIT but didn’t perfect it until 1978 when he turned it into a paper presented at Siggraph, the annual computer graphics conference. And it was part of his PhD dissertation at Utah in the meantime. Figure 7.31 shows his first animatable bump-mapped sphere (with bumpless silhouettes), in raster-scan order, from 1977.71
Blinn 最终加入了帕萨迪纳的喷气推进实验室。他在那里开花,并因制作航海者号飞船飞越电影而声名鹊起。每部电影都模拟了航海者号经过木星等行星之一的过程。对于纹理贴图,他使用了航海者号本身实际送回喷气推进实验室的行星的最新照片。这让他忙了好几年,并把 JPL 放在了计算机图形学重要地点的地图上。
Blinn wound up joining the Jet Propulsion Laboratory in Pasadena. He flowered there and made a name for himself with the production of Voyager spacecraft flyby movies. Each movie simulated the passage of Voyager by one of the planets, like Jupiter. For texture maps, he used the latest photos of the planets that had actually been sent back to JPL by Voyager itself. This kept him busy for years, and placed JPL on the map of important places in computer graphics.
图 7.31
Figure 7.31
1977 年,Ed 将另外两名犹他州的同事带到了长岛。Ephraim Cohen 和 Duane Palyka (“Pal kah”) 都不是犹他州的正式学生,但他们让自己变得有用,所以 Ed 在 NYIT 聘请了他们。两人都是艺术家和程序员。
Ed brought two more Utah colleagues out to Long Island in 1977. Neither Ephraim Cohen nor Duane Palyka (“Pal kah”) was a formal student at Utah, but they’d made themselves useful, so Ed hired them at NYIT. Both were artists and programmers.
Ephraim 是前一章中的艺术家,他在 MIT 的 TX-2 上与 Ron Baecker 的 Genesys 动画程序一起工作。作为一名艺术家,他以揭示性的漫画让我们高兴,例如 1977 年左右的实验室人员之一(图 7.25)。他为实验室贡献了许多像素处理程序,包括另一个绘画程序。多年后,在纽约理工学院之后,他最引人注目的 Digital Light 贡献——真正的 Digital Light 寺庙——将是他帮助设计和实施的曼哈顿纳斯达克时代广场多层立面。
Ephraim was the artist in the preceding chapter who worked with Ron Baecker’s Genesys animation program on the TX-2 at MIT. As an artist, he delighted us with revealing caricatures, such as the one of the Lab personnel circa 1977 (figure 7.25). He contributed many pixel manipulation programs to the Lab, including another paint program. Years later, post-NYIT, his most visible Digital Light contribution—a Digital Light temple really—would be the Times Square multistory façade for NASDAQ in Manhattan, which he helped design and implement.
Duane Palyka 被收录在 1968 年的经典节目 Cybernetic Serendipity中,并出现在一本名为Artist and Computer的书的封面上,他用电脑绘画程序和一面镜子画了一张自己的照片。他贡献了 NYIT 为数不多的渲染 3D 物体的程序之一。慢得令人痛苦主要是为了提醒我们我们多么需要摩尔定律来实现它的承诺。72
Duane Palyka was included in the classic 1968 show Cybernetic Serendipity and was featured on the cover of a book called Artist and Computer, painting a picture of himself—with a computer paint program and a mirror. He contributed one of the few programs at NYIT that rendered three-dimensional objects. It was painfully slow and served mostly to remind us of how much we needed Moore’s Law to manifest its promise.72
我们在 NYIT 的实验室已经开始使用 Tween、TintFill 和 Paint3 进行二维数字生产,但我们的软件开发环境仍停留在黑暗时代。我们永远不会以这么慢的速度去看电影。我不是在谈论低摩尔定律功率,而是低效的软件工具。我们知道在目前的摩尔定律水平上我们可以做得比我们更好。我们需要的是一种“好的”编程语言。
Our Lab at NYIT had the beginnings of two-dimensional digital production under way—with Tween, TintFill, and Paint3—but our software development environment was stuck in the Dark Ages. We would never get to The Movie at this slow pace. I’m not talking about low Moore’s Law power, but inefficient software tools. We knew we could do better at the present Moore’s Law level than we were. What we needed was a “good” programming language.
Ed Catmull 和我都知道坏人是什么样的。我们都教过 Fortran 编程语言——正如我们所说,它是由 IBM 强加给公众的——但都讨厌它。我们很早就决定不在 NYIT 使用它。相反,我们将使用繁琐的汇编语言(参见图灵章节)进行编程,并等待一种好的编程语言出现。
Ed Catmull and I both knew what a bad one was like. We had both taught the Fortran programming language—foisted, as we put it, on the public by IBM—and both detested it. We decided early on that we wouldn’t use it at NYIT. Instead we would program in tedious assembly language (see the Turing chapter) and wait for a good programming language to come along.
然后有一天,我们的克制得到了回报。我们了解了一种称为 C 的优雅编程语言(是的,我们被告知只有一个字母)。它是作为新操作系统的一部分出现的,称为 Unix。两者都很可爱且合乎逻辑,我们立即以大约 100 美元的大学价格收养了它们。Ron Baecker 曾向 Ed 讲述过 Unix,这是该人的又一贡献。
Then one day our restraint paid off. We learned about an elegant programming language called C (yes, the one letter, we were told). It came as part of a new operating system, called Unix. Both were lovely and logical, and we adopted them immediately at the university price of about $100. Ron Baecker had told Ed about Unix, yet another contribution by that man.
正如我在图灵一章中解释的那样,操作系统是一个始终在运行的程序,例如 Windows、MacOS 或 Android OS(操作系统的 OS)。它故意处于无限循环中。它负责业务:哪些应用程序正在运行?他们需要多少内存?需要哪些输入或输出设备?是否存在需要立即关注的电气紧急情况?它还处理无数其他“管道”问题。这是一种需要特殊思维的深度程序。系统程序员就是那些人。
As I explained in the Turing chapter, an operating system is a program that’s always running—like Windows, MacOS, or Android OS (OS for operating system). It’s in an infinite loop on purpose. It takes care of business: Which apps are running? How much memory do they need? What input or output devices are required? Is there an electrical emergency that demands instant attention? And it handles a myriad other “plumbing” concerns. It’s a deep kind of program that takes a special kind of mind. Systems programmers are those people.
贝尔实验室的 Ken Thompson 和 Dennis Ritchie 创造了 Unix,Ritchie 设计了 C 语言,他们因此获得了 1983 年的图灵奖。Unix 现在是世界上的基本操作系统之一——MacOS 是一种改编——C 是它非常流行的编程语言。Ken Thompson 亲自将 Unix C 的早期副本交给了纽约理工大学。他直接从新泽西州的贝尔实验室乘坐黄色 Corvette Stingray 抵达。73
Ken Thompson and Dennis Ritchie at Bell Labs had created Unix, with Ritchie designing the C language, and they were awarded the Turing Award in 1983 for this accomplishment. Unix is now one of the fundamental operating systems in the world—MacOS is an adaptation—with C its very popular programming language. Ken Thompson himself hand-delivered an early copy of Unix C to NYIT. He arrived in a yellow Corvette Stingray directly from Bell Labs in New Jersey.73
那时,我们实验室里没有人关心系统编程,也没有人能胜任 Unix。我们需要一位 Unix 专家。Ron Baecker 再次提出了一个宝贵的建议:我们应该考虑他在多伦多大学指导的一个学生。这就是我们认识汤姆·达夫的方式。1976 年,他在 NYIT 面试了这份工作。他新鲜而与众不同,不是来自犹他州、E&S 或 PARC。实验室里唯一的另一个加拿大人是亚历克斯叔叔本人。74
None of us at the Lab then cared much for systems programming, and none of us were competent with Unix. We needed a Unix expert. Ron Baecker again made a valuable suggestion: We should consider a student he supervised at the University of Toronto. So that’s how we met Tom Duff. He interviewed for the job at NYIT in 1976. He was fresh and different, not being from Utah, E&S, or PARC. The only other Canadian at the Lab was Uncle Alex himself.74
但汤姆出奇地害羞。在他的采访之旅中,他几乎没有说话。因此,他与各种实验室成员的谈话很短。我们很快发现自己都在摆弄拇指,想知道在预定出发前的剩余时间里,我们沉默的访客该怎么办。
But Tom was surprisingly shy. He barely spoke up during his interview trip. Consequently, his talks with various Lab members were quite short. We soon found ourselves collectively twiddling our thumbs, wondering what to do with our silent visitor for the remaining hours before his scheduled departure.
有人建议汤姆尝试一下加兰·斯特恩(Garland Stern)创建的 Unix 游戏——一个多选文本游戏。一个正确的答案把你带到了另一个级别的 Unix 难度。游戏的目标是教我们其他人 Unix 是如何工作的。我们谁也解决不了。Unix 的细节太晦涩难懂了——即使对 Garland 来说,他也知道得比我们其他人多。
Someone proposed that Tom try his hand at a Unix game that Garland Stern had created—a multiple-choice text game. A correct answer took you to another level of Unix difficulty. The goal of the game was to teach the rest of us how Unix worked. None of us could solve it. Unix details were too obscure—even for Garland, who knew barely more than the rest of us.
当汤姆听说这个游戏时,他抓起一个键盘,在大约五分钟内完成了它。这对他来说是儿戏。他显然是我们的 Unix 专家!我们抢购了他——直到最近(2021 年),他一直在皮克斯工作,他是一位黑客大师和老大爷。他的天才远远超出了 Unix,还延伸到了计算机图形学。
When Tom heard about the game, he grabbed a keyboard and ripped his way through it in about five minutes. It was child’s play for him. He was obviously our Unix expert! We snapped him up—and he was at Pixar until very recently (2021), a hacker guru and grand old man. And his genius extends far beyond just Unix to computer graphics.
尽管 Digital Light 有很多部分,但我选择只关注通往数字电影的途径。也就是说,我专注于他们在千禧年大数字融合中的作用。所以,我在这里忽略了所有的图像处理、所有的实时模拟器和游戏、所有的应用程序界面,以及所有不适用于长篇角色动画的计算机图形。出于实际原因——一章的篇幅限制,以及我不想让外行读者用无穷无尽的名字列表淹没——我坚持通向皮克斯、梦工厂和蓝天这三个公司的路径。这意味着,除了少数例外,我几乎没有提到参与数字光革命的计算机图形部分的许多其他公司和研究人员。这也意味着我对梦工厂和蓝天的轻视。
Despite the many parts of Digital Light, I choose to focus only on pathways to the digital movies. That is, I concentrate on their part in the Great Digital Convergence at the millennium. So, I ignore here all image processing, all real-time simulators and games, all app interfaces, and all computer graphics not intended for feature-length character animation. For practical reasons—the space limitations of one chapter and my wish not to swamp the lay reader with interminable lists of names—I stick to the pathways leading to three companies, Pixar, DreamWorks, and Blue Sky. This means, with few exceptions, that I barely mention the many other companies and researchers involved in the computer graphics part of the Digital Light revolution. It also means that I treat DreamWorks and Blue Sky lightly.
由于我的个人经验是 NYIT-Lucasfilm-Pixar 轴,我会比其他人更多地谈论这条道路。但这种处理方式远不及那条非凡赛道的详细历史。相反,我只关注那些导致数字电影的故事的软件线索。而且这一章肯定与另外两条路径的详细历史相去甚远——太平洋数据影像——梦工厂和 MAGI——蓝天。我更感兴趣的是展示这些股如何相互作用和相互影响,而不是展示千禧年其他两条通往数字电影的主要途径的所有人和技术。
Since my personal experience is the NYIT–Lucasfilm–Pixar axis, I will say far more about that path than the others. But this treatment is nowhere near a detailed history of even that remarkable track. Rather I follow just those software strands of the story that led to digital movies. And this chapter is certainly not anywhere near a detailed history of the two other paths—of Pacific Data Images–DreamWorks and of MAGI–Blue Sky. I’m more interested in showing how the strands interacted and influenced each other than in presenting all the people and technologies of the other two main paths to digital movies at the millennium.
我把它留给别人写详细的历史。梦工厂和蓝天的那些还没有写出来。在 NYIT–Lucasfilm 的岁月里,我几乎无法超越迈克尔鲁宾 2006 年出版的著作《Droidmaker》。鲁宾基于对我们这些在场的人的采访,它几乎在所有细节上都是准确的。同样,我推荐《皮克斯之触》( The Pixar Touch),这是历史学家大卫·普莱斯(David Price)在 2008 年稍晚一点的卢卡斯影业和皮克斯早期的精彩历史,他是根据档案材料而不是新闻传闻撰写的。在这里,我只讲述了 NYIT 和卢卡斯影业在那些继续组建以皮克斯这个名字命名的电影制作团队的成员方面的高点。75
I leave it to others to write the detailed histories. Those for DreamWorks and Blue Sky are yet to be written. For the NYIT–Lucasfilm years I can hardly top Michael Rubin’s 2006 book, Droidmaker. Rubin based it on interviews with those of us who were there, and it’s accurate in nearly all details. Similarly, I recommend The Pixar Touch, the excellent 2008 history of the slightly later Lucasfilm and early Pixar days by the historian David Price, who wrote from archival materials rather than journalistic hearsay. Here I recount only the high points of the NYIT and Lucasfilm years as regards those members who went on to form the movie-making group that took the name Pixar.75
特别是,汤姆·达夫、埃德·卡特莫尔、大卫·迪弗朗西斯科和我将前往卢卡斯影业,然后前往皮克斯。NYIT 的另外两个人也将走上同样的道路。马尔科姆布兰查德是最初的四名骑士之一,早在我们其他人之前就离开了纽约理工学院,但他会在卢卡斯影业重新加入我们。比赛后期加入纽约理工学院的新人是拉尔夫·古根海姆,他将在随后转会卢卡斯影业的过程中发挥关键作用。Ed 和我将共同创立 Pixar,而 David、Malcolm 和 Ralph 都将成为创始员工。76
In particular, Tom Duff, Ed Catmull, David DiFrancesco, and I would proceed to Lucasfilm and then to Pixar. Two others from NYIT would follow the same path. Malcolm Blanchard, one of the original four horsemen, left NYIT long before the rest of us, but he would rejoin us at Lucasfilm. A newcomer to NYIT late in the game was Ralph Guggenheim, who would play a key role in the subsequent move to Lucasfilm. Ed and I would cofound Pixar, and David, Malcolm, and Ralph would all become founding employees.76
但我们并不是唯一致力于实现大数字融合的人。在康奈尔大学和 MAGI,人们都在探索技术的边缘。
But we weren’t the only ones working toward the Great Digital Convergence. Like minds were exploring the edges of technology at Cornell and MAGI.
纽约理工学院的计算机图形实验室位于纽约市以东几英里的长岛。就在城市北部的威彻斯特县,是另一个早期的计算机图形中心,即数学应用集团公司 (MAGI)。1972 年,它在其其他数学产品中添加了计算机图形学。因此 NYIT 和 MAGI 是下游图形学的所在地。
The Computer Graphics Lab at NYIT was located on Long Island, a few miles east of New York City. Just north of the city, in Westchester County, was another early computer graphics center, the Mathematical Applications Group Inc. (MAGI). It had added computer graphics to its other mathematical offerings in 1972. So NYIT and MAGI were the downstate graphics loci.
北部同时期的所在地是康奈尔大学的唐·格林伯格(Don Greenberg)的小组。它以马克·莱沃伊和其他格林伯格学生为特色,他们在 1972 年创作了康奈尔电影。
The upstate contemporaneous locus was Don Greenberg’s group at Cornell University. It featured Marc Levoy and other Greenberg students who had created the Cornell movie in 1972.
多年来,我们在 NYIT 进行了一两次实地考察,但与我们联系更紧密的团体是康奈尔大学——一个像我们一样的学术团体。格林伯格确保我们要么访问他在伊萨卡的设施,要么他和他的学生每年访问 NYIT 一次或两次。
We at NYIT took a field trip or two to MAGI over the years, but the group we bonded more closely with was Cornell—an academic group like ourselves. Greenberg made sure that either we visited his facility in Ithaca, or he and his students visited NYIT once or twice a year.
我们有一位富有的赞助人,亚历克斯舒尔叔叔,所以我们在顶级设备上总是领先于康奈尔大学,但康奈尔大学从来没有落后太多。我们在 NYIT 拥有了世界上第一个 24 位帧缓冲区。大约一年后,康奈尔大学有了一个。我们与纽约理工学院的动画师合作。很快,康奈尔大学的马克·莱沃伊就与以弗林特斯通闻名的汉娜-巴贝拉动画电影公司合作。我终于在 1978 年将我在 1974 年在 Xerox PARC 实施的 HSB(又名 HSV)颜色变换算法写成了一篇论文。在同一期刊上,康奈尔大学的 George Joblove 也发表了类似的颜色算法。77
We had a rich patron, Uncle Alex Schure, so we were always ahead of Cornell in top-of-the-line equipment, but Cornell was never far behind. We had the first 24-bit framebuffer in the world at NYIT. A year or so later Cornell had one. We worked with animators at NYIT. Soon Marc Levoy at Cornell was working with the Hanna-Barbera animated film company, of Flintstones fame. I finally wrote up the HSB (aka HSV) color transform algorithm I had implemented in 1974 at Xerox PARC as a paper in 1978. In the same journal was a similar color algorithm by George Joblove from Cornell.77
与MAGI的早期关系也形成了。它始于 NYIT 的 David DiFrancesco 和他为实验室寻找具有电影质量的电影录像机。他的关注点很快缩小到两家公司,Celco 和 Dicomed。出于同样的原因——电脑动画——MAGI 也对电影录音机感兴趣,并正在考虑 Celco。方便的是,Celco 顾问 Carl Ludwig 在 MAGI 召开了一次会议。因此,大约在 1975 年或 1976 年,我们与 MAGI 进行了第一次重大接触。大卫最终选择使用 Dicomed。但他与卡尔·路德维希建立了终生的友谊,我们第一次在 MAGI 内部看到。十多年后,卡尔将成为蓝天工作室的联合创始人。78
An early relationship with MAGI also formed. It began with NYIT’s David DiFrancesco and his search for a film recorder of movie quality for the Lab. His focus soon narrowed to two companies, Celco and Dicomed. For the same reason—computer animation—MAGI was also interested in a film recorder and was considering Celco. Conveniently, Carl Ludwig, a Celco consultant, set up a meeting at MAGI. Thus, in about 1975 or 1976, we had our first major contact with MAGI. David eventually elected to go with a Dicomed. But he had established a lifelong friendship with Carl Ludwig, and we’d seen inside MAGI for the first time. And Carl would become a cofounder of Blue Sky Studios over a decade later.78
1974 年,我在 Xerox PARC 使用彩色光栅图形制作了一个艺术视频。我称之为Vidbits。当我从加利福尼亚回到纽约市的视频艺术界时,它成了我的名片。他们从未见过这样的事情。79
I’d made an art video using color raster graphics at Xerox PARC in 1974. I called it Vidbits. When I returned from California to the video art scene in New York City, it became my calling card. They’d never seen anything like it.79
因此,当著名的视频艺术家 Ed Emshwiller 来纽约理工学院拍摄电影时,我抓住了这个机会。“Emsh”在巴黎开始了他的抽象油画创作生涯。在 1950 年代,他因为Galaxy和The Magazine of Fantasy & Science Fiction绘画封面而出名。然后他发现了 16 毫米电影制作,并成为该媒体的艺术领袖。然后是视频艺术的领导者。然后是视频磁盘艺术。
So when the well-known video artist Ed Emshwiller visited NYIT wanting to make a movie, I leapt at the chance. “Emsh” had begun his artistic career painting abstract oils in Paris. In the 1950s he made a name for himself painting covers for Galaxy and The Magazine of Fantasy & Science Fiction. Then he discovered 16 mm filmmaking and became an artistic leader in that medium. And then a leader in video art. Then video disk art.
我们从 PBS 电视特别节目中发现了 Emsh。令我们惊讶的是,我们得知他住在附近莱维敦的长岛!有人说:“我们请他过来吧。” 我说:“我认为我们不需要。他会找到我们的。” 80
We had discovered Emsh from a PBS television special about him. To our surprise, we learned that he lived on Long Island, in nearby Levittown! Someone said, “Let’s invite him over.” I said, “I don’t think we need to. He’s going to find us.”80
这就是发生的事情。显然,Emshwiller 正在追踪新媒体的高科技优势。正如预期的那样,有一天他出现在实验室,并宣布他有一个古根海姆奖学金来制作一部三小时的电影。他想和我们一起使用它,他有六个月的时间。我们爆发出一阵笑声。我们不得不向他解释,心烦意乱和困惑,这是早期的日子。他很幸运能在六个月内完成三分钟。
And that’s what happened. Obviously Emshwiller was tracking the high-technology edge of new media. One day he showed up at the Lab, as predicted, and announced that he had a Guggenheim Fellowship to make a three-hour movie. He wanted to use it with us, and he had six months. We burst into laughter. We had to explain to him, upset and puzzled, that these were the early days. He’d be lucky to get three minutes done in six months.
但我们致力于它,因此开始了我生命中第二次重要的艺术合作,继大卫·迪弗朗切斯科之后。我是一个有艺术倾向的技术型人。我喜欢艺术。Emsh 是一个具有艺术倾向的人,具有技术倾向。他热爱技术。我们一拍即合,就像大卫和我之前所做的一样。
But we committed to it, and thus began the second important artistic collaboration of my life, after David DiFrancesco. I was a technically oriented person with artistic leanings. I loved art. Emsh was an artistically oriented person with technical leanings. He loved technology. We hit it off, much as David and I had earlier.
我们的工作风格是这样的:Emsh 会呈现一个艺术概念。例如,他提出的第一个是一张人脸穿过一块石头。我从我的技术知识和对摩尔定律的理解中做出了回应:“我们总有一天会做到的,Emsh,但现在还不行。但是如果你这样修改你的概念,那我就可以了。” 我解释说,如果只看到正面,我可以制作一张穿过石头的脸的二维表示。然后他说:“好吧,如果你能做到,那怎么样。. 。” 如此反复,直到我们共同决定了一个我可以在那个痛苦缓慢的计算中真正实现的艺术想法。这是另一种形式的“干扰”。图 7.32(左)显示了我们两个在Sunstone上工作(Emsh 在我的右边) 。太阳图像诡异地漂浮在彩色显示屏之外的空间中,这是相机在两次曝光的中间被轻微推挤的结果——房间里的灯打开捕捉我们,然后关闭捕捉屏幕。我们同意,这个“错误”完美地捕捉到了我们的创造性思维。
Our working style went like this: Emsh would present an artistic concept. For example, the first one he proposed was a human face pushing its way through a block of stone. I responded from my technical know-how and a sense of Moore’s Law: “We’ll be able to do that someday, Emsh, but not yet. But if you modify your concept this way, then I can do it.” I explained that I could make a two-dimensional representation of a face pushing through stone, if seen face-on only. Then he said, “Well, if you can do that, then what about . . .” and so forth, back and forth, until we had decided mutually on an artistic idea that I could actually implement in that day of painfully slow computation. It was another form of “jamming.” Figure 7.32 (left) shows the two of us at work (Emsh on my right) on Sunstone. The sun image floats eerily in space off the color display, the result of the camera’s being jostled slightly in the middle of a double exposure—room lights on to capture us, then off to capture the screen. This “error” captured, we agreed, our creative mindset perfectly.
图 7.32
Figure 7.32
(右)来自Sunstone的一帧,1979 年,由 Ed Emshwiller 创作。
(Right) One frame from Sunstone, 1979, by Ed Emshwiller.
纽约理工学院的两位同事 Lance Williams 和 Garland Stern 也参加了会议。兰斯贡献了一个在屏幕上漂浮的“舌头”,加兰完成了一个模拟视频记录的二维实时数字化,该视频记录描绘了埃姆什的儿子斯通尼(这件作品的名字就是以此命名的)。Garland 使用同一台机器对这些视频帧进行数字化,这与他在他的扫描和绘画系统中用于对动画师的绘图进行数字化。他从现实世界中,从单色录像带中获取这些像素,而不是用计算机制作它们。但是,他没有使用灰色像素,而是通过 8 位颜色图来运行它们以获得彩虹伪色效果。因此, Sunstone是图像处理数字光和计算机图形数字光的混合体。
Two NYIT colleagues, Lance Williams and Garland Stern, also participated. Lance contributed a “tongue” that floated around the screen, and Garland accomplished a two-dimensional real-time digitization of an analog video recording that portrayed Emsh’s son, Stoney (for whom the piece was named). Garland used the same machine for digitizing these video frames that he used for digitizing animators’ drawings in his scan-and-paint system. He took these pixels from the real world, from a monochrome videotape, rather than making them with a computer. But, instead of gray pixels, he ran them through an 8-bit colormap for a rainbow pseudocolor effect. Thus Sunstone was a mixture of image processing Digital Light and computer graphics Digital Light.
Sunstone将成为纽约现代艺术博物馆收藏的第一个彩色光栅图形。它不是数字视频——它还不存在——但每一帧都是像素光栅,因此是数字光。只有交付媒介还没有数字化。直到 1998 年 HDTV 标准化时,才发生这种情况。
Sunstone would become the first color raster graphics in the collection of New York’s Museum of Modern Art. It wasn’t digital video—which didn’t exist yet—but every frame was a raster of pixels and hence Digital Light. Only the delivery medium wasn’t yet digital. That wouldn’t happen until the Great Digital Convergence—when HDTV was standardized in 1998.
我们为Sunstone使用了三种不同的 Digital Light 技术:二维交互式绘制像素、数字化实时视频和完全非实时的三维计算机图形。
We used three different Digital Light technologies for Sunstone: two-dimensional interactively painted pixels, digitized real-time video, and three-dimensional completely non-real-time computer graphics.
绘制的像素是使用 Paint3 创建的。使用 Garland Stern 为 NYIT 的扫描和绘制系统构建的数字化系统对视频像素进行实时数字化。但是在 1979 年,摩尔定律根本没有足够的能力在长时间的动画中渲染几个物体的完整 3D 场景——去掉锯齿。当然,那会到来,但它还没有完全存在。所以我写了一个程序叫Texas(用于纹理应用系统)。它将世界简化为嵌入在三维世界中的二维平面。我把每架飞机称为舞台制作中的“公寓”,这些公寓合起来就是“舞台布景”。每个公寓都贴有图片纹理。通过改变每一帧的纹理,一个平面可以在它穿过三维空间时显示二维动画。也就是说,这些公寓可以以任何方式放置在三维“舞台”上。中心教条在这个程式化的世界中生效:一个虚拟摄像机观察舞台,并以文艺复兴时期的视角将其视图渲染为最终帧以供展示。
The painted pixels were created with Paint3. The video pixels were digitized in real-time using the digitizing system that Garland Stern had built for NYIT’s scan-and-paint system. But in 1979 there simply wasn’t enough Moore’s Law power to render full three-dimensional scenes of several objects in a prolonged animation—with jaggies removed. That would come, of course, but it didn’t fully exist yet. So I wrote a program called Texas (for Texture-Applying System). It simplified the world to two-dimensional planes embedded in a three-dimensional world. I called each plane a “flat” as in a stage production, and together the flats were a “stage set.” There was a picture texture-mapped onto each flat. By changing the texture at each frame, a flat could display a two-dimensional animation as it moved through three-dimensional space. That is, the flats could be positioned in any way on a three-dimensional “stage.” The Central Dogma was in effect in this stylized world: a virtual camera observed the stage and its view was rendered in Renaissance perspective into final frames for display.
为了衡量此时所涉及的痛苦——即使限制为单位——在Sunstone中仅 18 秒长的爆炸立方体序列需要 56 小时来计算。但它是 3D 完全抗锯齿纹理映射光栅图形。其中三个立方体面在飞入太空时带有二维动画——一张是 Emsh 手绘的动画,另一张是 Garland Stern 拍摄的实时视频,第三张是我制作的动画太阳。
As a measure of the pain involved at this time—even with the restriction to flats—an exploding cube sequence in Sunstone that was only 18 seconds long took 56 hours to compute. But it was three-dimensional fully antialiased texture-mapped raster graphics. Three of the cube faces carried two-dimensional animations as they whirled off into space—one face held a hand-painted animation by Emsh, another the real-time video grabbed by Garland Stern, and the third an animated sun that I did.
Emsh 于 1979 年底离开实验室,成为 CalArts 的教务长,这所学校正是沃尔特·迪斯尼 (Walt Disney) 为他的工作室培训动画师而创立的学校。我第一次去加州艺术学院是去看 Emsh,最后是在 1990 年与数百人一起庆祝他的生命并哀悼他的死。CalArts 将在我们的未来占据显着地位。埃姆什和我开发的工作风格预示着艺术创意和技术创意的结合,最终在皮克斯会很好地发挥作用。
Emsh departed the Lab in late 1979 to become provost at CalArts, the very school that Walt Disney founded to train animators for his studio. My first visits to CalArts were to see Emsh, and finally in 1990 to celebrate his life and mourn his death with hundreds of others. CalArts would figure prominently in our future. And the working style Emsh and I developed presaged the coupling of the artistically creative and the technically creative that would work so well eventually at Pixar.
在过去的几年里,纽约理工学院发生了一个警示事件。Ed Catmull 聘请了来自犹他州的博士学位的 Jim Clark 加入实验室并制造了一个头戴式显示器——就像 Ivan Sutherland 的一样。吉姆帮助揭示了我们的赞助人亚历克斯叔叔也是一个小暴君,尽管不在拿破仑、斯大林或山姆大叔的联盟中。
A cautionary event unfolded during the last couple of years at NYIT. Ed Catmull hired Jim Clark, with a PhD from Utah, to join the Lab and build a head-mounted display—like Ivan Sutherland’s. Jim helped reveal that our patron Uncle Alex was a minor tyrant too, though not in the league of Napoleon, Stalin, or Uncle Sam.
吉姆对我来说是一个惊喜。他来自德克萨斯州,说话和我一样。作为宅男,我们很快一拍即合。他在德克萨斯州普莱恩维尤长大,距离我的家乡新墨西哥州克洛维斯以东约 80 英里。但相似之处到此为止。吉姆被踢了出于战斗的普莱恩维尤高中。他加入了海军,在一次智力测试中发现自己是一个非常聪明的人。因此,他参加了夜校并设法被各所大学录取,最终在犹他大学获得计算机图形学博士学位。81
Jim was a surprise to me. He came from Texas and talked like me. We quickly hit it off as homeboys. He grew up in Plainview, Texas, about 80 miles straight east of my hometown of Clovis, New Mexico. But the similarity ended there. Jim had been kicked out of Plainview High School for fighting. He joined the Navy and discovered from an intelligence test that he was a very smart person. So he took night classes and managed to get admitted to various colleges, ultimately resulting in a PhD in computer graphics at the University of Utah.81
但在纽约理工学院,他和亚历克斯舒尔几乎立即发生了冲突。回头看,我明白为什么了。与实验室的其他人不同,吉姆有很强的创业精神。舒尔将他视为竞争对手,而不是贡献者。Jim 很快发现了问题,意识到这对 Schure 不起作用,于是开始写信寻找另一份工作。他在实验室用文字处理器写了它们,这已经变得很普遍了。
But at NYIT, he and Alex Schure clashed almost immediately. Looking back, I can see why. Unlike the rest of us at the Lab, Jim had a strong entrepreneurial streak. Schure saw him as a competitor, not a contributor. Jim quickly detected the problem, realized it wasn’t going to work with Schure, and started writing letters in search of another job. He wrote them at the Lab with a word processor, which was just becoming common.
一天早上,舒尔用这些信件的打印件与吉姆对质,并指责他准备窃取我们的秘密并将它们带到别处。舒尔当场解雇了他。这对我们没有任何意义。Jim并没有隐瞒他正在寻找其他地方去的事实。而且他太聪明了,不需要窃取我们的技术。我们的“秘密”是我们拥有当时最好的硬件。在该硬件上实施的想法是公共知识。简而言之,我们不相信舒尔的指控。82
One morning Schure confronted Jim with a printout of these letters and accused him of preparing to steal our secrets and take them elsewhere. Schure fired him on the spot. None of this made any sense to us. Jim hadn’t hidden the fact that he was looking for somewhere else to go. And he was too smart to need to steal our technology. Our “secret” was that we had the best hardware available at the time. The ideas that were implemented on that hardware were public knowledge. In short, we didn’t believe Schure’s accusations.82
我们也不知道打印输出的来源。舒尔无法进行数字窥探。那只能意味着我们在实验室里有一颗痣!我们知道它可能是谁,但一直不确定。没关系,因为Jim离开了,露出了愤怒、报复心的舒尔。他不公平地对待我们的朋友,所以我们的警告旗帜上升了。
Nor did we understand where the printouts came from. Schure was incapable of digital snooping. That could only mean that we had a mole in the Lab! We knew who it probably was but were never sure. It didn’t matter because Jim left, having revealed an angry, vindictive Schure. He’d treated our friend unfairly, so our caution flags went up.
至于企业家吉姆·克拉克(Jim Clark),他将继续与他人共同创立了对计算机图形学很重要的硬件公司 Silicon Graphics,以及后来的互联网浏览器先驱公司 Netscape。
As for Jim Clark, the entrepreneur, he would go on to cofound Silicon Graphics, a hardware company that was important to computer graphics, and later Netscape, the pioneering internet browser company.
我们越来越怀疑舒尔和他制作电影的能力。埃德和我几乎每年都去迪斯尼朝圣,并继续这样做。我们认为,应该是迪斯尼资助我们,而不是舒尔。他们是我们俩小时候都喜欢的动画公司,他们有钱。我们确信沃尔特本人不会犹豫。但每年在迪士尼都是一样的老故事。首先是,“你们男孩会做泡泡吗?” 嗯,不,那一年我们做不到,但第二年他们发现我们还做不到其他事情——比如蒸汽或烟雾。
Our doubts about Schure and his ability to produce a movie were growing. Ed and I had been making a pilgrimage to Disney almost every year and continued doing so. It should’ve been Disney funding us, not Schure, we thought. They were the animation company that both of us had loved as children, and they had the money. We were sure that Walt himself wouldn’t have hesitated. But every year it was the same old story at Disney. First it was, “Can you boys make bubbles?” Well, no we couldn’t that year, but the next year it was something else they found we couldn’t yet do—such as steam, or smoke.
在 1977 年 1 月的迪斯尼之旅中,我和 Ed 由 Dick Shoup 陪同。我们会见了动画负责人 Don Duckwall(是的!),并举办了一场研讨会。从我的笔记中:
In our January 1977 trip to Disney, Ed and I were accompanied by Dick Shoup. We met with Don Duckwall (yes!), head of animation, and presented a seminar. From my notes:
我们对 Don Duckwall 的出现感到惊讶和高兴,并表达了积极的(但不是绝大多数)反应:“我相信你现在可以做泡泡了。” 他建议他可能对我们的特殊效果感兴趣。大约 30 人的一大群人出现在研讨会上——大多数是热爱他们所看到的东西——尤其是 3-D 的东西的年轻热切的家伙。83
We were surprised and pleased that Don Duckwall showed up and expressed positive (but not overwhelmingly so) reactions: “I believe you can now do bubbles.” He suggested that he might be interested in us for special effects. A large group of about thirty people showed up for the seminar—most were young eager guys who loved what they saw—especially the 3-D stuff.83
但这次访问的最大收获是会见了伟大的老动画师弗兰克托马斯和奥利约翰斯顿。我们也向他们展示了我们的东西。
But the big treat of the visit was meeting the grand old animators, Frank Thomas and Ollie Johnston. We showed them our stuff too.
他们似乎很喜欢他们所看到的——问了很多问题——但不知道如何处理这些信息。84
They seemed to like what they saw—asked lots of questions—but didn’t know what to do with the info.84
弗兰克和奥利将一直是我们热情的朋友,直到他们 90 多岁时去世。
Frank and Ollie would remain our enthusiastic friends until their deaths, when they were in their 90s.
然而,迪士尼的技术人员确切地知道我们能做什么。其中之一,戴夫斯奈德,警告我们不要指望他的更高管理层会发生任何事情。他们不会支持我们。另一方面,“Ub 会的,”他说。从某种意义上说,艾沃克斯是迪斯尼与沃尔特的联合创始人,斯奈德公开钦佩他。85
The technical people at Disney, however, knew exactly what we could do. One of them, Dave Snyder, warned us not to expect anything to happen with his higher management. They wouldn’t support us. On the other hand, “Ub would have,” he said. Iwerks was a cofounder, in a sense, of Disney with Walt, and Snyder openly admired him.85
这些旅行中最尴尬的一次发生在我们纽约理工学院逗留快结束时。大约一周后,亚历克斯·舒尔参观了迪士尼。“哦,艾德和阿尔维刚刚在这里,”迪斯尼的某个人告诉他——后来在电话中担心地告诉我们。舒尔从来没有提到过,我们也没有。显然,两次访问都没有任何结果,但我们很紧张,目睹了舒尔对吉姆克拉克的治疗。
The most awkward of these trips occurred near the end of our NYIT sojourn. Alex Schure visited Disney about a week after we did. “Oh, Ed and Alvy were just here,” someone at Disney told him—and worriedly informed us later in a phone call. Schure never mentioned it, and we didn’t either. Obviously nothing came of either visit, but we were nervous, having witnessed Schure’s treatment of Jim Clark.
NYIT 的计算机图形学小组设法不以任何方式参与Tubby the Tuba (1975)(图 7.33)。David DiFrancesco 和我致力于标题概念。幸运的是,他们从来没有得到任何牵引力。有一天,我们都聚集在曼哈顿米高梅的放映室,观看Tubby的首映。这不怎么样。一部 cel 动画电影可能出现的所有问题都有——例如,框架上的灰尘,以及画线下的阴影。
The computer graphics group at NYIT managed not to get involved in any way with Tubby the Tuba (1975) (figure 7.33). David DiFrancesco and I worked on titling concepts. Luckily, they never got any traction. One day we all gathered at MGM’s screening room in Manhattan to see the first showing of Tubby. It was bad. Everything that could go wrong with a cel-animated film had—dust on the frames, for example, and shadows under the drawn lines.
但Tubby确实起到了激励我们多年的愿景的目的。不是Tubby本身,而是它的生产。Tubby制作的单调乏味,当我们了解它的细节时,我们清楚地知道,计算机可以极大地帮助电影制作,如果没有其他原因,只是为了减轻工作量,跟踪大量的物流,增加质量。从那以后,我们突然想到,有一天,不知何故,我们可以成为第一个制作完全由计算机生成的电影的团体。Lance Williams 很快提出了一部名为The Works的电影,该电影由一个名为 Ipso Facto 的机器人主演,作为第一辆车。但 Ed 和我做了粗略的摩尔定律计算,并意识到工程在当时是不可行的。我们谁都不知道要实现第一部数字电影的愿景还需要 20 年。
But Tubby did serve the purpose of inspiring us with the vision that would drive us for years. Not Tubby itself but the production of it. The sheer tedium of Tubby’s production, as we came to learn its details, made it clear to us that computers could greatly assist in moviemaking, if for no other reason than to ease the workload, keep track of the massive logistics, and increase the quality. And from that we leapt to the thought that someday, somehow, we could be the first group to make a completely computer-generated movie. Lance Williams soon proposed a movie called The Works, starring a robot named Ipso Facto, as the first vehicle. But Ed and I did back-of-the-envelope Moore’s Law calculations and realized that The Works was infeasible at the time. None of us knew it would take another 20 years to realize the vision of the first digital movie.
图 7.33
Figure 7.33
为什么花了这么长时间?大多数情况下,摩尔定律还不够,可以这么说。但我们知道这只是时间问题。从技术上讲,我们必须解决几个关键问题。最重要的是运动模糊问题。在艺术上,我们必须弄清楚如何优雅地将艺术家与我们的机器连接起来。Tween 示例向我们展示了一个困难的界面是行不通的。我们必须掌握一种为 3D 对象设置动画的新方法。我们必须找到可以舒适地使用我们的硬件和软件的艺术家。
Why did it take so long? Mostly it was not enough Moore’s Law, so to speak. But we knew that was just a matter of time. Technically, we had to solve several key problems. The most important was the motion-blur problem. Artistically, we had to figure out how to interface artists to our machines gracefully. The Tween example had shown us that a difficult interface wouldn’t work. We had to master a new way of animating three-dimensional objects. And we had to find artists who could work comfortably with our hardware and software.
X(1980–1985)X (1980–1985)然后突然间地球移动了——比平时更剧烈。1979 年初的一个早晨,卢卡斯影业的乔治·卢卡斯联系了纽约理工学院的拉尔夫·古根海姆。好吧,不是那个人本人,而是代表鲍勃·金迪(Bob Gindy)。
Then suddenly the earth moved—more than usual. On one morning in early 1979 Ralph Guggenheim at NYIT was contacted by George Lucas of Lucasfilm. Well, not the man himself, but a representative, Bob Gindy.
我们原以为有一天我们会接到迪斯尼的电话,但这个电话是一个惊喜。我们唯一确定的是,卢卡斯影业的《星球大战》(1977)以其视觉效果震惊了所有人——尤其是我们——。有传言说卢卡斯曾使用电脑制作这部电影,尽管我们不确定这究竟意味着什么。我们肯定注意到,他包含了我们的朋友拉里·库珀(Larry Cuba)由计算机生成的一系列黑白书法作品——用于策划对死星的袭击。卢卡斯是一位成功的电影制片人,而舒尔则不然。也许这是我们的重大突破?
We had imagined that one day we’d get a call from Disney, but this one was a surprise. All we knew for sure was that Lucasfilm’s Star Wars (1977) had astounded everyone—especially us—with its visual effects. And rumor was that Lucas had used computers to make the movie, although we were unsure exactly what that meant. We definitely noticed that he had included a computer-generated sequence of black-and-white calligraphics by our friend Larry Cuba—for planning the attack on the Death Star. Lucas was a successful filmmaker where Schure was not. Perhaps this was our big break?
根据拉尔夫的说法,金迪在 1979 年 1 月或 2 月给他打电话,说他是卢卡斯影业的开发主管,乔治·卢卡斯正在寻求用计算机技术使电影业现代化。
According to Ralph, Gindy called him in January or February 1979, stating that he was head of development for Lucasfilm and that George Lucas was looking to modernize the film industry with computer technology.
“乔治有四个他想追求的项目。”
“George has four projects he wants to pursue.”
“好吧,他们是什么?” 拉尔夫回答。
“OK, what are they?” Ralph replied.
Gindy 提到了计算机化剪辑、计算机化声音设计和混音以及计算机化特效。
Gindy mentioned computerized editing, computerized sound design and mixing, and computerized special effects.
“第四个呢?” 拉尔夫问。
“And the fourth?” asked Ralph.
“公司账簿的计算机化会计。”
“Computerized accounting for the company’s books.”
他这样说,就好像这和其他三个人一样具有挑战性。他不断地用花絮来打断谈话,说加州马林县的生活有多美好,那里的房地产价值有多高。
He stated this as if it was just as challenging as the other three. And he kept punctuating the conversation with tidbits about how wonderful life in California’s Marin County was and how great the real estate values there were.
拉尔夫问:“对不起,你说你的头衔是什么?”
At that Ralph asked, “I’m sorry, what did you say your title was?”
“嗯,”金迪承认,“我是乔治的房地产开发主管。”
“Well,” Gindy admitted, “I’m head of real estate development for George.”
他接着说:“我们公司没有人对计算机一无所知,所以我打电话给斯坦福大学计算机系的负责人。当我描述乔治想要什么时,他说,‘我们在这里并没有真正做那种工作,但你应该联系 CMU 的 Raj Reddy。他喜欢那些图形的东西。'” 1
He went on, “No one at our company knows anything about computers, so I called the head of the computer department at Stanford. When I described what George wanted, he said, ‘We don’t really do that kind of work here, but you should contact Raj Reddy at CMU. He’s into that graphics stuff.’”1
拉尔夫·古根海姆 (Ralph Guggenheim) 是雷迪认识的卡内基梅隆大学 (Carnegie Mellon University) 刚毕业的学生,这导致金迪最终给纽约理工学院的拉尔夫打电话。Ed 和我在 Gerry House 的一个房间里会面,这是 NYIT 的豪宅,是实验室的所在地,这时 Ralph 突然说 Lucas 打来了电话——意思是 Gindy。由于舒尔对吉姆克拉克的态度,我们立即让拉尔夫闭嘴,并告诉他在他说其他话之前先关上门。
Ralph Guggenheim was a recent Carnegie Mellon University graduate known to Reddy, and that led Gindy finally to call Ralph at NYIT. Ed and I were meeting in a room of Gerry House, the NYIT mansion which housed the Lab, when Ralph burst in saying that Lucas had called—meaning Gindy. Because of Schure’s treatment of Jim Clark, we immediately shushed Ralph and told him to shut the door before he said anything else.
后来我们才发现,卢卡斯无意在他的电影中使用我们的图形绘画技巧。他只是想要数字专业知识来使好莱坞使用的机器现代化,并帮助电影制作的后勤工作。但我们突然得出结论,卢卡斯希望我们为他的电影制作内容,就像拉里古巴所做的那样。毕竟,“电脑特效”和会计一样在金迪的名单上。
We would only discover later that Lucas had no intention of using our graphics pictorial skills in his movies. He just wanted digital expertise to modernize the machines used by Hollywood and to help with the logistics of moviemaking. But we leapt to the conclusion that Lucas wanted us to make content for his movies, as Larry Cuba had done. After all, “computerized special effects” was on Gindy’s list as well as accounting.
下一步是进行正式接触并表达兴趣。因为有痣,我和 Ed 不信任纽约理工学院的电脑。我们开车离开校园,来到附近格伦科夫的一家打字机租赁公司,租了一台巨大的黑色老式铸铁打字机——让人联想到德国的 Enigma 机器。然后我们前往 Ed 的家中给 Lucasfilm 写了一封信。
The next step was to make formal contact and express interest. Because of the mole, Ed and I didn’t trust the computers at NYIT. We drove off campus to a typewriter rental company in nearby Glen Cove and rented one of those giant black old-fashioned typewriters made of cast iron—reminiscent of the German Enigma machine. Then we proceeded to Ed’s home to compose a letter to Lucasfilm.
这将是我们一生中最重要的一封信。几个小时以来,Ed 和我小心翼翼地把它拼凑起来,然后我把它打了出来。我的一个遗憾是我们没有保留那封信的副本。但我确实记得一些亮点。其中一个特别不寻常。我们拥有世界上最舒适的实验室,我们不想走下坡路。因此,重要的是,我们敦促卢卡斯影业的某个人访问纽约理工学院,看看我们受到了怎样的待遇——甚至是奢侈的待遇。我们明确表示访问应该是匿名的。
This would be the most important letter of our lives. For hours, Ed and I carefully wordsmithed it, and I typed it. One of my sorrows is that we didn’t preserve a copy of that letter. But I do remember some highlights. One was particularly unusual. We had the most comfortable lab in the world, and we didn’t want to go downhill. So it was important, we urged, that someone from Lucasfilm visit NYIT to see how well—even luxuriously—we were treated. And we made it clear that the visit should be anonymous.
卢卡斯影业确实造访过,但几乎不是匿名的。房地产经理鲍勃·金迪来了。他足够安静,但伴随着他的是卢卡斯影业的奥斯卡奖获得者特殊视觉效果负责人 Richard Edlund。Edlund 戴着一个巨大的皮带扣,上面印着大字母的星球大战。埃德和我咽了咽口水,但继续示威。有人对皮带扣发表了评论,但没有人推断出它的重要性。2
Lucasfilm did make the visit, but it was hardly anonymous. Bob Gindy, the real estate manager, came. He was quiet enough, but he was accompanied by Richard Edlund, Lucasfilm’s Academy Award–winning head of special visual effects. Edlund sported a giant belt buckle with Star Wars emblazoned in large letters. Ed and I gulped but proceeded with the demonstrations. Comments were made about the belt buckle, but nobody deduced its significance.2
我问 Edlund 在那重要的一天剩下的时间里他在做什么。他去过曼哈顿吗?不,他没有。我晚上要进去,我告诉他,他欢迎加入我。“我没有任何特别的计划。我只是进去看看会发生什么。” 他也很乐意这样做。我们那天晚上的大部分时间都在曼哈顿附近闲逛。那是一个温暖的夜晚,街上有很多人。三张纸牌锐器出来了,埃德伦德在工作中拍下了他们的照片。我们找到了进入村庄和参加前卫音乐会的路。我们谈了又谈。最后,大约凌晨 4 点,我们在一家咖啡馆喝着阿芙佳朵酒结束了这一夜。我相信我们那天晚上建立的友谊会在卢卡斯影业受到热烈欢迎。我从来没有想过 Edlund 不是在寻找我们的内容,而是我们的硬件和软件专业知识。
I asked Edlund what he was doing the remainder of that important day. Had he ever been to Manhattan? No, he hadn’t. I was going in for the evening, I told him, and he was welcome to join me. “I don’t have any particular plan. I just go in and see what happens.” He was happy to do the same. We spent most of that night roaming around Manhattan. It was a warm night with many people on the streets. Three-card-monte sharps were out, and Edlund snapped photos of them at work. We found our way into the Village and into an avant-garde music concert. We talked and talked. Finally, about 4 a.m. we wound up the night in a coffee house sipping affogatos. I was convinced that the friendship we established that evening would result in a warm welcome at Lucasfilm. It never occurred to me that Edlund wasn’t looking to us for content, but for our hardware and software expertise.
埃德和我很快受邀参观了位于洛杉矶的卢卡斯影业总部蛋厂。我们去了一趟,遇到了卢卡斯影业的总裁查尔斯·韦伯。我们没有见到乔治卢卡斯,但取得了进展。随后,埃德被邀请进行第二次访问,这次是在旧金山附近的马林县与乔治卢卡斯会面,该县很快将成为卢卡斯影业的新总部。
Ed and I were soon invited to visit Lucasfilm headquarters, The Egg Factory, in Los Angeles. We made the trip, and met the president of Lucasfilm, Charles Webber. We didn’t meet George Lucas, but progress was made. Subsequently, Ed was invited for a second visit, this time to meet George Lucas in Marin County, near San Francisco, which would soon become the new Lucasfilm headquarters.
卢卡斯影业聘请 Ed 作为第二次会议的结果。根据 Ed 的说法,Lucas 对 Ed 愿意将我们的竞争对手命名为替代员工印象深刻,但事实并非如此。Ed 于 1979 年年中离开 NYIT,以实现 Lucas 在硬件和软件方面的愿景——我们仍然相信 Lucas 打算将我们的数字图像包含在他的电影中。3
Lucasfilm hired Ed as the result of this second meeting. By Ed’s telling, Lucas was impressed that Ed was willing to name our competitors as alternative hires, whereas the reverse was not true. Ed left NYIT in mid-1979 to implement Lucas’s vision in hardware and software—and we continued to believe Lucas meant to include our digital imagery in his movies.3
我们的计划是:聘请 Ed。完毕。然后当他可以的时候,他会把我和大卫·迪弗朗西斯科带进来。我们不能突袭 NYIT 或带走它的任何技术。
Our plan was this: Get Ed hired. Done. Then when he could, he would bring me in and also David DiFrancesco. We couldn’t raid NYIT or take any of its technology with us.
作为计划的一部分,为了避开诉讼舒尔,正如我们所说,大卫和我“洗白”了自己,正如我们所说,于 1979 年 10 月离开纽约理工大学,并在加利福尼亚州帕萨迪纳的喷气推进实验室加入我们的老朋友吉姆·布林. 我们和他一起在 Carl Sagan 的Cosmos电视连续剧中工作。这是与 NYIT 的彻底决裂,并打算采取这种方式。我们和吉姆在喷气推进实验室的老板鲍勃·霍尔兹曼非常清楚,一旦埃德向北加州的卢卡斯影业招手,我们就会离开。他说:“也许我可以改变你的想法。” “我们不这么认为,”我们都回答道。卢卡斯影业具有巨大的吸引力。这是一家真正的电影公司。
As part of the plan, and to stay clear of the litigious Schure, David and I “laundered” ourselves, as we put it, by leaving NYIT in October 1979 and joining our old friend Jim Blinn at the Jet Propulsion Laboratory in Pasadena, California. We worked with him on Carl Sagan’s Cosmos television series. This was a clean break with NYIT and intended to be taken that way. We were very clear with Bob Holzman, Jim’s boss at JPL, that we were going to leave as soon as Ed beckoned us to Lucasfilm in Northern California. He said, “Perhaps I can change your mind.” “We don’t think so,” we both responded. Lucasfilm had tremendous appeal. It was a real movie company.
在卢卡斯影业的几个月里,埃德决定他需要启动三个硬件项目——计算机图形、数字音频和视频编辑——以满足卢卡斯的硬件和软件愿景。(卢卡斯会在大约一年后要求他添加第四个项目,游戏。)我们应该注意到当时没有任何关于数字内容的明确说明。同样,我们只是假设它是有意的。
During his months alone at Lucasfilm, Ed determined that he needed to start three hardware projects—Computer Graphics, Digital Audio, and Video Editing—to satisfy Lucas’s hardware and software vision. (Lucas would ask him a year or so later to add a fourth project, Games.) We should’ve noticed then that there was nothing said explicitly about digital content. Again, we just assumed it was intended.
因为我会指导计算机图形部分,所以当我还在 JPL 时,Ed 就开始给我发简历。这个词正在泄露发生的事情在卢卡斯影业。Ed 开始与 David 就建立卢卡斯影业需要的电影读者兼作家进行更深入的对话。电影仍然是电影的媒介,我们必须将我们的数字技术与它结合起来。
Since I would direct the computer graphics portion, Ed began sending me résumés of people while I was still at JPL. The word was leaking out about something happening at Lucasfilm. And Ed started holding deeper conversations with David about building a film reader-writer that we would need at Lucasfilm. Film was still the medium of movies, and we would have to interface our digital technology to it.
Ed 终于在 1980 年初给了我期待已久的电话,我加入了他在卢卡斯影业的行列。几周后,大卫接到了电话。我们三个和乔治的妻子玛西娅·卢卡斯共用一个办公室,在马林县圣安塞尔莫的一家小古董店楼上,从旧金山穿过金门大桥。Ed 正式任命我为计算机图形项目的主管,该项目是他管理的整个组织的计算机部门的一部分。大卫的电影录像机项目是计算机图形项目的一部分。
Ed finally gave me the long-awaited call in early 1980, and I joined him at Lucasfilm. Then a couple of weeks later, David got the call. We all three shared an office with Marcia Lucas, George’s wife, above a small antique store in San Anselmo, Marin County, across the Golden Gate Bridge from San Francisco. Ed officially appointed me Director of the Computer Graphics Project, part of the Computer Division, which was the overall organization that he managed. David’s film recorder project was part of the Computer Graphics Project.
埃德和我开始通过雇佣来充实我们在卢卡斯影业世界的一部分。这并不难。每个人都想出演电影。例如,当我们第一次与斯坦福大学的安迪·穆勒(Andy Moorer)就数字音频项目的负责人进行接触时,他在我们进门时从椅子上跳了起来,我们还没说一句话,就向房间里宣布:“如果你来这里的原因是我认为你是,答案是肯定的!”
Ed and I proceeded to flesh out our part of the Lucasfilm world with hires. It wasn’t hard to do. Everyone wanted to be in the movies. For example, when we first approached Andy Moorer at Stanford about heading the Digital Audio Project, he leapt from his chair as we entered, before we had said a word, and announced to the room, “If you’re here for the reason I think you are, the answer is yes!”
计算机图形项目的主要指定任务是用数字等效物代替光学胶片打印机。1980 年,光学打印机可能是好莱坞最不为人知的工具。但它对于特殊效果至关重要。这是第一次星球大战中合成图像的模拟方式电影。光学打印机将不同胶片条上的图像组合成一条胶片。例如,通过在蓝屏前移动物理模型来拍摄高速飞行的航天器。然后在光学打印机中,镜头的蓝色部分可以单独替换为星场镜头。或者可以将几个单独的航天器组合在一起,比如与小行星带一起,在一个星域上空。毫不奇怪,我们会使用 Alpha 通道以数字方式合成它们。David 的激光扫描打印机将成为我们将要建造的数字光学打印机的输入输出设备。
The principal designated task of the Computer Graphics Project was to replace the optical film printer with a digital equivalent. In 1980 an optical printer was perhaps the least understood instrument in Hollywood. But it was fundamentally important for special effects. It was the analog way of compositing images in the first Star Wars movie. An optical printer combines images on separate strips of film into a single strip of film. A speeding spacecraft, for example, was shot by moving a physical model in front of a blue screen. Then in an optical printer the blue parts of the shot could be replaced with a star field shot separately. Or several separate spacecrafts could be composited, say with an asteroid belt, over a star field. We would, no surprise, use an alpha channel to composite them digitally. David’s laser scanner-printer was to be the input-output device for the digital optical printer we would build.
David DiFrancesco 将目光投向了可以读取和写入胶片的基于激光的胶片扫描仪。但以前没有人为 35 毫米电影彩色胶片制造过激光读写器。大卫谨慎地接近它,用相互竞争的激光技术制造了两个这样的设备,开始了他从艺术家和摩托车爱好者到激光扫描打印机和数字摄影科学专家的神奇转变。4
David DiFrancesco set his sights on a laser-based film scanner that could both read and write film. But nobody had ever built a laser reader-writer for 35 mm motion-picture color film before. David approached it cautiously by building two such devices with competing laser technologies, beginning his magical transformation from artist and motorcycle enthusiast to a laser scanner-printer and digital photoscience expert.4
当然,我们在卢卡斯影业需要帧缓冲区。我很快与北卡罗来纳州 Ikonas Graphics Systems 的 Nick England 和 Mary Whitton 签约,为我们构建一个具有四个通道的帧缓冲区——这是第一个商业广告带有 alpha 通道的帧缓冲区作为标准设备。这就是 Tom Porter 的 RGBA 绘制程序的硬件基础——在第 6 章中让 Ravi Shankar 感到惊讶的样条曲线。5
We needed framebuffers at Lucasfilm, of course. I soon contracted with Nick England and Mary Whitton—a husband-wife power pair—at Ikonas Graphics Systems in North Carolina to build us a framebuffer with four channels—the first commercial framebuffer with an alpha channel as standard equipment. This was the hardware basis of Tom Porter’s RGBA paint program—the one with splines that astonished Ravi Shankar in chapter 6.5
亚历克斯·舒尔(Alex Schure)向旧金山南部发明录像带的公司 Ampex 出售了 NYIT 的绘画程序,这让我很沮丧。不是我复杂的 24 位程序 Paint3,而是更简单的 8 位版本 Paint。那里的一位年轻的受过斯坦福培训的编码员 Tom Porter 致力于将其改编为 Ampex Video Art (AVA) 产品。所以我聘请了汤姆,我第一个直接雇佣的计算机图形师,来编写卢卡斯影业的绘画程序。
Alex Schure had dismayed me by selling an NYIT paint program to Ampex, the company south of San Francisco that invented videotape. Not my sophisticated 24-bit program, Paint3, but the much simpler 8-bit version, Paint. A young Stanford-trained coder there, Tom Porter, had worked at adapting it to the Ampex Video Art (AVA) product. So I hired Tom, my first direct computer graphics hire, to write the Lucasfilm paint program.
绘图程序直接创建颜色像素,而不是从透视的三维计算机模型渲染它们的中心法则方法。Paint3 可以绘制比 Paint 更多的颜色。但更重要的是,因为它可以访问如此多的颜色,它可以将带有柔和边缘的笔画融合到帧缓冲区中已经存在的任何颜色中。结果,笔画和背景图像之间没有硬的锯齿状边缘,这种情况困扰着具有 8 位帧缓冲区且只有 256 种颜色可用的 Paint。
A paint program creates color pixels directly, as opposed to the Central Dogma method of rendering them from a three-dimensional computer model seen in perspective. Paint3 could paint in vastly more colors than Paint. But more importantly, because it could access so many colors, it could meld a paint stroke with soft edges into whatever colors were already in a framebuffer. As a result, there wasn’t a hard, jagged edge between the paint stroke and the background image, a condition that afflicted Paint with its 8-bit framebuffer and only 256 colors available.
在卢卡斯影业,Tom 超越了 8 位 Paint 和 24 位 Paint3,编写了世界上第一个 RGBA 绘画程序。这个 RGBA 绘图程序也可以绘制一个 Alpha 通道。当您将带有柔和边缘的 24 位笔画绘制到帧缓冲区的颜色(RGB 或红色、绿色、蓝色)通道中时,您同时将每个像素的不透明度绘制到 alpha (A) 通道中。一旦 Paint3 绘制了笔画,它就永久地成为图像的一部分。但是 RGBA 笔画可以在其他背景上重复使用。这就是 Ravi Shankar 演示的样条形笔触如何放置在任意背景上并且可以重复使用。要完全控制数字图像,我们也必须能够完全控制其 Alpha 通道。具有 32 位像素的 RGBA 绘画就是这样一种重要的工具——在任何地方都结合了新的 Alpha 通道。
At Lucasfilm, Tom went beyond 8-bit Paint and 24-bit Paint3 to write the first RGBA paint program in the world. What this RGBA paint program could do was paint an alpha channel too. As you paint a 24-bit paint stroke with soft edges into the color (RGB, or red, green, blue) channels of the framebuffer, you simultaneously paint the opacity of each pixel into the alpha (A) channel. Once Paint3 painted a stroke, it became part of the image permanently. But an RGBA paint stroke could be reused on other backgrounds. That’s how the spline-shaped strokes for the Ravi Shankar demo were laid down over arbitrary backgrounds and could be reused. To have full control of a digital image, we had to be able to have full control over its alpha channel too. RGBA paint, with 32-bit pixels, was one such important tool—incorporating the new alpha channel everywhere.
在 1980 年代初期在卢卡斯影业设计我们的数字光学打印机时,我们观察到我们可以制造一台比通用计算机快四倍的专用计算机。这是因为我们的数据是 RGBA 像素,这意味着我们可以同时在一个像素的所有四个通道上计算相同的东西。它将是一台专用计算机,只是因为它假设其数据是像素。否则它将是一台可以计算任何东西的通用计算机渠道。另一种说法是,我们的计算机将成为像素的通用计算机。这就是我们建造的。
In designing our digital optical printer at Lucasfilm in the early 1980s, we observed that we could build a special-purpose computer that would go four times faster than a general-purpose computer. This was because our data was RGBA pixels, meaning that we could compute the same thing on all four channels of a pixel simultaneously. It would be a special-purpose computer only in that it assumed its data was pixels. Otherwise it would be a general-purpose computer that could compute anything on the channels. Another way to say it was that our computer would be a general-purpose computer for pixels. And that’s what we built.
四倍不是一个数量级,但它仍然是一个显着的加速。这台机器,后来被称为皮克斯图像计算机,是在我们等待摩尔定律正常提供给我们时获得额外计算能力的权宜之计。我不会在这里详述它,因为摩尔定律确实很快取代了它。然而,它确实在短时间内为我们提供了比任何其他计算机图形工具都多的功能。但是这个名字是从哪里来的呢?
A factor of four is not an order of magnitude, but it’s still a substantial speedup. This machine, which came to be called the Pixar Image Computer, was a stopgap to get additional computational power while we waited for Moore’s Law to give it to us normally. I won’t dwell on it here because Moore’s Law did supplant it rather rapidly. It did, for a short time, however, give us more horsepower than any other computer graphics facility had. But where did that name come from?
有一天,我在一次汉堡午餐中向图形组中的四个人提议,我们以激光为灵感,并用一个看起来像西班牙语动词的名词来命名我们的机器。使用我的新墨西哥传统,我解释说西班牙语动词以-ir、-er或-ar结尾。我提出了pixer,to picture或to make pictures,发音为西班牙语“peeks Air”。四人之一的 Loren Carpenter 说:“你知道,Alvy,雷达这个词听起来很高科技。” 我跳了起来,“好吧,皮克斯也是一种有效的西班牙语形式。” 我发音为“peeks Ahr”。就是这样。这台机器有一个名字,一个看起来像(假的)西班牙语动词的名词,意思是拍照。我们很快将西班牙语发音改为“Pix ahr”。这个词,最初是卢卡斯影业机器的名称,在我们的未来中占有很高的地位,罗伦也是。
I proposed to four people in the graphics group at a hamburger lunch one day that we take laser as inspiration and name our machine with a noun that looked like a Spanish verb. Using my New Mexican heritage, I explained that a Spanish verb ends in -ir, -er, or -ar. I proposed pixer, to picture or to make pictures, pronounced in Spanish “peeks Air.” Loren Carpenter, one of the four, said, “You know, Alvy, the word radar has a really high-tech sound to it.” And I jumped, “Well, pixar is a valid Spanish form too.” I pronounced it “peeks Ahr.” And that was it. The machine had a name, a noun that looked like a (fake) Spanish verb meaning to make pictures. We quickly dropped the Spanish pronunciation, to “Pix ahr.” This word, originally the name of a Lucasfilm machine, would figure highly in our future, as would Loren.
Loren Carpenter 发送了我在 JPL 的插曲中看到的最令人印象深刻的简历。他发送的并不是真正的简历。这是几张 8 x 10 的彩色照片,由计算机渲染的一座类似于西雅图雷尼尔山的山脉,位于他工作的波音公司附近。很明显,Loren 已经掌握了分形,这是一种用令人信服的自然细节对自然场景(如白雪覆盖的山)进行建模的新方法。洛伦是个很聪明的人。他知道他所要做的就是给我们看照片,我们就会知道他能做什么。的确,我们必须拥有他!
Loren Carpenter had sent the most impressive résumé I reviewed during the interlude at JPL. What he sent wasn’t really a résumé. It was several 8 by 10 color photographs of computer renderings of a mountain resembling Seattle’s Mount Rainier, near Boeing where he worked. It was obvious that Loren had mastered fractals, a new way of modeling natural scenes—like a snow-covered mountain—with convincingly natural detail. Loren’s a very smart guy. He knew that all he had to do was show us the pictures, and we would know what he could do. Indeed, we had to have him!
我立即取得了联系,但 Loren 拒绝进一步讨论任何事情,直到我看到他为即将于当年夏末(1980 年)举行的大型年度计算机图形会议 Siggraph 制作的计算机动画电影西雅图。当 Loren 终于放映他的短片Vol Libre时,Ed 和我坐在 Siggraph 电影展的前排。它以分形山脉为特色——茶壶埋在广阔的“自然”景观中——并把房子倒塌了。在他具有里程碑意义的演讲之后,我冲上舞台说:“现在?” 他说:“现在。” 我们立即为卢卡斯影业聘请了他。
I immediately got in touch, but Loren refused to discuss anything further until I had seen a computer-animated movie he was making for the upcoming Siggraph, the big annual computer graphics conference, to be held in late summer that year (1980), in Seattle. Ed and I were sitting in the front row at that Siggraph film show when Loren finally showed his short movie Vol Libre. It featured fractal mountains—with a teapot buried in the vast “natural” landscape—and brought the house down. I rushed the stage after his landmark presentation and said, “Now?” He said, “Now.” We hired him immediately for Lucasfilm.
分形是使用放大将计算机图形模型中的一个三角形变成数百万的一种绝妙方法。简单的想法如图 8.1 所示。唯一的最上面一行显示了我们作为微不足道的人类所采取的明确步骤:我们取三角形一侧的中点并在三个维度上将其位移一小部分。例如,我们可能会将中点抬高到原始三角形平面上方的距离与边长相比很小。类似地,我们置换另外两条边的中点。每种情况下的实际位移取随机方向和随机高度,新定位的中点用直线相互连接。换句话说,原来的三角形被替换为如图所示的四个较小的三角形,它们存在于三维空间而不是两个。这是第 1 步。
Fractals are a nifty way of using Amplification to turn one triangle in a computer graphics model into millions. The simple idea is illustrated in figure 8.1. The only explicit step we take as puny human beings is shown in the top row: We take the midpoint of one side of a triangle and displace it, in three dimensions, by a small amount. For instance, we might raise the midpoint above the plane of the original triangle by a distance that is small compared to the length of the side. Similarly, we displace the midpoints of the other two sides. The actual displacement in each case is taken in a random direction and a random height, and the newly located midpoints are connected to one another with straight lines. In other words, the original triangle is replaced with four smaller triangles as shown, and they exist in three-dimensional space instead of two. That’s step 1.
图 8.1
Figure 8.1
图片由皮克斯动画工作室提供。
Images courtesy of Pixar Animation Studios.
我们的人类工作已经完成。计算机以其令人敬畏的放大功能接管,并将相同的技巧应用于步骤 1 刚刚创建的四个三角形中的每一个。结果是底行左侧的第一张图片。四个三角形变成十六个。这是第 2 步。然后计算机在第 2 步中创建的每个三角形上重复该技巧,以获得底行中的第二张图片。以此类推,直到我们原来的三角形开始看起来很像一座山。Amplification 仅用 5 个步骤将模型中的一个三角形替换为 1,024 个三角形。每一步对人类来说都变得越来越困难,但对计算机来说却毫无意义。在十个步骤中,这种分形山技术将我们一个微不足道的三角形变成了超过一百万个三角形。十五步将产生超过十亿个小三角形。几乎没有比工作中令人敬畏的放大更清晰的例子了。这也证明了我们是多么容易被复杂性所愚弄。
Our human work is done. The computer takes over with its awesome Amplification capability and applies the same trick to each of the four triangles that step 1 just created. The result is the first picture on the left in the bottom row. Four triangles become sixteen. That’s step 2. Then the computer repeats the trick on every triangle created in step 2 to get the second picture in the bottom row. And so forth, until our original triangle starts to look a lot like a mountain. Amplification has replaced one triangle in our model with 1,024 triangles in just five steps. Each step gets increasingly difficult for a human but is nothing to a computer. In ten steps this fractal mountain technique takes our one puny triangle into over a million triangles. And fifteen steps would yield over a billion tiny triangles. There’s hardly a clearer example of awesome Amplification at work. It’s also a testimony to how easily we are fooled with complexity.
Loren 发给我的是用这种方式创建的分形山的照片。他把每个三角形都渲染成合适的颜色,看起来像一座由土褐色和树木繁茂的绿色覆盖的雪山。很明显,他掌握了分形技术。
What Loren had sent me was photographs of a fractal mountain created this way. He had rendered each triangle into an appropriate color to look like a snow-capped mountain of earthy browns and wooded greens. It was obvious that he had mastered fractal technology.
我们现在知道如何制作山脉,但另一个问题是计算机图形表面似乎总是由塑料制成。查看第 10X步的 Phong 着色示例,大约在 1973 年(图 7.19)。球是闪亮的蓝色,带有清晰的白色亮点。它似乎是一个蓝色的塑料球。
We now knew how to make mountains, but another problem was that computer graphics surfaces always appeared to be made of plastic. Look at the Phong shading example at the 10X step, circa 1973 (figure 7.19). The ball is shiny blue with a white, sharply defined highlight. It appears to be a blue plastic ball.
那时人们对计算出来的图片应该是什么样子有先入之见。他们假设在计算机上创建的任何东西都必须看起来很僵硬、锯齿状或多面——总之,“计算机化”。随着这些问题特征中的每一个都得到解决,“计算机”的概念不断发展,塑料成为定义计算机图片外观的新标准。塑料具有肤浅或人工的社会意义,这无助于人们早期对计算机的认识。
People had preconceptions back then about what computed pictures had to look like. They assumed that anything created on a computer had to look rigid or jagged or faceted—in a word, “computery.” As each of these problem characteristics was solved, the notion of “computery” evolved, and plastic became the new standard for defining the look of computer pictures. It didn’t help people’s early perception of computers that plastic had taken on the social meaning of shallow or artificial.
但罗布·库克,唐·格林伯格在康奈尔大学的研究生之一,已经想出了如何将塑料留在身后。他的新技术产生了似乎由铜、木头或铝制成的渲染表面,而不是塑料。他将更多的物理学融入到计算机图形学中,即光与材料的相互作用。高光的颜色和形状是我们人类模拟什么材料的线索。无论是哑光还是光泽也很重要。这些都构成了计算机模型的外观因素。有了这个概念,阴影就具有了更大的意义。
But Rob Cook, one of Don Greenberg’s graduate students at Cornell, had figured out how to leave plastic behind. His new technique yielded rendered surfaces that appeared to be made of, say, copper, wood, or aluminum rather than plastic. He had incorporated more physics into computer graphics, namely the interaction of light with materials. The color of the highlight, and its shape, were clues to us humans of what material was simulated. Whether it was matte or glossy mattered too. These all constituted appearance factors for a computer model. With this notion, shading took on yet a larger meaning.
我们也必须有这个人!所以我给罗伯打电话,给了他一份工作。他想知道他是否可以在康奈尔多呆一会儿,完成他的科学硕士学位。“这个提议是暂时的,”我说。他接受了。后来我得知,唐·格林伯格打算创办一家拥有罗伯才华横溢的公司。唐虽然很失望,但告诉我阻止罗伯加入卢卡斯影业令人兴奋的团队是不公平的。罗布最终确实完成了与唐的学位。
We must have this guy too! So I called Rob and offered him a job. He wanted to know if he could stay at Cornell a little longer and complete his master’s degree in science. “The offer is for now,” I said. And he accepted it. I learned later that Don Greenberg had intended to start a company featuring Rob’s tremendous talent. Disappointed as he was, Don told me that it would have been unfair to stop Rob from joining the exciting group at Lucasfilm. And Rob did eventually complete his degree with Don.
在卢卡斯影业,Rob Cook 的天才再次绽放。他用一种叫做阴影语言的新颖概念将阴影发挥到了极致。也就是说,他创建了一个用于讨论阴影的语法。向语言的飞跃始终是计算机科学的重大进步。仅次于库克的是纽约大学的肯·佩林(Ken Perlin),他的想法大致相同。6
At Lucasfilm Rob Cook’s genius flowered again. He took shading to the limit with a novel concept called a shading language. That is, he created a grammar for talking about shading. The leap to a language is always a significant advance in computer science. And just slightly behind Cook was Ken Perlin at New York University with much the same idea.6
图灵章节中描述的计算是一系列精心定义的步骤,这些步骤执行无意义的操作,例如将每个 1 交换为 0,反之亦然,或者将所有位向右移动一个位置。图灵自己通过引入子程序实现了语言概念的第一次飞跃:一个简短的无意义步骤列表一次又一次地被赋予一个名字;然后程序员可以将计算视为子程序名称的列表,而不是底层繁琐的指令。
A computation, as described in the Turing chapter, is a list of carefully defined steps doing meaningless things like exchanging each 1 for a 0, and vice versa, or shifting all bits one position to the right. Turing himself made the first leap toward the notion of a language by introducing the subroutine: a short list of the meaningless steps that is used again and again is given a name; then a programmer can think of a computation as a list of the subroutine names, instead of the underlying tedious instructions.
我将子程序的概念比作将一本书分成章节,将章节分成段落,将段落分成单词。像这样使用层次结构让人类可以跟踪大量微小的无意义的步骤——或者写一本书的单词。这个级别的程序员通常知道无意义的步骤和子程序,就像作者知道单词和它们的单元组织一样。
I compared the subroutine notion to breaking up a book into chapters, the chapters into paragraphs, and the paragraphs into words. Using hierarchy like this lets mere humans keep track of immense numbers of tiny meaningless steps—or words in the case of writing a book. A programmer at this level generally knows both the meaningless steps and the subroutines, as an author knows both the words and their organization into units.
向语言的下一次飞跃使我们人类完全无法了解潜在的无意义步骤。我们可以用对特定领域有意义的术语进行思考,例如着色或渲染的计算机图形。“术语”被实现为具有固定名称的子程序。但是由这些名称组成的语言的用户不必知道这些术语是如何实际实现的。他们只需要知道有人这样做是正确的。
The next leap toward a language divorces us humans from knowing about the underlying meaningless steps altogether. We can think in terms that are meaningful to a specific field, such as shaded, or rendered, computer graphics. The “terms” are implemented as subroutines with fixed names. But users of the language made of these names don’t have to know how the terms are actually implemented. They just have to know that somebody has done so correctly.
考虑一下流行的文字处理程序 Microsoft Word,我用它来撰写这些页面。作为用户,您可以将键盘上的字符或菜单中的图标视为 Word 语言中的术语。您不必知道每个术语调用的计算机中一长串无意义的步骤。很少有人知道他们。考虑输入字母“A”。实际上,这样做会启动一长串步骤,在当前字体、当前大小、当前颜色、当前位置、当前页面上放置一个“A”,并导致字母的呈现出现在当前页面的屏幕显示上。如果您已将字母插入到已显示的句子中,则基本指令必须移动页面模型中的字母,以便为新的句子留出空间。键入“A”会导致很多事情发生,而您,用户,永远不必关心。您必须知道的是,在当前位置键入“A”会导致“A”出现在您想要的位置。相似地,剪切、复制和粘贴是 Word 语言中的术语,它们会在下面发生惊人的事情,而您却看不到。插入图片和插入超链接等术语也是如此。
Consider the popular word-processing program Microsoft Word, which I’m using to compose these very pages. As a user, you can think of the characters on the keyboard or icons in the menus as terms in the Word language. You don’t have to know the long sequences of meaningless steps in your computer that each term invokes. Very few people know them. Consider typing the letter “A.” In effect, doing so kicks off a long sequence of steps that places an “A” in the current font, at the current size, in the current color, in the current location, on the current page, and cause a rendering of the letter to appear on a screen display of the current page. And if you’ve inserted the letter amid an already displayed sentence, then the underlying instructions must move the letters in the model of the page around to give space for the new one. Typing an “A” causes a great many things to happen that you, the user, never have to care about. All you must know is that typing an “A” at the current location results in an “A” appearing where you want it. Similarly, Cut, Copy, and Paste are terms in the Word language that cause amazing things to happen underneath, unseen by you. So do terms like Insert Picture and Insert Hyperlink, and so forth.
随着摩尔定律将越来越多的领域带入计算领域,库克和佩林的着色语言概念遵循了计算机科学中已为人熟知的路径。这个想法是,通过创建正式捕获它的计算机语言来结晶一个领域。在 1980 年代中期,Cook 和 Perlin 将语言理念带入了广阔的未知领域:通过引入着色语言来推广着色。
Cook’s and Perlin’s notion of a shading language followed a pathway that has become familiar in computer science as Moore’s Law brings more and more realms into the province of computation. The idea is that a field is crystalized by the creation of a computer language that formally captures it. In the mid-1980s Cook and Perlin took the language idea into vast uncharted territory: the generalization of shading by introduction of a shading language.
到目前为止,我们已经考虑了一些着色技术:纹理映射、凹凸映射、Gouraud 着色、Phong 着色、透明度和材质外观因素。我们可以继续解释一种又一种这样的技术。但是 Cook 和 Perlin 真正的大想法是,任何计算都可以用来影响渲染表面的“阴影”。
We have considered a handful of shading techniques so far: texture mapping, bump mapping, Gouraud shading, Phong shading, transparency, and material appearance factors. We could continue to explain one such technique after another. But Cook and Perlin’s really big idea is that any computation can be used to affect the “shading” of a rendered surface.
假设我想要纹理贴图和凹凸贴图一个三角形。或者假设我希望它是带有凹凸的黄铜。或以上所有的组合。着色语言概括了着色的概念。可以用着色语言编写的着色程序数不胜数。这就是计算的本质——延展性的奇迹。
Suppose I wanted to texture map and bump map a triangle. Or suppose I wanted it to be brass with bumps. Or combinations of all the above. Shading language generalized the notion of shading. There’s a digital infinity of shading programs that can be written in a shading language. That’s the essence of what it means to compute—the miracle of Malleability.
是时候了解使用 3D 几何图形描述的虚拟场景(以及精心指定的阴影)如何以彩色渲染成二维图片,例如数字电影的一帧。我们已经看到了如何渲染构成场景的三角形,但是这些渲染不是彩色的。并且只渲染了三角形的轮廓。
It’s time to understand how a virtual scene described with three-dimensional geometry—and carefully specified shading—is rendered in color into a two-dimensional picture, say one frame of a digital movie. We’ve already seen how to render the triangles that make up the scene, but these renderings were not in color. And only the outlines of the triangles were rendered.
然后我们看到渲染的彩色三角形相对于像素间距很大。在这里,我们采用更实用的现代案例,数百个三角形小到可以落入像素位置之间的裂缝中。
And then we saw rendered colored triangles that were large with respect to pixel spacing. Here we take on the more practical modern case of hundreds of triangles small enough to fall in the cracks between pixel locations.
让我们采用与以前相同的策略:我将向您展示每个像素的基本思想是多么简单。然后,我将使用 Epoch 2 Amplification 的魔力来处理为整个帧或最终为整部电影实现它实际上需要的大量计算。这部分是不人道的,但一旦你理解了基本的计算,就不难理解了。
Let’s pursue the same strategy as before: I’ll show you how simple the basic idea is at each pixel. Then I’ll allow the magic of Epoch 2 Amplification to take care of the immense number of computations that are actually required to implement it for an entire frame, or eventually, an entire movie. That part is inhuman, but not hard to understand once you understand the essential computations.
所以,把自己想象成相机。眼睛固定在固定位置看世界。你从两个维度和透视中看世界。(为了明确起见,假设您闭上一只眼睛,所以只有一只眼睛是相机。)计算机图形学中的虚拟相机做同样的事情。它看到的“世界”是无形的几何图形。但它是经过仔细定义的,并且将其投影到透视的二维框架上的数学是很好理解的。
So, think of yourself as the camera. Look out at the world with your eyes held in fixed position. You see the world in two dimensions and in perspective. (To be unambiguous, let’s assume you have one eye closed, so only one eye is the camera.) The virtual camera in computer graphics does the same thing. The “world” it sees is invisible geometry. But it’s carefully defined, and the math that projects it onto a two-dimensional frame in perspective is well understood.
换句话说,我们知道的足够多,可以计算出在我们要渲染的场景模型中哪个三角形在另一个三角形前面。使用所有模型都是(可能是数百万个)三角形的集合的简化,这意味着我们可以计算渲染三角形的顺序。
In other words, we know enough to calculate which triangle is in front of another triangle in the model of the scene we want to render. Using the simplification that all models are collections of (perhaps millions of) triangles, this means that we can calculate what order to render the triangles in.
我不会过于简单化。三角形的排序需要大量的计算工作,但最重要的是由我们忠实的计算机处理。我们真正需要了解的是,从虚拟相机中可以看出,确定两个三角形中的哪一个是前面的那个是相当简单的。相机可以看到哪些三角形?我们已经讨论了两种寻找可见表面的方法(许多可能的方法):深度缓冲和几何排序。
I’m not going to oversimplify. The ordering of triangles takes a lot of computational work, but the brunt of it is handled by our faithful computers. All we really need to understand is that it’s rather straightforward to determine which of two triangles is the one in front, as seen from the virtual camera. Which triangles can the camera see? We’ve discussed two approaches (of many possible) to finding the visible surfaces: depthbuffering and geometric sorting.
基本问题是将虚拟相机的世界视图渲染为一帧彩色像素,当它们显示时可以看到。这里有一个简单的方法来理解这个问题:想象一个窗纱将你的眼睛与可见的世界隔开。窗纱的电线将二维可见字分成小方块。再次警告:这些不是像素!作为该问题的第一个近似值,让我们假设这些微小的窗口屏幕视图中的每一个确实会在最终图像中产生一个像素。这种近似值在过去糟糕的日子里很常用,并且是造成像素是小正方形的错误观念的重要原因——即使在从业者中也是如此。
The basic problem is to render the virtual camera’s view of the world to a frame of color pixels that can be seen when they’re displayed. Here’s an easy way to understand the problem: Imagine that a window screen separates your eye from the visible world. The wires of the window screen divide the two-dimensional visible word into little squares. Caution, yet again: these are not pixels! As a first approximation to the problem, let’s assume that each one of these tiny window-screen views of the world does result in one pixel in the final image. This approximation was commonly used in the bad old days and was a large contributor to the false notion that a pixel is a little square—even among practitioners.
因此,渲染场景视图的问题已经简化为为每个窗口屏幕单元渲染一个像素的问题。哪一种颜色代表虚拟相机看到的落在那个小正方形中的所有三角形或三角形的一部分?
So the problem of rendering a view of a scene has been reduced to the problem of rendering one pixel for each window-screen cell. What one color represents all the triangles, or parts of triangles, that fall in that tiny square as seen by the virtual camera?
我在斯德哥尔摩市中心的老岛 Gamla Stan 一间美妙公寓的整洁厨房里写下这篇文章。我放眼世界,看到蓝色架子上的蓝白色盘子,另一个是香料,另一个是水杯,小煤气炉上方的黑色煎锅和器皿,干花,一排挂着的不锈钢刀,水槽旁边的洗碗器,等等。我的视野左侧有一个大窗口。一株盛开的白色天竺葵和其他植物填满了宽阔的窗台。外面,我看到一棵栗树,部分遮住了旧斯德哥尔摩的黄色建筑,再往前是积云的蓝天。
I write this from the tidy kitchen of a wonderful apartment in Gamla Stan, the old island at the heart of Stockholm. I look out at the world and see the blue-and-white dishes on the blue shelves, the spices on another, water glasses on another, black skillets and utensils above the little gas stove, dried flowers, a rack of hanging stainless steel knives, a dish drainer next to the sink, and so forth. There’s a large window at the left of my visual field. A white geranium in bloom and other plants fill the wide sill. Outside I see a chestnut tree partially obscuring the yellowish buildings of old Stockholm, and beyond that the blue sky with cumulus clouds.
接下来我想象一个窗口屏幕将我与我刚才描述的场景分开。我的工作是只选择一种颜色来表示通过窗口屏幕网格的每个单元所看到的视觉场景。你可以想象一个四面的金字塔,它的顶点在我的眼睛,它通过窗纱正好在一个线栅处,并随着它向无穷远方向延伸而变宽。从我的眼睛看,一种颜色(!)必须代表落在那个小金字塔中的所有东西。
Next I imagine a window screen separating me from the scene I just described. My job is to choose just one color to represent the visual scene as seen through each cell of the window-screen grid. You can imagine a four-sided pyramid, with its apex at my eye, that passes through the window-screen at exactly one wire grid and broadens as it proceeds to infinity beyond. One color (!) has to represent everything that falls in that little pyramid, as seen from my eye.
在某些情况下,这非常简单。例如,一些细胞只能看到远处的蓝天。那是他们像素的颜色。有些人只看到这个厨房的淡蓝色墙壁。那里的金字塔与隔壁的建筑物相交这一事实并不重要。墙壁是不透明的,因此厨房墙壁颜色隐藏了所有建筑物墙壁颜色。这些都是隐藏的表面。厨房墙壁颜色是这些像素的颜色。
In some cases, this is very simple. For example, some of the cells see only the far blue sky. That’s the color for their pixels. Some see only the pastel blue wall of this kitchen. The fact that the pyramid there intersects the buildings next door doesn’t matter. The wall is opaque so the kitchen wall color hides all those building wall colors. Those are all hidden surfaces. The kitchen wall color is the color for these pixels.
通过成堆的盘子窥视的细胞更困难但更简单。我在看一堆嵌套的蓝白色汤碗。我眼中的小金字塔一次与几个碗相交,但它们是不透明的,因此只有通过窗纱单元直接可见的表面才能产生颜色。我这里需要的颜色将是蓝色和白色的加权组合,具体取决于每个窗口屏幕单元格的小金字塔相交的比例。其他的碗无所谓,碗外的蓝色架子墙无所谓,墙外的斯德哥尔摩老建筑无所谓,天外的天空也无所谓。虽然它们在小金字塔内,但它们都隐藏在我的视线之外。
The cells that peer through stacks of dishes are more difficult but straightforward. I’m looking at a stack of nested blue-and-white soup bowls. The little pyramid from my eye intersects several bowls at a time, but they are opaque so only the surfaces directly visible through the window-screen cell contribute to the color. The color I need here would be a weighted combination of blue and white depending on the proportions of each intersected by the little pyramid for one window-screen cell. The other bowls don’t matter, the blue shelf wall beyond the bowls doesn’t matter, the old buildings in Stockholm beyond the wall don’t matter, the sky beyond doesn’t matter. Although they’re inside the little pyramid, they’re all hidden from my view.
搁置眼镜的架子比较困难。我的一些窗纱单元可以透过五层玻璃看到远处淡蓝色的架子墙,这意味着架子墙的蓝色被 10 块部分透明的玻璃墙修饰,将它与我隔开。
The shelf holding glasses is more difficult. Some of my window-screen cells can see through five layers of glasses to the pastel blue shelf wall beyond, which means that the blue of the shelf wall is modified by 10 partially transparent glass walls that separate it from me.
真正困难的案例是向窗外看的牢房。其中一些可以看到天竺葵植物、窗外部分打开的窗框、窗外的栗树,以及斯德哥尔摩建筑物或树外天空中的云,或两者兼而有之。但问题仍然存在:确定每个单元格的哪些表面是可见的,以及每个单元格按可见区域按比例贡献的颜色。然后为相应像素选择的最后一种颜色是这些颜色的平均值。在这种情况下,小金字塔与数十个甚至数百个表面相交,每个表面都可能为最终平均值贡献一点点颜色。
The really difficult cases are the cells that look out the window. Some of these can see the geranium plant, the partially open window casing beyond, the chestnut tree beyond the window, and either Stockholm buildings or clouds in the sky beyond the tree, or both. But the problem remains the same: determine for each cell what surfaces are visible and what color each contributes proportionally by visible area. Then the final one color chosen for the corresponding pixel is the average of those colors. The little pyramids in this case intersect dozens, perhaps hundreds, of surfaces, each of which might contribute a tiny bit of color to the final average.
计算机图形学不会发生在漂亮的斯德哥尔摩厨房里。它发生在计算机内部。没有天竺葵或盘子,但可能有一棵树、一堆汤碗、一个装满玻璃的架子等等的几何模型。否则也是同样的问题。虚拟摄像机在每个窗口屏幕位置看到什么,那里的平均颜色是什么?
Computer graphics doesn’t happen in a pretty Stockholm kitchen. It happens inside a computer. There are no geraniums or dishes, but there might be a geometric model of a tree, of a stack of soup bowls, of a shelf full of glasses, and so forth. It’s the same problem otherwise. What does a virtual camera see at each window-screen location, and what’s the average color there?
这是一幅自画像,描绘了艺术家在左手支撑的镜面球体中的倒影。埃舍尔的脸在中间,但可以看到他办公室的几何扭曲渲染。在那的背景是一扇窗户。当然,这是从至少 9300 万英里以外的地方聚集的光线。关键是,为了对一个像闪亮的球一样简单的物体进行忠实的 3-D 计算机图形渲染,理论上,你必须考虑到宇宙中的每个物体。
It was a self-portrait depicting the artist reflected in a mirrored sphere supported in his left hand. Escher’s face was in the middle, but a geometrically distorted rendering of his office could be seen around it. In the background of that was a window. This, of course, was gathering in light from at least ninety-three million miles away. The point being that in order to make a faithful 3-D computer graphics rendering of an object as simple as a shiny ball, you would, in theory, have to take into account every object in the universe.
——尼尔·斯蒂芬森,秋季;或者,躲避地狱,2019 7
—Neal Stephenson, Fall; or, Dodge in Hell, 20197
如果目标是模拟真实世界的光学器件,那么上一节的描述中就会缺少一些东西。想象一下,从您的眼睛中通过窗纱中的一个单元向外面的世界发出一束光线。眼睛不发射光线,但让我们表现得像他们在这个练习中所做的那样。这种虚假的“眼睛光线”是真实光线的反面,例如,从某个表面反射到我们的眼睛中。在前面,每条眼睛的光线都在进行直线进入世界,直到遇到不透明的表面,然后停下来。(把天空和云彩想象成无限远处的不透明平面。)如果眼睛光线穿过窗户或水玻璃,它会直接穿过窗户到达远处的任何表面。
If the goal is to simulate real-world optics, then there’s something missing from the description in the preceding section. Imagine sending out one ray from your eye through a cell in the window screen to the world beyond. Eyes don’t emit rays, but let’s act like they do for this exercise. Such a fake “eye ray” is the reverse of a real light ray reflected, say, off some surface into our eye. In the preceding, each eye ray proceeds in a straight line out into the world until it encounters an opaque surface, then stops. (Think of the sky and clouds as an opaque painted flat at infinity.) If the eye ray passes through a window or through a water glass, it passes directly through it to whatever surface is beyond.
图 8.2
Figure 8.2
© 2020 MC Escher 公司—荷兰。版权所有。
© 2020 The M. C. Escher Company—The Netherlands. All rights reserved.
但是真正的光线会受到它们穿过的材料的影响。眼镜镜片就是一个明显的例子。它的全部目的是弯曲光线以更好地服务于我们的眼睛。通常,光线在穿过透明材料时会改变方向——它会折射。
But real light rays are affected by the materials they pass through. An eyeglass lens is an obvious example. Its whole purpose is to bend light rays to the better service of our eyes. Generally, a light ray changes direction—it refracts—when it passes through a transparent material.
考虑场景中的一面镜子。光线以与第一次遇到镜子时相同的角度从镜子表面反射。这通常是这样表述的:反射角等于入射角。
Consider a mirror in the scene. A light ray reflects off a mirror surface at the same angle at which it first encounters the mirror. This is usually stated this way: the angle of reflection equals the angle of incidence.
通常,光线会被真实世界的材料部分折射和部分反射。也就是说,一条光线在穿过世界的一个表面时会分裂成两条光线。
Generally, a light ray is both partially refracted and partially reflected by a real-world material. That is, a light ray splits into two light rays as it passes through a surface in the world.
我在这里几乎没有暗示材料的复杂光学特性。在完整的中心法则现实主义中,假设由真实世界的材料制成的场景必须模拟这些实际的光学特性——从各个方向进入眼睛的光线,而不仅仅是直线。密切遵循这些属性的渲染器称为光线追踪器。
I’ve barely hinted here at the complex optical properties of materials. In full Central Dogma realism, a scene supposedly made of real-world materials must simulate these actual optical properties—rays coming into the eye from all sorts of directions, not just straight ahead. A renderer that closely honors these properties is called a ray tracer.
光线追踪自 1960 年代后期以某种形式出现,但在 1979 年,在传说中的新泽西州贝尔实验室的 Turner Whitted 的一篇论文中,它爆发出完整的计算机图形学之花。他的论文不是关于光线追踪本身,而是关于他所谓的“全局照明”——将现实的完整光学物理考虑在内。光线追踪是他认真对待中心法则的方法——摩尔定律支持他向“基于物理的渲染”迈进。在 1979 年的 Siggraph 会议上,特纳展示了震撼计算机图形界的图片(图 8.3)。事实上,这是他制作的动画中的一帧,由围绕玻璃球运行的华夫格球体制作,带有适当的阴影和扭曲。Turner 获得了 Siggraph 颁发的 2013 年 Coons 奖。8
Ray tracing had been around since the late 1960s in some form, but it burst into full computer graphics flower in 1979 in a paper by Turner Whitted of the fabled Bell Labs in New Jersey. His paper wasn’t about ray tracing per se but about what he called “global illumination”—taking the full optical physics of reality into account. Ray tracing was his method for getting fully serious about the Central Dogma—and Moore’s Law supported him in this huge advance toward “physically based rendering.” At the 1979 Siggraph conference, Turner showed the picture that rocked the computer graphics community (figure 8.3). In fact, this is a frame from an animation he made of the waffled sphere orbiting the glass sphere, with appropriate shadows and warpings. Turner received the 2013 Coons Award from Siggraph.8
带有或不带有光线追踪的中心法则渲染通常被描述为逼真的。光线追踪显然有助于提高照片写实感,但它也鼓励我们所谓的超写实主义——为了纯粹的乐趣而庆祝光学效果,而不是为了某种叙事目的。图 8.4 是“法国 3D 艺术家”Gilles Tran 的一个很好的例子。9
Central Dogma renderings, with or without ray tracing, are often described as photorealistic. Ray tracing obviously contributes to heightened photorealism, but it also encourages what we might call hyper-photorealism—a celebration of optical effects for the sheer joy of it, as opposed to serving some narrative purpose. Figure 8.4 is an excellent example by “French 3D artist” Gilles Tran.9
计算机图形渲染中最重要的技术之一被证明是猴子和人类使用的技术。它被称为随机采样(或分布式光线追踪),但我们必须小心随机的含义。图 8.5 是恒河猴眼睛如何对现实世界进行采样的图片。它来自 1983 年的《科学》杂志。白点是猴子视网膜中光感受器的位置。10
One of the most important techniques ever devised in computer graphics rendering turns out to be one used by monkeys—and human beings. It’s called random sampling (or distributed ray tracing), but we must be careful about what random means. Figure 8.5 is a picture of how a Rhesus monkey eye samples the real world. It’s from a 1983 issue of Science. The white dots are the locations of photoreceptors in a monkey retina.10
这表明大自然母亲没有使用均匀采样的网格来查看现实世界,而是使用嘈杂的网格。就好像像素位置从固定的网格位置略微随机偏移。(这里的重要信息——当我们专注于细节时不要忽视——是大自然母亲使用采样!)
This suggests that Mother Nature doesn’t use an evenly sampled grid for viewing the real world, but rather a noisy one. It’s as if pixel locations are offset slightly and randomly from fixed grid locations. (The important message here—not to be overlooked as we concentrate on the details—is that Mother Nature uses sampling!)
图 8.3
Figure 8.3
特纳惠特,1979 年。
By Turner Whitted, 1979.
如果我们将随机“抖动”的网格理念与二次采样理念相结合,则会得到一个很好的近似值。图 8.6 显示了与单个像素(大点)相关的 4 x 4 子样本阵列,左侧没有随机距离的抖动,右侧有这种抖动。左边的模式在之前的二次抽样讨论中提出过(图 7.10)。将右侧的采样模式与刚刚呈现的猴子视网膜进行比较。用于子样本偏移的数学确保了一种有限的随机性,没有样本聚集或某些子样本未访问的大区域。
A good approximation results if we mix the randomly “jittered” grid idea with the subsampling idea. Figure 8.6 shows the 4 by 4 array of subsamples associated with a single pixel (big dot), without jittering by random distances on the left, and with such jittering on the right. The pattern on the left was presented previously in the subsampling discussion (figure 7.10). Compare the sampling pattern at the right to the monkey retina just presented. The math used for the subsample offsets ensures a restricted kind of randomness with no clumping of the samples, or large areas unvisited by some subsample.
图 8.4
Figure 8.4
Gilles Tran,眼镜,2006。
Gilles Tran, Glasses, 2006.
数学表明,这种“猴子”解决方案用令人反感的噪声代替了令人反感的混叠(例如锯齿)。我们只是看不到低幅度噪声。没有可感知的模式。这种抖动的概念有很多应用,而不仅仅是在计算机图形学中。总的想法被称为蒙特卡洛方法(以摩纳哥著名的赌场命名),它正是用于模拟氢弹爆炸的蒙特卡洛方法,Eniac+(在我们的讲述中,它与第一台计算机与 Baby 并列) ) 作为它的第一个程序执行。11
The math shows that this “monkey” solution replaces objectionable aliasing—such as jaggies—with unobjectionable noise. We just don’t see low amplitude noise. There is no perceivable pattern. This jittering notion has many applications, and not just in computer graphics. The general idea is called the Monte Carlo method (named for the famous casino in Monaco), and it was exactly the Monte Carlo method applied to simulations of H-bomb explosions that Eniac+ (which tied for first computer with Baby, in our telling anyway) executed as its first program.11
考虑一下计算机图形解决方案的大胆:只有一种颜色最终会代表一个窗口屏幕单元内的视觉场景中可能存在的巨大复杂性。要了解这意味着什么,图 8.7 显示了 Pixar's Monsters, Inc. (2001) 中著名的毛茸茸角色 James P. “Sulley” Sullivan。(我们暂时离开严格的摩尔定律时间线来说明这一点——有关皮草的更多信息,请参见注释。)他的照片旁边是一个窗口屏幕的特写细胞对苏利皮毛的看法。(这里完全披露:怪物不是在这个非常高分辨率下计算的!这只是一个演示,如果它是在那个分辨率下计算的,底层毛皮模型会提供什么。)我们寻求的计算机图形解决方案是一种颜色(像素的位于大白点处)以实际使用的分辨率表示该毛茸茸的细胞的所有复杂性 - 左侧显示的 Sulley 的分辨率。这个想法是使用抖动二次采样,因为计算实际的平均颜色太难了。我们不必知道这个方形单元格中每个点所描绘的颜色。我们只需要知道 16 个随机选择的点的颜色。12
Consider the audaciousness of the computer graphics solution: only one color will ultimately represent the immense complexity that might exist in a visual scene inside one window-screen cell. To see what that means, figure 8.7 shows a famous hairy character, James P. “Sulley” Sullivan, from Pixar’s Monsters, Inc. (2001). (We depart momentarily from strict Moore’s Law timeline here to make this important point—see the annotation for more about fur.) Next to his picture is a closeup of one window-screen cell’s view of Sulley’s fur. (And full disclosure here: Monsters was not computed at this very high resolution! This is simply a demonstration of what the underlying fur model offered if it was computed at that resolution.) The computer graphics solution we seek is one color (of the pixel located at the large white dot) to represent all the complexity of that furry cell, at the resolution actually used—the one shown of Sulley at the left. The idea is to use jittered subsampling because computing the actual average color would be too difficult. We don’t have to know the colors as depicted at every point in this square cell. We need know only the colors at the 16 randomly selected points.12
图 8.5
Figure 8.5
经 AAAS 许可。
With permission from AAAS.
图 8.6
Figure 8.6
图 8.7
Figure 8.7
概念和图片由 Thomas Porter 提供。©皮克斯。
Concept and pictures courtesy of Thomas Porter. © Pixar.
让我们在继续之前重新审视那个小平方近似。我说一个像素的最终颜色是每个窗口屏幕单元格中可见颜色的平均值。换句话说,假设将使用盒式滤波器作为扩展器,从离散像素重建颜色连续体。盒式过滤器为每个子样本赋予相等的权重。但是我们从 Kotelnikov 的章节中知道,箱式滤波器是可用于采样理论的最差扩展器。
Let’s revisit that little-square approximation before moving on. I say that the final color of a pixel is an average of the colors visible in each window-screen cell. In other words, assume that a box filter will be used as a spreader to reconstruct the color continuum from the discrete pixels. A box filter gives each subsample equal weight. But we know from the Kotelnikov chapter that the box filter is the worst spreader that can be used in sampling theory.
箱式过滤器远不及理想过滤器或理想的几个众所周知的近似值,如 Catmull-Rom 吊具或 B 样条吊具,它们的中间隆起和圆肩。这些不会对子样本进行同等加权,并且会考虑来自相邻像素周围区域的贡献。尽管如此,计算机图形学几十年来一直使用箱形滤波器作为粗略的近似,主要是因为摩尔定律直到最近才开始提供足够的计算能力来使用更好的采样和重建。随着摩尔定律的不断发展,现在才正在探索对几何定义世界的正确采样的更好近似以及更好的扩展器。提高图像质量始终是目标。13
A box filter is nowhere near the ideal filter or the several well-known approximations to the ideal, like the Catmull-Rom spreader or the B-spline spreader, with their middle humps and rounded shoulders. These would not weight the subsamples equally, and they would consider contributions from areas around neighboring pixels. Nevertheless, computer graphics has used the box filter as a crude approximation for decades, mostly because Moore’s Law has only recently begun to deliver enough computational horsepower to use better sampling and reconstruction. Better approximations to the correct sampling of a geometrically defined world, with better spreaders, are only now being explored as Moore’s Law continues to deliver. Improved image quality is always the goal.13
在上面关于渲染电影的讨论中,我省略了一个非常重要的步骤。在电影和动画章节中,我们讨论了电影帧中的运动模糊如何成为我们大脑如何感知每秒投射的 24 个静止帧的运动的主要线索。我们很早就知道没有运动模糊的动画会失败——经典的失败是雷·哈里豪森在Jason and the Argonauts (1963) 中颤抖的骨骼,也在该章中讨论过。
I omitted one very important step in the discussion above about rendering a movie. In the movies and animation chapter we discussed how motion blur in a movie film frame is a major clue to our brains about how to perceive motion from 24 still frames projected per second. We early understood that animation without motion blur would fail—the classic failure being Ray Harryhausen’s juddering skeletons in Jason and the Argonauts (1963), also discussed in that chapter.
尤其是 Ed Catmull,让我们纽约理工学院的其他人都能看到运动模糊的需求,他在 1970 年代中期开始研究一种在计算机动画中提供它的解决方案。后来在卢卡斯影业,他通过举办一场比赛来强调这个问题。他当然认为他会赢得比赛,因为他多年来一直在研究这个问题。令人惊讶的是,他没有赢,但他的领导力赢了。罗布·库克、洛伦·卡彭特和汤姆·波特——卢卡斯影业和后来皮克斯的天才三重威胁——解决了这个问题。
Ed Catmull, in particular, kept the need for motion blur visible to the rest of us at NYIT, and he began working on a solution to provide it in computer animation back then, in the mid-1970s. Later at Lucasfilm he emphasized the problem by starting a competition. Surely he thought he would win the competition because he’d been working on the problem for years. The surprise was that he didn’t win, but his leadership did. Rob Cook, Loren Carpenter, and Tom Porter—a genius triple threat at Lucasfilm and later Pixar—solved the problem.
Rob 和 Loren 提出了空间抗锯齿的抖动二次采样方法。然后汤姆意识到同样的想法也可能及时奏效。它做了。一种技术解决了这两个问题。这个想法是将虚拟相机快门打开的时间细分为“子帧”。例如,假设要使用空间中的 4 x 4 抖动子样本阵列对每个正方形区域进行二次采样时间分为 16 个子帧,快门打开和快门关闭之间的 16 个时间片(图 8.8)。然后在单独的(时间)子帧中获取每个(空间)子样本,并在子帧占用的时间片内随机抖动。结果在空间和时间上进行平均,以使一种颜色代表运动模糊的单元格。前一个图像的 4 x 4 抖动空间子样本被推入时域,16 个子帧中的每一个,并在其子帧占据的时间片内进一步随机抖动。每条虚线都从“快门打开”子帧开始。对于第七和第十二子帧,详细显示了两个子样本的空间和时间坐标。为清楚起见,仅显示它们的两条虚线延伸到“快门关闭”子帧。
Rob and Loren came up with the jittered subsampling method of antialiasing in space. Then Tom realized that the same idea might work in time as well. It did. One technique solved both problems. The idea is to subdivide the time that a virtual camera’s shutter is open into “subframes.” For example, each square area that is to be subsampled with a 4 by 4 array of jittered subsamples in space is assumed to be subsampled in time into 16 subframes, 16 slabs of time between shutter open and shutter closed (figure 8.8). Then each (spatial) subsample is taken in a separate (temporal) subframe and randomly jittered within the time slice occupied by the subframe. The results are averaged in space and time to make the one color to represent the motion-blurred cell. The 4 by 4 jittered spatial subsamples of the previous image pushed into the time domain, one to each of 16 subframes, and further randomly jittered within the time slice occupied by its subframe. Each dashed line begins in the “shutter open” subframe. The space and time coordinates for two subsamples are shown in detail, for the seventh and twelfth subframes. For clarity, only their two dashed lines are shown extended to the “shutter closed” subframe.
图 8.8
Figure 8.8
概念由皮克斯的 Thomas Porter 提供。
Concept courtesy of Thomas Porter, Pixar.
汤姆·波特 (Tom Porter) 为中心教条的突破性时刻创造了一幅令人惊叹的画面(图 8.9)。他自然而然地将其命名为1984 年,并于当年在 Siggraph 上首映。它不仅展示了抖动二次采样的使用解决运动模糊,也解决其他几个问题,比如软阴影。由库克、卡彭特和波特组成的令人惊叹的团队——我称他们为无产阶级——用一个绝妙的想法解决了许多问题。汤姆的标志性形象在 1984 年登上了Science84杂志的封面,标题为“这张照片是假的”。14
Tom Porter, in a tour de force, created a breathtaking picture (figure 8.9) for that breakthrough moment of the Central Dogma. He titled it 1984, naturally, and premiered it at Siggraph that year. It demonstrated not only the use of jittered subsampling to solve motion blur, but also the solution of several other problems, such as soft shadows. The amazing team of Cook, Carpenter, and Porter—I called them The Proletariat—had mastered a host of problems with one beautiful idea. Tom’s iconic image graced the cover of Science84 magazine in 1984, with the title “This Picture is a Fake.”14
图 8.9
Figure 8.9
托马斯·波特,1984 年,1984 年,以及特写。©皮克斯。
Thomas Porter, 1984, 1984, and a closeup. © Pixar.
这是完全荣耀的中央教条,除了一件事。台球中的反射并不是几何模型中三维物体光学精确光线追踪的结果。几何模型中没有窗户、台球运动员或棕榈树,也没有啤酒标志。相反,我们的美术动画师 John Lasseter 使用 Tom 的绘图程序绘制了它们。汤姆将它们贴图到场景中毫无特色的台球室墙壁上。因此,在从其中一堵墙反弹后撞击池球的光线从上面的纹理贴图中拾取颜色。
It’s the Central Dogma in full glory, save for one thing. The reflections in the pool balls aren’t the result of optically accurate ray tracing of three-dimensional objects in the geometric model. There is no window, pool player, or palm tree in the geometric model, nor are there beer signs. Rather, our artist-animator John Lasseter painted them with Tom’s paint program. And Tom texture-mapped them to featureless poolroom walls that were in the set. Thus a light ray that impacted a pool ball after bouncing off one of those walls picked up color from the texture map on it.
Porter's 1984使用随机采样技术进行光线追踪。这张照片介于令人愉悦的真实感和超真实感之间,那些手绘的台球室纹理贴图与完整的教条背道而驰。这些技术可以很好地帮助我们制作电影,而照片写实不是目标。
Porter’s 1984 was ray-traced using the random sampling technique. The picture rides the line between pleasing photorealism and hyper-photorealism, those hand-painted poolroom texture maps being the one departure from the full Dogma. The techniques would serve us well in making The Movie, where photorealism would not be the goal.
我们一直在 Lucasfilm 追求渲染路径。但与此同时,建模和动画路径必须并行发展。奇怪的是,他们的几个重要贡献者首先是 Unix 系统程序员,然后是计算机图形学家。这正如我之前提到的,当 Tom Duff 还在 NYIT 时,Unix-to-graphics 高速公路已经为我们带来了我们。汤姆在那里证明了自己既是图形专家又是系统专家。例如,他编写了一个用于渲染椭圆形物体的三维程序。他称它为Soid,并在 NYIT 用它制作了几部动画。我使用 Soid 来制作拍手(图 5.17)。
We’ve been pursuing the rendering path at Lucasfilm. But meanwhile, the modeling and animation paths had to develop in parallel. Oddly, several important contributors to them came first as Unix system programmers and then as computer graphicists. The Unix-to-graphics highway had already brought us Tom Duff while he was still at NYIT, as I mentioned previously. Tom had proved himself there to be a graphics guru as well as a system expert. He had programmed, for example, a three-dimensional program for rendering ellipsoid-shaped objects. He called it Soid and had made several animations with it at NYIT. I used Soid to make the clapping hands (figure 5.17).
在 Ed Catmull、David DiFrancesco 和我离开 NYIT 前往 Lucasfilm 之后,Tom 是唯一一个仍然在 NYIT 的人,他弄清楚了他必须做些什么才能被包括在内。由于亚历克斯舒尔的暴虐倾向,埃德非常小心,没有偷猎,但当汤姆宣布他离开纽约理工学院时,他迅速采取行动。Lucasfilm 也将成为 Unix 商店,需要 Unix 专家。但更重要的是,汤姆将在卢卡斯影业创建关键的 3D 建模程序。他成为计算机图形项目的一部分。15
After Ed Catmull, David DiFrancesco, and I departed NYIT for Lucasfilm, Tom was the only person still at NYIT who figured out what he had to do to be included too. Because of Alex Schure’s tyrannical tendencies, Ed was very careful not to poach but quick to move when Tom announced that he’d left NYIT. Lucasfilm would be a Unix shop too and needed Unix experts. But more importantly, Tom would create the crucial three-dimensional modeling program at Lucasfilm. He became part of the Computer Graphics Project.15
另一位 Unix 专家兼计算机图形学专家比尔·里夫斯(Bill Reeves)以一种惊人的平行方式——与多伦多大学罗恩·贝克尔(Ron Baecker)小组的加拿大人汤姆·达夫(Tom Duff)一样——将为卢卡斯影业编写关键的动画程序。Ed 聘请他是因为他在 Unix 方面的专业知识,但 Bill 很快就进入了计算机图形组,在那里他将发挥重要作用。Siggraph 2018 表彰比尔对该领域的全面影响,使他成为新的从业者奖的第一位获得者。
In a surprisingly parallel way, Bill Reeves, another Unix expert cum computer graphics expert—and, like Tom Duff, a Canadian from Ron Baecker’s group at the University of Toronto—would write the crucial animation program for Lucasfilm. Ed hired him for his Unix expertise, but Bill soon found his way into the computer graphics group where he would play a major role. Siggraph 2018 honored Bill for his total impact on the field, by making him the first recipient of its new Practitioner Award.
另一位杰出的程序员(虽然不是加拿大人),Eben Ostby,后来加入了卢卡斯影业,沿着 Unix 到图形的道路前进。在比尔聘请他加入我们的系统组之前,埃本曾在传说中的贝尔实验室任职。Eben 很快就证明了自己也擅长建模、动画和渲染软件。
And yet another outstanding programmer (though not a Canadian), Eben Ostby, later joined Lucasfilm and advanced along the Unix-to-graphics pathway. Eben had served a stint at the fabled Bell Labs before Bill hired him into our systems group. And Eben soon proved himself adept too at modeling, animation, and rendering software.
比尔和埃本将成为皮克斯的 40 名创始员工之一。奇怪的是,汤姆达夫不会。他在皮克斯开始之前就离开了卢卡斯影业,只是在成立后重新加入我们,并在 . . . 除了贝尔实验室,还有其他地方。
Bill and Eben would be among the 40 founding employees of Pixar. Oddly, Tom Duff would not. He exited Lucasfilm before Pixar began, only to rejoin us after the founding, having spent the intervening years at . . . where else, but Bell Labs.
有些东西不能方便地用几何建模。比尔·里夫斯对数字光的主要贡献之一是他称之为粒子系统的东西。考虑云、火和水。或者烟花、星星和烟雾。它们是模糊的物体。1982 年,在卢卡斯影业,比尔提出了使用许多微小粒子的集合来模拟模糊物体的概念。把每个粒子想象成一个小但非零大小的点。粒子系统随着时间的变化,系统中的粒子诞生到系统中,在系统内移动或变化,然后从系统中消亡。每个粒子都有一个生命周期,在此期间它遵循一个轨迹。它可能具有某些特征,例如颜色、透明度或大小,这些特征可能会在其生命周期内发生变化。粒子根据需要随机移动或变化模糊对象建模。在每个时刻,活粒子都被渲染成图像。16
Some things just don’t lend themselves conveniently to modeling with geometry. One of Bill Reeves’s major contributions to Digital Light was something he called particle systems. Consider clouds, fire, and water. Or fireworks, stars, and smoke. They are fuzzy objects. In 1982 at Lucasfilm, Bill came up with the notion of modeling a fuzzy object using a collection of many tiny particles. Think of each particle as a dot with small but nonzero size. A particle system changes in time, with particles in the system being born into the system, moving or changing within it, and then dying out of the system. Each particle is programmed with a lifetime during which it follows a trajectory. It might have some feature such as color, transparency, or size that could change during its lifetime. A particle moves or changes randomly according to the needs of the fuzzy object modeled. At each time instant, the living particles are rendered into an image.16
比尔对他的新技术的第一个应用是火。每个粒子都有一种颜色,通常是红色,但有些是随机的绿色。每个人在平坦的表面上都有一个随机位置,并从那里以随机方向向上射击。一个粒子的轨迹是由一个想象的引力场决定的,所以它会弧形回到地面。每个都有一个随机的初始大小和透明度。每个粒子都是运动模糊的。也就是说,在每一帧中,都会计算粒子沿其轨迹的开始和停止位置,通常是一小段距离。粒子将在渲染时沿着该路径涂抹。
One of Bill’s first applications of his new technique was fire. Each particle had a color, usually red, but some were randomly green. Each had a randomized location on a flat surface and shot up from there in a randomized direction. A particle’s trajectory was determined by an imagined gravitational field, so it arced back to the ground. Each had a randomized initial size and transparency. And each particle was motion blurred. That is, in each frame the start and stop locations of a particle along its trajectory were calculated, typically a small distance. The particle would be smeared at rendering time along that path.
这个粒子系统模型在每一步的渲染都是通过在单个帧中渲染每个粒子的开始和停止位置之间的抗锯齿直线来完成的。回想一下,Malcolm Blanchard 在 1976 年左右在 NYIT 引入了抗锯齿(无锯齿)线段,而 Dick Shoup 在此之前于 1973 年在 Xerox PARC 渲染了它们。因此,边缘柔和、通常为红色的短线段将实现粒子的拖尾沿着它的运动路径。线段的颜色只是在帧缓冲区中添加在一起。由于少数随机分配的绿色,这些添加导致火的中心在从地表爆炸时发出炽热的橙黄色光芒。然后随着粒子的消亡,它们会趋向于大部分是红色的,并且似乎正在冷却。
The rendering of this particle system model at each step was accomplished simply by rendering an antialiased straight line between the start and stop positions of each particle in a single frame. Recall that Malcolm Blanchard had introduced antialiased (no jaggies) line segments at NYIT in about 1976 and Dick Shoup had rendered them before that at Xerox PARC in 1973. So a soft-edged, typically red short line segment would implement the smear of a particle along its path of motion. The colors of the line segments were just added together in a framebuffer. Because of the few randomly assigned greens, these additions resulted in a hot yellow-orange glow at the heart of a fire as it exploded from the surface. Then as the particles died off, they would tend toward mostly red and appear to be cooling.
汤姆·达夫、比尔·里维斯、罗伯·库克、罗伦·卡彭特、汤姆·波特。我们在卢卡斯影业组建了一支由计算机图形明星组成的世界级团队。Jim Blinn 从 JPL 加入我们,但就像他之前在 NYIT 所做的一样,Jim 在他自己独特的编程世界之外感到不舒服,于是回到了 JPL。我们将来自 JPL 的 Jim 团队的 Pat Cole(另一位具有开创性的早期女性)加入了该小组。17
Tom Duff, Bill Reeves, Rob Cook, Loren Carpenter, Tom Porter. We were assembling a world-class team of computer graphics stars at Lucasfilm. And Jim Blinn joined us from JPL, but just as he had earlier at NYIT, Jim became uncomfortable outside his own peculiar programming world and returned to JPL. And we added Pat Cole, from Jim’s team at JPL, another pioneering early woman, to the group.17
我们假设乔治卢卡斯会在任何一天敲我们的门,要求为他的一部电影提供计算机图形内容。但他从来没有来过。终于,我恍然大悟。乔治卢卡斯不知道他有什么!他犯了一个典型的错误,认为我们只是一群做硬件和软件的“技术人员”,而他和他的团队是制作电影内容的“创意人”。我以为我们已经明确表示我们也是内容创建者,但信息并没有被采纳。
We assumed that George Lucas would knock on our door any day with a request for computer graphics content for one of his movies. But he never came. Finally, it dawned on me. George Lucas didn’t know what he had! He had made the classic mistake of assuming we were only a bunch of “technoids” doing hardware and software, while he and his team were the “creatives” making movie content. I thought we’d made it clear that we were content creators as well, but the message hadn’t taken.
派拉蒙影业公司让卢卡斯了解我们的能力。为了我们的下一次幸运休息,派拉蒙与卢卡斯影业的特效部门 Industrial Light & Magic (ILM) 接洽,为《星际迷航 II:可汗之怒》(1982)工作。派拉蒙的人想要星际迷航 II中的一些计算机图形,但工业光魔没有计算机图形学。ILM 告诉他们,“隔壁”的新人做到了。就在那时他们叫我进来。
It took Paramount Pictures to enlighten Lucas about our capabilities. For our next lucky break, Paramount approached Industrial Light & Magic (ILM), Lucasfilm’s special-effects division, for work on Star Trek II: The Wrath of Khan (1982). The Paramount people wanted some computer graphics in Star Trek II, but ILM didn’t do computer graphics. The new guys “next door” did, ILM told them. That’s when they called me in.
我听过派拉蒙的人描述他们在电影中想要什么。它将解释一种称为“创世纪效应”的关键叙事手段,它可以瞬间将死亡转化为生命。他们提出的想法是漂浮在水族馆中的一块岩石,不知何故,会被绿色苔藓覆盖。我不解地看着他们说:“你知道我们现在可以用计算机图形做什么,不能做什么吗?” 他们承认他们没有。所以我建议我离开一天,然后带着一个可以满足他们叙事需求的镜头建议返回,并且成为我们在 1980 年代初期实际上可以经济高效地计算的东西。他们同意了。但后来我想起了一个关键问题。“我们还不能做电影分辨率。我们只能做视频分辨率。” “这不是问题!这是应该的成为柯克上将的视频演示。”
I listened to the Paramount people describe what they wanted in the film. It was to be something that explained a key narrative device called “the Genesis effect,” which converted death to life instantaneously. The idea they pitched was a rock floating in an aquarium that would, somehow, become covered with green moss. I looked at them puzzled and said, “Do you have any idea what we can and can’t do with computer graphics at this time?” They admitted that they didn’t. So I suggested that I depart for a day and return with a shot proposal that would satisfy their narrative needs and be something that we could actually compute cost-effectively in the early 1980s. They agreed. But then I remembered a crucial problem. “We can’t do movie resolution yet. We can only do video resolution.” “That’s not a problem! This is supposed to be a video demo to Admiral Kirk.”
我走出那个房间,离地面大约十英尺。就是这样!我们刚刚获得了重大突破!终于有机会上大银幕了!我们刚刚被要求自己制作一个完整的镜头!在一部注定要成功的主要电影中。
I walked out of that room about ten feet off the ground. This was it! We had just been given the big break! Finally, a chance at the big screen! We had just been asked to create a complete shot—on our own!—in a major motion picture that was surely destined to be successful.
我整晚都在设计镜头。它将使用——它必须使用——我们组装的计算机图形神童团队的所有才能,它必须解释创世纪效应。我画了一个故事板,讲述了后来被称为 Genesis Demo 的故事。它仅由六块原始面板组成,这些面板是在我当时广泛使用的绿色工程垫纸上绘制的。就在我将它呈现给 ILM 和派拉蒙之前,我认为使用标准的 ILM 故事板格式来修饰故事板是一个好主意。图 8.10 显示了我为提议的镜头绘制的最终版本中的两个清理后的故事板面板。
I was up all night designing the shot. It would use—it had to use—all the talents of our assembled team of computer graphics wunderkinder and it had to explain the Genesis effect. I sketched a storyboard of what became known as the Genesis Demo. It consisted of just six crude panels drawn on the green engineering pad papers that I used extensively at the time. Just before I presented it to ILM and Paramount, I thought it would be a good idea to dress up the storyboards a bit by using standard ILM storyboard format. Figure 8.10 shows two cleaned-up storyboard panels from the final version I drew for the proposed shot.
吉姆·布林 (Jim Blinn) 在喷气推进实验室 (JPL) 的航海者号宇宙飞船行星飞行是主要灵感来源。我故事板中的(看不见的)宇宙飞船环绕着一颗满是陨石坑的死去的类似月球的行星。Loren Carpenter 将设计星域和航天器轨迹。汤姆达夫会用凹凸贴图制作陨石坑。帕特科尔将模拟从航天器向死亡星球发射的射弹。弹丸的影响引发了一场大火。Bill Reeves 将使用他的新粒子系统来实现火灾。一堵火墙戏剧性地吞没了这颗行星并融化了它的表面。从熔融表面出现分形山脉,洛伦将使用前面描述的分形技术制作。大海会形成,山会变凉变绿。随着航天器的加速,这颗死去的行星将被重新揭示为活的和地球一样的。Tom Porter 将通过他的绘画程序和纹理映射来监督最后一部分。创世效应不会如所希望的那样瞬间发生,但只需一分钟就能解释清楚。18
Jim Blinn’s Voyager spacecraft planetary flybys at JPL were the prime inspiration. The (unseen) spacecraft in my storyboard circled a dead Moon-like planet covered with craters. Loren Carpenter would design the star field and spacecraft trajectory. Tom Duff would make the craters with bump maps. Pat Cole would model the projectile fired from the spacecraft toward the dead planet. The impact of the projectile starts a conflagration. Bill Reeves would implement the fires, using his new particle systems. A wall of fire dramatically engulfs the planet and melts its surface. From the molten surface arise fractal mountains, which Loren would make using the fractal technique described earlier. Seas would form and the mountains would cool and turn green. As the spacecraft speeds away, the dead planet would be newly revealed as living and Earth-like. Tom Porter would oversee this last part with his paint program and texture mapping. The Genesis Effect wouldn’t be instantaneous, as desired, but it would take only a minute to explain.18
图 8.10
Figure 8.10
图片由皮克斯动画工作室提供。
Images courtesy of Pixar Animation Studios.
尽管故事板很粗糙,我们还是得到了这份工作。我把团队召集到一个房间里,宣布:“我们刚刚取得了重大突破”,并告诉他们我们将做一项一流的工作——满足派拉蒙的叙事需求并取悦《星际迷航》的观众。然后我的主要信息是:“但这个镜头的真正意义是,给乔治卢卡斯一个 60 秒的广告,这样他就会知道他得到了什么。”
Despite the crude storyboards, we got the job. Gathering the team into a room, I announced, “We just got our big break,” and told them that we were going to do a first-rate job—satisfying Paramount’s narrative needs and pleasing the Star Trek audience. Then my main message: “But what this shot really is, is a 60-second commercial to George Lucas so that he’ll know what he’s got.”
我知道乔治的一个秘密,并打算利用它:当他看电影时,他会时刻注意摄像机和摄影师的决定。他不会被这种情绪所吸引。如果你仔细想想,一个不能让你沉浸在他或她的电影情感中的导演是失败的。尽管如此,乔治卢卡斯可以避免情绪并跟踪相机,或者两者兼而有之。我向小组解释了这一点。“所以我们要在这个镜头中加入一个真正的相机不可能做到的镜头移动。不会是无偿的。它将具有完美的叙事意义。但这会让乔治大吃一惊。”
I knew a secret about George and planned to exploit it: When he watches a movie, he’s constantly aware of the camera and the cameraman’s decisions. He doesn’t get sucked in by the emotion. If you think about it, a director who can’t pull you into the emotion of his or her film has failed. Nevertheless, George Lucas could avoid the emotion and track the camera, or perhaps do both. I explained this to the group. “So we’re going to put a camera move in this shot that no real camera could possibly make. It won’t be gratuitous. It’ll make perfect narrative sense. But it will blow George’s socks off.”
这就是我们继续做的事情。Loren Carpenter 通过数十只鸭子设计了一个复杂的多维样条曲线来描述相机的移动。这是形状章节中介绍的样条线概念的另一种用法。在这里,样条曲线在四维时空(空间三,时间一)中插值了相机的位置和方向。摄像机注视着正在逼近的死亡星球,旋转以跟踪星球表面的动作,停留在移动的火墙前方,凝视下方快速生长的山脉,然后回头看现在还活着的绿色星球,随着我们的宇宙飞船加速离开,完成它的行星飞行。图 8.11 是几个 Genesis Demo 元素的组合。
And that’s what we proceeded to do. Loren Carpenter masterminded a complex multidimensional spline through dozens of ducks to describe the camera’s move. This was another use of the spline concept introduced in the Shapes chapter. Here the spline interpolated the camera position and orientation in four-dimensional spacetime (three of space, one of time). The camera looks at the approaching dead planet, rotates to track the action on the planet surface, staying just ahead of a traveling wall of fire, gazes down at the growing mountains speeding by below, and then looks back at the now living green planet, with an atmosphere, as our spacecraft speeds away, completing its planetary flyby. Figure 8.11 is a composite of several Genesis Demo elements.
图 8.11
Figure 8.11
图片由皮克斯动画工作室提供。
Image courtesy of Pixar Animation Studios.
在《星际迷航 II:可汗之怒》 (1982 年)首映后的第二天,乔治·卢卡斯在我看来是一个相当害羞的人,一只脚走进了我的办公室。“很棒的相机动作!” 他说。然后他就走了。他明白了!在他的下一部电影《绝地归来》(1983 年)中,他加入了我们小组的汤姆·达夫和比尔·里夫斯创作的短片。而且,重要的是,他一定告诉了他的好朋友史蒂文·斯皮尔伯格关于我们的事。斯皮尔伯格将卢卡斯影业的计算机图形学纳入他的《年轻的夏洛克·福尔摩斯》(1985 年)。有一种新方法可以制作引人入胜的电影内容的消息开始传播开来。终结者2:审判日(1991) 计算机生成的光栅图像已进入好莱坞技术领域。我们朝着我们的目标迈出了重要的一步——成为皮克斯团队的第一个团队努力。
The day after the premiere of Star Trek II: The Wrath of Khan (1982), George Lucas, a rather shy man it seemed to me, stepped one foot into my office. “Great camera move!” he said. Then he was gone. He’d got it! In his next movie, Return of the Jedi (1983), he included a short sequence created by Tom Duff and Bill Reeves of our group. And, importantly, he must have told his good friend Steven Spielberg about us. Spielberg would include Lucasfilm computer graphics in his Young Sherlock Holmes (1985). And the word began to spread that there was a new way to make captivating film content. By Terminator 2: Judgment Day (1991) computer-generated raster imagery had entered the Hollywood technological firmament. And we’d made a major step toward our goal—the first team effort by the group who would become Pixar.
但 1982 年的 Genesis Demo 并不是电影。电影仍然需要千禧年的大数字融合,但工作正在进行中。星际迷航 II是该团队的早期锻炼,最终成为皮克斯并创建了玩具总动员(1995)。我们为 Genesis Demo 感到自豪,但这只是特效。在那个领域,我们是远非孤单。Tron是 1982 年跟随Trek仅一个月的狂热宠儿,最能说明这一点。Tron为演变成 Blue Sky 并制作Ice Age (2002)的团队提供了相同的功能。
But the 1982 Genesis Demo wasn’t The Movie. The Movie still needed the millennium’s Great Digital Convergence, but work was underway. Star Trek II was an early workout for the group that eventually became Pixar and created Toy Story (1995). We were proud of the Genesis Demo, but it was just special effects. In that domain, we were far from alone. Tron, a cult favorite that followed Trek by only a month in 1982, best illustrates this. Tron served the same function for the group that evolved into Blue Sky and made Ice Age (2002).
从 1980 年到 1985 年,摩尔定律 1000X步见证了许多公司的诞生,这些公司准备好提供数字特效以供出租。迪士尼使用其中四个来制作Tron:加利福尼亚的 Robert Abel and Associates 和 Triple-I(信息国际公司),以及纽约的 Digital Effects 和 MAGI(数学应用集团公司)。其中两个在这里持续受到关注:好莱坞附近的 Triple-I 是小约翰·惠特尼和加里·德莫斯的故乡,卢卡斯影业作为电影竞赛中的重要竞争对手,我们非常关注。正如我刚才提到的,正是 MAGI,后来出现了 Blue Sky 集团。注释列出了这个形成时代的许多其他公司。
The Moore’s Law 1,000X step from 1980 to 1985 saw the birth of many companies ready to supply digital special effects for hire. Disney used four of them to produce Tron: Robert Abel and Associates and Triple-I (Information International Inc.) in California, and Digital Effects and MAGI (Mathematical Applications Group Inc.) in New York. Two of these are of continued interest here: Triple-I, near Hollywood, was home to John Whitney Jr. and Gary Demos, and of great concern to us at Lucasfilm as a serious competitor in the race to The Movie. And it was MAGI from which, as I just mentioned, the Blue Sky group would later emerge. The annotation lists many other firms from this formative era.
导演 Steven Lisberger 在前Xerox PARC 的 Alan Kay 的建议下,将Tron的概念带到了迪士尼——他将观点等同于 80 点的智商。Lisberger 出身于经典的角色动画背景,但在 Kay 的坚持下,他将电脑动画推广到了迪士尼。但不是电脑角色动画。Tron中的所有角色都是由红色或蓝色霓虹管组成的真人演员。这使它们看起来像发光的卡通人物,但这实际上是模拟后期制作过程的结果。这个项目对迪士尼来说是不寻常的,这家公司通常不会向外寻求帮助。值得称赞的是,沃尔特·迪斯尼的女婿罗恩·米勒 (Ron Miller) 是迪斯尼的高管,他给了Tron继续。19
The director Steven Lisberger brought the concept of Tron to Disney, on the advice of Alan Kay, formerly of Xerox PARC—he who equated point of view with 80 points of IQ. Lisberger came from a classic character animation background, but with Kay’s insistence he promoted computer animation to Disney. But not computer character animation. All the characters in Tron would be live human actors made up with what appeared to be red or blue neon piping. This made them look like glowing cartoon characters, but it was really the result of an analog post-production process. The project was unusual for Disney, a company that didn’t normally go outside itself for help. To his credit Ron Miller, Walt Disney’s son-in-law, was the Disney executive who gave Tron the go-ahead.19
其计算机效果动画的数字制作是后勤方面的噩梦。它需要整合来自东海岸和西海岸的四家公司的工作,具有四种不同的外观和四种不同的硬件和软件基础。他们一起设法制作了 15 分钟左右的计算机图形,并被纳入最终电影。这种关于大量屏幕时间的说法很难评估,因为它肯定包括由 Digital Effects 贡献的 Bit 的所有外观。Bit 是一个很小的多面体“字符”,只能以蓝色和黄色两种交替颜色存在,并且占用的屏幕空间很小。20
The digital production of its computer effects animation was a logistical nightmare. It required integrating work from four companies, on the East and West Coasts, with four different looks and four different hardware and software bases. Together they managed to produce a reported 15 minutes or so of computer graphics that was incorporated into the final movie. This claim of substantial screen time is difficult to assess because it surely included all the appearances of the Bit, contributed by Digital Effects. The Bit was a tiny polyhedral “character” that could exist in only two alternating colors, blue and yellow, and occupied little screen space.20
最令人难忘的Tron计算机图形是 MAGI 在纽约威彻斯特县制作的“光周期”序列(图 8.12)。整个场景长约三分钟,包括至少约一分钟的插播真人镜头。重要的是,光循环序列给当时在迪士尼工作的年轻动画师约翰·拉塞特留下了深刻印象:“这绝对让我大吃一惊!脑海中的一扇小门打开了。我看着它说,‘就是这个!这就是未来!’”后来,他加入皮克斯后,要说,“没有创战,就没有玩具总动员。” 21
The most memorable Tron computer graphics was the “light cycle” sequence produced by MAGI in Westchester County, New York (figure 8.12). The whole scene is about three minutes long, including about one minute at least of intercut live-action footage. Importantly, the light-cycle sequence impressed a young animator, John Lasseter, working at Disney then: “It absolutely blew me away! A little door in my mind opened up. I looked at it and said, ‘This is it! This is the future!’” Later, after he had joined Pixar, he was to say, “Without Tron, there would be no Toy Story.”21
图 8.12
Figure 8.12
Mathematical Applications Group Inc. 成立于 1966 年,使用蒙特卡罗射线追踪评估核辐射。该公司很快意识到他们可以用他们的技术模拟光线,而不仅仅是核辐射。1972 年,他们创建了一个名为 MAGI/SynthaVision 的计算机图形部门,以利用这一概念并制作早期的电视广告。因此,MAGI 一直使用光线追踪作为其渲染技术,这使其与其他公司区别开来。从上图中的光周期来看,到 1981 年,当迪斯尼聘请他们制作Tron效果时,他们还没有利用光线追踪的超真实感。MAGI 聘请 Chris Wedge 作为Tron (1982) 序列的动画师,这一决定对数字电影的未来非常重要。22
Mathematical Applications Group Inc. was founded in 1966 to evaluate nuclear radiation using Monte Carlo ray tracing. The company soon realized that they could simulate light rays with their technique, not just nuclear radiation. In 1972 they created a computer graphics division called MAGI/SynthaVision to exploit this notion and make early television commercials. So MAGI had always used ray-tracing as its rendering technology, which set it apart from other firms. Judging by the light cycles in the figure above, they hadn’t yet exploited ray tracing’s hyper-photorealism by 1981 when Disney hired them for Tron effects. MAGI hired Chris Wedge as an animator for the Tron (1982) sequences, a decision that was very important for the future of digital movies.22
1983 年,迪斯尼与 MAGI 签订合同,根据莫里斯·森达克 (Maurice Sendak) 广受欢迎的儿童读物《荒野之地》( Where the Wild Things Are ) 制作一部测试电影,历史潮流再次交织在一起。Wild Things 测试的概念是角色 Max 和他的狗将按照传统方式使用二维 cel 动画创建,但在三维计算机图形背景上。MAGI 的 Chris Wedge 和其他人制作了 3D 线框背景。迪斯尼动画师约翰·拉塞特和格伦·基恩为这些背景手工制作了动画。因此,两位对数字电影的未来如此重要的动画师克里斯·韦奇和约翰·拉塞特首次相互接触,并与数字好莱坞接触。23
The historical flows braided again in 1983 when Disney contracted with MAGI to make a test film based on Maurice Sendak’s popular children’s book, Where the Wild Things Are. The notion for the Wild Things test was that the characters Max and his dog would be created traditionally with two-dimensional cel animation, but over a three-dimensional computer graphics background. Chris Wedge and others at MAGI produced three-dimensional wireframe backgrounds. Disney animators John Lasseter and Glen Keane hand animated to those backgrounds. Thus Chris Wedge and John Lasseter, two animators so important to the future of digital movies, made their first contact with each other and with digital Hollywood.23
正如本章的流程图所示,有三个地点直接通向了在千禧年制作第一部数字电影的三个工作室。MAGI 于 1972 年通过其 SynthaVision 部门进入该行业。NYIT 于 1974 年开始了它的计算机动画实验室,实验室。第三个地点是加利福尼亚的太平洋数据图像 (PDI)。
As the flow chart for this chapter shows, there were three loci that that led directly to the three studios who produced the first digital movies at the millennium. MAGI entered the business in 1972 with its SynthaVision division. NYIT started its computer animation laboratory, the Lab, in 1974. The third locus was Pacific Data Images (PDI) in California.
Carl Rosendahl 从他父亲那里借了 25,000 美元,并于 1980 年创办了 PDI,将计算机图形商业化。1980 年,我和 Ed Catmull、David DiFrancesco 刚刚在卢卡斯影业的玛西娅·卢卡斯的办公室里开了一家店。我们只是一个研究小组,根本不是自给自足的。我们甚至没有想到我们可以支持自己做计算机图形。
Carl Rosendahl borrowed $25,000 from his father and started PDI in 1980 to commercialize computer graphics. For perspective on the risk he took, Ed Catmull, David DiFrancesco, and I had just set up shop at Lucasfilm in Marcia Lucas’s office in 1980. We were a research group and not self-supporting at all. It hadn’t even occurred to us that we could support ourselves doing computer graphics.
1982 年 3 月,Richard Chuang 和 Glenn Entis 加入 Rosendahl,成为动画公司 PDI 的三位联合创始人。后两人编写了 PDI 的动画软件,他们三人在 1994 年获得了 PDI 动画系统技术学院奖。
Rosendahl was joined by Richard Chuang in March 1982 and Glenn Entis a month later to become the three cofounders of PDI, the animation company. The latter two wrote PDI’s animation software, and the three of them received a technical Academy Award for the PDI animation system in 1994.
Chuang 从 Ed Catmull 和我们其他人在 Lucasfilm 教授的课程视频中学习了计算机图形学。Entis 作为布鲁克林的一名计算机科学专业学生和曼哈顿的一名程序员,曾在附近的纽约理工学院学习计算机图形学——在 1970 年代后期,纽约理工学院的 Ed 和我们其他人教授的课程中。当我聘请汤姆加入卢卡斯影业时,Entis 接替了汤姆波特的 Ampex 的 AVA 项目。24
Chuang learned computer graphics from videos of a class taught by Ed Catmull and others of us from Lucasfilm. Entis, as a computer science student in Brooklyn and a programmer in Manhattan, had learned computer graphics at nearby NYIT—in a class Ed and others of us from NYIT taught in the late 1970s. And Entis took over from Tom Porter on Ampex’s AVA project when I hired Tom into Lucasfilm.24
我们比其他计算机图形公司更密切地跟踪 PDI 的商业进展,因为正如同事 Loren Carpenter 所说,它“做正确的图形”。对于初学者来说,它们是一个 Unix 公司,用 C 语言编写。但在我们看来,PDI 还没有成为 The Movie 的竞争对手。MAGI 也没有——还没有。这份名单上只有一家公司,Digital Productions。
We tracked PDI’s commercial progress more closely than other computer graphics houses because it was “doing graphics right” as colleague Loren Carpenter put it. For starters, they were a Unix house and wrote in the C language. But PDI didn’t—yet—appear to us to be a competitor for The Movie. Nor did MAGI—yet. There was only one company on that list, Digital Productions.
小约翰·惠特尼 (John Whitney Jr.) 和加里·德莫斯 (Gary Demos) 在 Triple-I 工作时,迪斯尼与它签订了Tron特效合同,这是四家此类公司之一。但两人很快就该项目所需的计算能力数量与管理层产生了分歧。他们于 1981 年离开 Triple-I,并于 1982 年在 Ivan Sutherland 的投资下开始了 Digital Productions。25
John Whitney Jr. and Gary Demos were at Triple-I when Disney contracted with it for Tron special effects, one of four such companies. But the pair soon disagreed with management over the amount of computing power needed for the project. They departed Triple-I in 1981 and started Digital Productions in 1982—with an investment by Ivan Sutherland.25
早在 1974 年,Sutherland 就曾试图与 Glen Fleck 一起创办 The Picture/Design Group 并进入好莱坞市场,但没有成功。Ed Catmull 一直在等待公司成立,直到他年轻的家人的要求迫使他在其他地方寻找工作。另一个年轻人 Gary Demos 也打算成为 Sutherland 公司的一员,可能还有来自才华横溢的惠特尼家族的 John Whitney Jr.。约翰(Jr.) 和 Gary 似乎是我们熟悉电影的计算机图形领域的固定装置。
Back in 1974 Sutherland had unsuccessfully sought to start The Picture/Design Group with Glen Fleck and enter the Hollywood market. Ed Catmull had waited for the company to form until demands of his young family forced him to seek employment elsewhere. Another young man, Gary Demos, also intended to be part of Sutherland’s company, and possibly also John Whitney Jr. from the talented Whitney family. John (Jr.) and Gary seemed to be fixtures in our part of the computer graphics universe that was aware of the movies.
埃德和我仔细追踪了他们。他们的不寻常之处在于他们使用非常强大的计算机进行计算并以非常高的分辨率拍摄。他们位于好莱坞附近,并与电影业的推动者和震动者联系在一起。1981 年,在弗朗西斯·科波拉 (Francis Coppola) 为《心之一》( One from the Heart ) (1982 年)的舞台上的一次午餐会上,我坐在一张大桌子对面,坐在约翰和女演员泰瑞·加尔的对面。当我意识到他们一起长大并且显然是老朋友时,我的心沉了下来。从外面来,我们还有机会吗?约翰和加里会在电影中击败我们吗?
Ed and I tracked them carefully. They were unusual in that they computed with very powerful computers and filmed at very high resolutions. They were located near Hollywood and tied into the movers and shakers of the movie business. In 1981 at a luncheon in Los Angeles on Francis Coppola’s stage set for One from the Heart (1982), I sat across a large table from John and the actress Teri Garr. My heart sank as I realized they’d grown up together and were clearly old friends. Coming from outside, did we even have a chance? Would John and Gary beat us to The Movie?
我们认为他们可能有充分的理由。他们已经参与了几部故事片。在 Triple-I,约翰为米高梅的《西部世界》(1973 年)贡献了数字图像处理场景,获得了财务上的成功。然后,他和加里在《未来世界》(1976 年)中用三维阴影图形渲染了演员彼得·方达的头部,这是一部不太成功的西部世界续集。我们对未来世界特别熟悉,因为它包括另外两个 3D 阴影光栅图形——Ed Catmull 的手和 Fred Parke 的脸(图 7.13),这是他们在 1970 年代初在犹他大学创建的灰度动画。26
We thought they might, with good reason. They had already been involved in several feature films. At Triple-I John contributed digital image processing scenes to MGM’s Westworld (1973), a financial success. Then he and Gary rendered the actor Peter Fonda’s head in three-dimensional shaded graphics in Futureworld (1976), a not so successful sequel to Westworld. We were especially familiar with Futureworld because it included two other pieces of three-dimensional shaded raster graphics—Ed Catmull’s hand and Fred Parke’s face (figure 7.13), grayscale animations they had created at the University of Utah in the early 1970s.26
约翰和加里随后在 Triple-I 制作了Looker (1981),这部电影以女演员苏珊戴伊全身扫描的三维渲染为特色。一个非凡的巧合是,Looker的故事涉及整形外科医生拉里·罗伯茨博士,他对追求身体完美的超级名模进行了微小的改造。编写剧本的迈克尔·克莱顿(Michael Crichton)可能没有意识到另一位拉里·罗伯茨(Larry Roberts)博士(他是 1963 年在麻省理工学院的三巨头)在完善透视(计算机)模型显示方面的开创性作用。但Looker只包含一点计算机图形。这也是财务上的失败。27
John and Gary then worked on Looker (1981) at Triple-I, a film that featured a three-dimensional rendering of a full body scan of the actress Susan Dey. In a remarkable coincidence, the Looker story concerns a plastic surgeon, Dr. Larry Roberts, who performs minor alterations on supermodels seeking bodily perfection. Michael Crichton, who wrote the screenplay, was probably unaware of the seminal role of another Dr. Larry Roberts—he of the Triumvirate at MIT in 1963—in perfecting the display of (computer) models in perspective. But Looker contained only a little computer graphics. And it too was a financial failure.27
但是,当 Ed 和我认为比赛结束的那一天终于到来了。计算机图形学的小世界里闪过消息:约翰和加里购买了一台克雷超级计算机!我们的 Cray 推销员 Bence Gerber 几年来一直试图在卢卡斯影业向我们出售价值数百万美元的 Cray,但我们无法理解这样的购买,也无法证明其成本合理。Cray 超级计算机与我们打算做的不太匹配。或者我们是这么想的,直到我们听说购买了 Digital Productions。埃德和我拿出众所周知的信封,再次进行计算。我们是不是哪里出错了?答案再次是否定的。购买只是没有经济意义。
But the day finally came when Ed and I thought the game was up. News flashed through the small world of computer graphics: John and Gary had purchased a Cray supercomputer! Our Cray salesman, Bence Gerber, had been trying for a couple of years to sell us a multimillion-dollar Cray at Lucasfilm, but we couldn’t make sense of such a purchase nor justify its cost. The Cray supercomputer just wasn’t a good match to what we intended to do. Or so we thought, until we heard about the Digital Productions purchase. Ed and I whipped out the proverbial envelope and made our calculations again. Had we gone wrong somewhere? The answer, again, was no. The purchase just didn’t make economic sense.
PDI 的联合创始人 Richard Chuang 几乎以同样的方式记住了当时的情况:
Richard Chuang, the cofounder of PDI, remembered the situation almost the same way:
我永远不会忘记 Digital Productions 宣布他们获得 Cray 的那一天。起初它是令人震惊的。哇,这个行业就这样了——他们买得起克雷——没有人能与之竞争。但那天晚些时候——我永远不会忘记——我、卡尔和格伦坐在地板上,讨论我们永远买不起克雷参加比赛,但一个小时后,我做了数学计算,回来说,等一下——这些人永远不会持久,他们负担不起——如果你有任何商业意识,你就会知道成本/价值主张——你可以计算出来。Cray 的投资回报并不能证明我们从事的业务是合理的。28
I will never forget the day Digital Productions announced they had got a Cray. Initially it was shocking. Wow, there goes the industry—they can afford a Cray—no one will be able to compete. But later that day—I will never forget—me, Carl, and Glenn sat on the floor, discussing that we could never afford a Cray to compete, but an hour later I did the maths and I came back and said, Wait a minute—these guys will never last, they can’t afford it—if you have any business sense you know the cost/value proposition—and you can calculate that. The return on investment on a Cray doesn’t justify the business we were in.28
约翰和加里进行了一场巨大的赌注——押注好莱坞的工作室会使用 Cray,如果他们可以使用的话,从而将成本分摊给几个有钱的用户。但那并没有发生。Cray 是一个错误,它注定了当时唯一真正让我们感到害怕的竞争对手。Digital Productions 在The Last Starfighter (1984) 中做出了崇高的努力,使用了 Cray,但他们 12 分钟的 3D 贡献远不能成为一部完整的电影。Digital Productions 于 1986 年因所有实际目的而停止存在,也就是皮克斯成立的那一年,被另一家制作公司以敌意收购的方式收购。29
John and Gary had taken a tremendous gamble—betting that studios in Hollywood would use the Cray, if readily available to them, thus spreading the cost across several moneyed users. But that didn’t happen. The Cray was a mistake, and it doomed the only competitors who truly frightened us at the time. Digital Productions made a noble effort with The Last Starfighter (1984), using the Cray, but their 12-minute three-dimensional contribution was far short of a complete movie. Digital Productions ceased existence for all practical purposes in 1986, the year Pixar began, purchased by another production house in a hostile takeover.29
直到后来我们才知道卢卡斯影业曾考虑与约翰和加里一起去,而是选择了我们。1978 年,还在 Triple-I 工作时,他们向卢卡斯影业提交了一部关于星球大战(1977)中美丽的 X 翼战斗机的电影测试,以三维建模并以非常高分辨率渲染。但他们没有对 X 翼的锋利边缘进行抗锯齿处理。他们认为高分辨率会使这些边缘的锯齿变得太小而无法看到。但事实并非如此。理查德·埃德伦德(Richard Edlund),同样是卢卡斯影业的特效大师,他带着他的《星球大战》大皮带扣在纽约理工学院拜访了我们,他立即发现了锯齿,并且无法容忍它们。
We didn’t know until later that Lucasfilm had considered going with John and Gary but had chosen us instead. In 1978 while still at Triple-I, they had submitted a film test to Lucasfilm of a beautiful X-wing fighter à la Star Wars (1977), modeled in three dimensions and rendered at very high resolution. But they didn’t antialias the sharp edges of the X-wing. They supposed that the high resolution would make the jaggies at these edges too small to see. But that wasn’t the case. Richard Edlund, the same Lucasfilm special effects master who had visited us at NYIT with his big Star Wars belt buckle, spotted the jaggies immediately and wouldn’t tolerate them.
尽管我们以低得多的分辨率进行渲染——因为这是我们可以合理负担的全部——但我们非常努力地对所有边缘进行抗锯齿处理。从一开始,“No Jaggies”就是我们卢卡斯影业的座右铭。这是关键的区别。事实上,我们在空间和时间上消除数字电影中的采样伪影将是我们成功的“秘诀”之一。图 8.13(左)中的照片显示了早期在卢卡斯影业的 Ed 和我(从左到右)与卢卡斯影业最早的计算机图形天才之一,我们的分形专家 Loren Carpenter。我穿着我们每个人都有的“No Jaggies” T 恤,它的标志在图 8.13(右)中显示得更清楚。
Although we rendered at much lower resolution—because that’s all we could justifiably afford—we took great pains to antialias all edges. From the beginning, “No Jaggies” was our Lucasfilm motto. It was the crucial difference. In fact, our care to rid digital movies of sampling artifacts, in both space and time, would be one of our “secrets” of success. The photo in figure 8.13 (left) shows Ed and me (left to right) at Lucasfilm in the early days with one of the earliest Lucasfilm computer graphics geniuses, Loren Carpenter, our fractal expert. I’m wearing the “No Jaggies” T-shirt that each of us had, its logo shown more clearly in figure 8.13 (right).
我们将 Digital Productions 视为我们的竞争对手是错误的吗?约翰和加里从未说过他们打算制作一部数字电影。他们的作品几乎都是其他电影的特效作品。但是有一个领域他们直接与我们竞争,或者我们是这么认为的。当我们向迪士尼提出计算机动画制作系统 (CAPS) 时——正如我在电影和动画章节中所描述的——迪士尼工作人员告诉我们,数字制作也在考虑之中。这强烈暗示了对角色动画的兴趣。无论对错,约翰和加里都赢得了我们的尊重。他们很聪明,准备好大展拳脚。多年后,在 1990 年代后期,当 Gary 在华盛顿特区寻求我的帮助以争取改变 HDTV 数字电视标准时,我很高兴能加入他的行列。
Were we wrong to think of Digital Productions as our competitor? John and Gary never stated that they intended to make a digital movie. Their work was nearly always special-effects work for other movies. But there was one area where they competed directly with us, or so we thought. When we proposed the Computer Animation Production System (CAPS) to Disney—as I described in the movies and animation chapter—Disney personnel told us that Digital Productions was being considered too. That hinted strongly of an interest in character animation. Rightly or wrongly, John and Gary gained our respect. They were smart, and ready to make the big play. Years later, in the late 1990s, when Gary asked for my help in Washington, DC, to fight for changes to the HDTV digital television standard, I was happy to join him.
图 8.13
Figure 8.13
(左)图片由皮克斯动画工作室提供。(右)Craig Reynolds 的概念。
(Left) Image courtesy of Pixar Animation Studios. (Right) Concept by Craig Reynolds.
Digital Productions 在The Last Starfighter中的作品令人印象深刻,但它没有数字角色。我们想做角色动画。但是我们缺少了一些必不可少的东西——一个角色动画师——一个有着难以形容的能力来激发草图线条或渲染三角形的人。
The work by Digital Productions in The Last Starfighter was impressive, but it had no digital characters. We wanted to do character animation. But we were missing something essential—a character animator—someone with that indescribable ability to inspirit sketched lines or rendered triangles.
一位伟大的动画师实际上访问了卢卡斯影业。1980 年,当我们还在圣安塞尔莫的古董店楼上与玛西娅·卢卡斯共用一个办公室时,布拉德·伯德曾看过我们。他想和我们一起拍一部动画电影。他是我见过的最有趣的人(现在仍然是)。当我们走在圣安塞尔莫的街道上聊天时,他让我不停地缝针。但我知道他对艺术太敏感了,无法忍受当时电脑的恶劣环境。他们很吵,需要寒冷的空调,而且经常失败。而且他们的速度慢得令人发指。
A great animator had actually visited Lucasfilm. Brad Bird had looked us up in 1980 while we were still above the antique store in San Anselmo sharing an office with Marcia Lucas. He wanted to make an animated movie with us. He was the funniest man I’d ever met (and still is). As we walked the streets of San Anselmo chatting, he had me in constant stitches. But I knew he was too artistically sensitive to put up with the harsh environment of computers at that time. They were noisy, required frigid air-conditioning, and failed often. And they were infuriatingly slow.
但仅仅几年后,我们得到了第二次机会。我们现在有足够的工具,终于有了足够的摩尔定律支持的计算,但我们缺少动画师。然后我和 Ed Catmull 遇到了制作电影所需的人:约翰·拉塞特。我们在一年一度的迪斯尼朝圣期间遇到了他,继续在我们加入卢卡斯影业之后。与纽约理工学院的大多数动画师不同,约翰一点也不害怕我们。约翰很兴奋。他已经与 MAGI 一起为Where the Wild Things Are进行了一个简短的测试。他见过特隆。他已经对使用计算机工作的感觉有所了解。
But just a few years later, we got a second chance. We had enough tools now, and finally had enough Moore’s Law–empowered computation, but we were lacking an animator. Then Ed Catmull and I met just the person we needed to make The Movie: John Lasseter. We met him during one of our annual pilgrimages to Disney, which continued after we joined Lucasfilm. John wasn’t the least bit frightened of us, unlike most of the animators at NYIT. John was excited. He had already worked with MAGI on a short test for Where the Wild Things Are. He had seen Tron. He already had a sense of what it was like to work with computers.
根据 Ed 和我的记录,我们实际上早先见过 John,第一次是 1983 年 2 月 16 日在卢卡斯影业,然后是 5 月 11 日,但当时他并没有给我们留下深刻的印象。这是在迪斯尼与他的第三次相遇,他的名字令人难忘。他把我们带到了迪斯尼档案馆,问我们想看什么。我口中的第一句话是,“普雷斯顿·布莱尔在幻想曲中跳舞的河马。” 他继续向我们展示了布莱尔的原画!他像动画师那样用拇指在布莱尔的床单边缘拍打。. . 河马风信子翩翩起舞!这对我来说是一个强大而神奇的时刻。接下来,我要求看《小飞象》中粉红色的大象场景,约翰继续答应了。我感觉到我们当时和那里的联系。30
According to Ed’s and my records, we had actually met John earlier, first at Lucasfilm on February 16, 1983, and again on May 11, but he didn’t make a strong impression on us then. It was the third encounter with him at Disney where his name registered unforgettably with us. He took us down into the Disney archives and asked what we wanted to see. The first thing out of my mouth was, “Preston Blair’s dancing hippo in Fantasia.” He proceeded to show us Blair’s original drawings! He fluttered the edges of Blair’s sheets with his thumb the way animators do . . . and Hyacinth the Hippo danced! This was a potent, magical moment for me. Next I asked to see the pink-elephant scene from Dumbo, which John proceeded to oblige. I felt us bonding then and there.30
但艾德和我不能碰约翰。他在迪斯尼工作。尽管如此,他还是给我们留下了深刻的印象。尽管他很年轻,但他曾两次在迪斯尼加州艺术学院的角色动画学校(沃尔特创立的学校)中获得“学生奥斯卡奖”最佳动画奖。
But Ed and I couldn’t touch John. He was working for Disney. Nevertheless, he had impressed us highly. Although very young he’d won the “student Academy Award” for best animation, twice, at Disney’s CalArts in its character animation school, the school that Walt had founded.
在从 1983 年的 Siggraph 回来的飞机上,我和 Ed 决定在 1984 年的下一次Siggraph 上,我们将向全世界宣布我们制作了角色动画。那将是我们的差异化因素。还在飞机上时,我再次在绿色的工程垫纸上勾勒出故事板的草图,我最初称之为我和安德烈的早餐,以向我们中的一些人特别欣赏的电影致敬,我和安德烈的晚餐(1981),由安德烈格雷戈里(André Gregory)主演(扮演安德烈)和华莱士肖恩(扮演沃利)。
On the plane back from the 1983 Siggraph, Ed and I decided that at the next Siggraph, in 1984, we would announce to the world that we did character animation. That would be our differentiator. While still on the plane, on green engineering pad paper again, I sketched the storyboard for what I initially called My Breakfast with André, in homage to a film several of us particularly admired, My Dinner with André (1981), starring André Gregory (playing André) and Wallace Shawn (playing Wally).
所以在我们的动画中,一个名叫安德烈的机器人会醒来,站起来,并大力伸展。太阳将升起,展现出丰富而美丽的自然景观。角色动画来了!这不是一个好故事,但我还看不到。
So in our animation, an android named André would awake, arise, and stretch mightily. The sun would rise revealing a rich and beautiful natural landscape. Character animation had arrived! It wasn’t a good story, but I couldn’t see that yet.
幸运的是,几个月后,埃德正在参加一个关于旧玛丽皇后号的会议,该会议永久停靠在长滩作为会议场所。我们正在打电话,每天都有业务更新电话,当 Ed 让我吃惊时说:“我刚看到 John Lasseter。他已经不在迪士尼了。” “现在就挂断电话,”我喊道,“去雇他!” 当然,Ed 知道这是一个绝妙的主意,并且确实做到了。31
Luckily, a couple of months later, Ed was attending a convention on the old Queen Mary, permanently docked in Long Beach as a meeting venue. We were on the phone, having our daily business update call, when Ed surprised me with, “I just saw John Lasseter. He’s no longer at Disney.” “Get off the phone RIGHT NOW,” I cried, “and go hire him!” Ed knew it was an excellent idea, of course, and did exactly that.31
只有一个捕获。乔治卢卡斯曾告诉埃德,计算机图形团队无法制作角色动画。他坚持说,只有迪士尼能做到这一点。所以我们在 1983 年末聘请了 John 作为“用户界面设计师”,而不是“动画师”,以使他远离 George 的视线。多年来,我们都不知道迪斯尼解雇了约翰,因为他想从事电脑动画。
There was only one catch. George Lucas had told Ed that the computer graphics team could not do character animation. Only Disney could do that, he insisted. So we hired John in late 1983 as a “user interface designer,” not “animator,” to keep him off George’s radar. We wouldn’t know for years that Disney had fired John for wanting to pursue computer animation.
约翰对我的早餐与安德烈故事板的回应是,“我可以提出一些建议吗?” “当然,这就是你来这里的原因!” 他继续保存这个项目。首先,他将机器人软化为更圆润、更可爱的安德烈。Ed 为他设计了一个更具延展性的身体,一个泪珠形状。它比球体的集合灵活得多。然后约翰建议添加另一个角色,一只大黄蜂。Ed的泪珠变成了它的腿。为了完成对我与安德烈共进晚餐的致敬,蜜蜂必须被命名为沃利,以纪念华莱士肖恩。事实上,他变成了 Wally B。我们将标题改为André & Wally B 历险记。这将是 John 与现在被称为 Pixar 的团队的第一次郊游,也是我作为导演的第二次尝试。
John’s response to my Breakfast with André storyboards was, “Can I make a few suggestions?” “Of course, that’s why you’re here!” And he proceeded to save the project. First, he softened the android into a rounder, cuter André. Ed designed a more malleable body, a teardrop shape, for him. It was far more flexible than a collection of spheres. Then John suggested adding another character, a bumblebee. Ed’s teardrops became its legs. To complete the tribute to My Dinner with André, the bee had to be named Wally in honor of Wallace Shawn. In fact, he became Wally B. We changed the title to The Adventures of André & Wally B. This would be John’s first outing with the group now known as Pixar, and my second shot as a director.
在约翰到来之前,我真的以为我会成为这部作品的动画师。毕竟,我做了那些美味的拍手。我还不了解一个真正的角色动画师必须具备的令人敬畏的才能,而我绝对没有。我可以让三角形移动,但我不能让它们有表情。我无法激励他们。我可以拍手,但我无法说服你它们属于有意识的存在。约翰可以做到这一切,而且他轻松自然地做到了。
Until John arrived, I truly thought I would be the animator of the piece. I had made those delicious clapping hands, after all. I didn’t yet understand the awesome talent that a true character animator has to have, and which I definitely did not. I could make triangles move, but I couldn’t make them emote. I couldn’t inspirit them. I could make hands clap, but I couldn’t convince you they belonged to a conscious being. John could do all that, and he did it easily and naturally.
到 1984 年在明尼阿波利斯举行的 Siggraph 之前,团队并没有完全完成André & Wally B.,但 Siggraph 官员还是允许我们展示它。没有什么比拥有数以千计的同龄人更甜蜜的了,他们确切地了解您的成就,为您的工作大喊大叫、跺脚和欢呼。现在我们从事角色动画业务,响亮而清晰,所有旗帜都在飘扬。
The team didn’t quite finish André & Wally B. by the 1984 Siggraph in Minneapolis, but Siggraph officials allowed us to show it anyway. There’s nothing sweeter than to have thousands of your peers, who understand exactly what you’ve accomplished, shouting and stomping and cheering your work. Now we were in the character animation business, loud and clear, all flags flying.
André & Wally B.显然是艺术上的突破,人们也是这样接受的。移动的不仅仅是人形物体。是两个角色情绪化。他们纵容了!还有一个故事。这很简单,也有点刻薄——一只巨大的蜜蜂威胁小男孩安德烈,他试图转移蜜蜂的注意力;有追逐;巨大的蜜蜂从小男孩身上蜇出贝耶苏斯——但这是一个故事。分蘖处有一位专业的角色动画师。
André & Wally B. was obviously an artistic breakthrough, and it was received that way. It wasn’t just human-shaped objects that moved. It was two characters who emoted. They connived! And there was a story. It was simple and a bit mean—a giant bee threatens little boy André, who tries to divert the bee’s attention; there’s a chase; the giant bee stings the bejesus out of the little boy—but it was a story. There was a professional character animator at the tiller.
这也是一项技术突破。它表明我们拥有足够复杂的建模、动画、渲染和电影录制程序,可以将 3D 角色的梦想带到电影屏幕上。它具有两项特定的技术进步。
It was also a technological breakthrough. It demonstrated that we had modeling, animation, rendering, and film recording programs sophisticated enough to bring the dream of three-dimensional characters to the cinema screen. And it featured two specific technological advances.
Bill Reeves 修改了他的粒子系统想法,该想法产生了 Genesis 演示中的行星融化火焰。将火粒子变为绿色,并在其遵循轨迹时留下渲染路径,然后您会得到 . . . 草。他还设计了他的系统的树生成版本,该系统创建了粒子云,如树叶,附着在树干和树枝上——落叶树为黄色和橙色,常绿树为深绿色。与分形一样,一些简单的计算重复了数百万次,将一个简单的数据库放大为一个令人满意的复杂“自然”森林。第一个。
Bill Reeves modified his particle system idea that had generated the planet-melting fires of the Genesis Demo. Turn a fire particle green and leave a rendered path behind as it follows a trajectory and you get . . . grass. He also devised a tree-generation version of his system that created clouds of particles, as leaves, attached to trunks and branches—yellows and oranges for deciduous trees and dark greens for evergreens. As with fractals, a few simple computations repeated millions of times Amplified a simple database into a satisfyingly complex “natural” forest. A first.
图 8.14
Figure 8.14
©皮克斯。
© Pixar.
最重要的是,André & Wally B.向 1984 年的 Siggraph 世界证明我们已经解决了运动模糊问题。Wally B. 的翅膀模糊了。安德烈的迅速离开使他陷入了困境。Cray 公司借给我们时间在他们的一台超级计算机上完成 Siggraph 的电影(也许最终吸引我们作为客户)。图 8.14 显示了四个连续的帧。根据在 Cray 监督计算的 Loren Carpenter 的说法,第三帧中的计算数量如此之多,以至于“让 Cray 崩溃了”。他决定没有人会注意到涂片不完整,并接受了不完整的框架。没有人注意到。
Most important of all, André & Wally B. demonstrated to the Siggraph world of 1984 that we had solved motion blur. Wally B.’s wings were blurred. André’s swift departure smeared him across a frame. The Cray company lent us time on one of their supercomputers in order to complete the film for Siggraph (and perhaps finally attract us as a customer). Figure 8.14 shows four successive frames. The number of computations in the third frame was so high that it “brought the Cray to its knees,” according to Loren Carpenter who was overseeing the computation at Cray. He decided that nobody would notice that the smear wasn’t complete and accepted the incomplete frame. Nobody noticed.
George Lucas 参加了André & Wally B.的首次放映,这让我们非常惊讶和高兴。他真的在城里看 Linda Ronstadt 的表演,但他也参加了我们的 Siggraph 首映式。卢卡斯终于要看看我们能做什么了!在一大群几乎可以肯定是热情的观众面前。多年后,当我从迈克尔鲁宾那里得知卢卡斯讨厌这部作品时,他正在研究他关于卢卡斯电影时代的书Droidmaker 。幸运的是,他没有这么说。它会伤透我们的心。
George Lucas attended that first screening of André & Wally B., much to our surprise and delight. He was really in town to see Linda Ronstadt perform, but he took in our Siggraph premiere too. Lucas was finally going to see what we could do! And in front of a large and almost certainly enthusiastic audience. It was years later when I learned from Michael Rubin, researching his book Droidmaker about the Lucasfilm days, that Lucas hated the piece. Luckily, he didn’t say so. It would have broken our hearts.
尽管在 Cray 超级计算机上使用了一段时间,但这件作品并不完整。一个场景仍然有线框前景字符,尽管在 Siggraph 看过它的人几乎没有人记得它们。另一方面,它并不像后来的拉塞特动画那样精致。这是他第一次使用 3D 动画模型拍摄完全由计算机生成的作品。在 Siggraph 观众中,几乎所有其他人,数以千计的人,都对已经取得的巨大进步表示赞赏,并且可以预见未来。但卢卡斯显然只能看到当时直接摆在他面前的东西。所以这是另一个案例,一个与我们不同的人无意中帮助我们实现了我们的。我们帮助他实现了他对数字化电影制作的清晰而重要的愿景。此外,几年后,他确实做出了改变。星球大战电影。
The piece wasn’t complete for one thing, despite the time on a Cray supercomputer. One scene still had wireframe foreground characters, although hardly anyone who saw it at Siggraph recalls them. For another, it wasn’t nearly as polished as later Lasseter animations became. This was his first shot at a completely computer-generated piece with three-dimensional animated models. Almost everybody else, thousands of them, in the Siggraph audience appreciated the immense advance that had been made and could see the future. But Lucas apparently could see only what was directly before him at the time. So here’s another case where a man with a different vision from our own inadvertently helped us realize ours. And we helped him realize his clear and important vision of digitizing film production. Furthermore, a few years later he did make the change. Lucas began to use computer-generated imagery more densely than any other moviemaker in his second series of Star Wars movies.
John Lasseter 和 Bill Reeves 在André 和 Wally B的制作过程中首次组成了他们的紧密组合。John 是合作的艺术创意成员,而 Bill 是技术创意成员。一个没有另一个就无法成功。
John Lasseter and Bill Reeves first formed their tight duo during the production of André & Wally B. John was the artistically creative member of the collaboration, and Bill the technically creative one. One couldn’t succeed without the other.
我很自豪我们在卢卡斯影业创造的环境,后来被带到皮克斯,不允许有害的技术与创意错误。我们在技术创意和艺术创意人士之间建立了一个相互钦佩的社会,在声望、薪水、晋升、福利,最重要的是尊严和尊重方面平等。
I’m very proud that the environment that we created at Lucasfilm, and carried later into Pixar, disallowed the pernicious technoid versus creatives error. We engendered a mutual admiration society between technically creative and artistically creative people, equal in prestige, salary, promotion, benefits, and most importantly, dignity and respect.
一个鲜为人知的“几乎”发生在我们在卢卡斯影业的最后几年。尽管乔治卢卡斯反对制作电脑动画电影,但我们几乎与一家日本公司合作制作了第一部《电影》。32
A little-known “almost” occurred in our last years at Lucasfilm. Despite George Lucas’s resistance to making a computer-animated movie, we almost made the first one, The Movie, with a Japanese firm.32
1984 年,代表日本大型印刷公司 Shogakukan(“Show gah khan”)的继承人的人向我们提出了一个宏伟的想法:制作第一部数字电影,并以日本儿童喜爱的淘气的孙悟空为基础——事实上,亚洲的大多数儿童。我认为这是一个神奇的概念,因为猴子多年来一直是我们世界的一部分。Lance Williams 在 NYIT 把我们介绍给了他。我们相信我们是这份工作的合适人选。所有的迹象都这么说。约翰·拉塞特立即开始为英雄进行角色研究(图 8.15)。
People representing the heir apparent of Shogakukan (“Show gah khan”), a major Japanese printing company, approached us in 1984 with a large idea: make the first digital movie, and base it on the mischievous Monkey King, beloved of Japanese children—indeed, most children in Asia. I thought this was a magical concept since Monkey had been part of our world for years. Lance Williams had introduced us to him at NYIT. We believed we were the right people for the job. All the signs said so. John Lasseter immediately got to work on character studies for the hero (figure 8.15).
但是我们应该为生产收取多少费用?以前没有人为一部长篇数字电影花钱,所以我从头开始这样做。我计算了数字,将我所知道的关于动画物流、像素分辨率的所有信息都考虑在内我们必须考虑到电脑的成本和速度、所需的存储空间、拍摄成本、人员和设备费用——除了营销和发行成本之外的一切。结果并不好。1985 年的成本约为 5000 万美元(今天约为 1.2 亿美元)。这太过分了两到三倍,尤其是对于这样一项冒险的事业——第一部具有 3D 角色和场景的数字电影。但更糟糕的是:计算它需要我们三年时间。Laurin Herr,我们的翻译和与日本人的业务接口,立即知道这三年是交易的破坏者。所以我们尽可能优雅地退出了这笔交易,并感谢大家。
But how much should we charge for production? Nobody had ever costed a feature-length digital movie before, so I proceeded to do so from scratch. I ran the numbers, factoring in everything I knew about the logistics of animation, the pixel resolution we must work at, the cost and speed of computers then, the storage space needed, the filming costs, the personnel and equipment expenses—everything but marketing and distribution costs. The results weren’t good. It would cost about $50 million in 1985 (about $120 million today). It was two to three times too much, especially for such a risky undertaking—the first digital movie with three-dimensional characters and sets. But worse: it would take us three years to compute it. Laurin Herr, our translator and business interface with the Japanese, knew immediately that the three years was the deal breaker. So we backed out of the deal as gracefully as possible, with thanks all around.
图 8.15
Figure 8.15
图片由皮克斯动画工作室提供。
Images courtesy of Pixar Animation Studios.
我们学到了宝贵的一课:我们仍然缺乏计算能力,无法经济高效地生成数字电影。我们需要另一个数量级的改进。1985 年,我们清楚地知道摩尔定律告诉我们,还需要五年时间才能获得电影。
And we had learned a valuable lesson: We were still too short of computational power to cost-effectively generate a digital movie. We needed another order-of-magnitude improvement. We knew in 1985 with detailed clarity informed by Moore’s Law that it would take five more years to attain The Movie.
在我们拒绝了孙悟空项目之后,我们开始考虑,当摩尔定律最终在硬件性能上达到这个数量级时,我们的软件技术是否足以制作电影,就像 1985 年那样。只是等待摩尔定律的问题吗?这是一个有效的问题,很难准确回答。
After our experience declining the Monkey King project, we started to consider if our software technology, as it stood in 1985, would be sufficient to make The Movie when Moore’s Law finally delivered that order of magnitude in hardware performance. Was it just a matter of waiting for Moore’s Law? This was a valid question and difficult to answer precisely.
当我们在 1970 年代在纽约理工学院第一次构思 The Movie 时,我们认为我们拥有足够的技术,Ed Catmull 的 Tween 程序和我用于前景的 TintFill 程序,我的 Paint3 程序用于背景,David DiFrancesco 的拍摄专业知识,以及用于合成的 alpha 通道. 对于硬件,我们有 18 个帧缓冲区、第一台用于测试的帧精确计算机控制的广播质量视频录像机,以及几台计算机。我们还拥有数字音频,以及我们从同样位于纽约理工学院校园的经典 cel 动画工作室学习的电影物流系统的开端。而且,从某种意义上说,我们可以接触到角色动画师,比如 Johnny Gent,与 Alex Schure 叔叔的Tubby the Tuba相关联工作室。我们周围都是真正制作过长片的人——并且正在制作另一部。这对我们来说并非不可能。
When we first conceived of The Movie, in the 1970s at NYIT, we thought we had enough technology, with Ed Catmull’s Tween program and my TintFill program for foregrounds, my Paint3 program for backgrounds, David DiFrancesco’s filming expertise, and the alpha channel for compositing. For hardware we had 18 framebuffers, the first frame-accurate computer-controlled broadcast quality video recorder for tests, and several computers. We also had digital audio, and the beginnings of a movie logistics system that we learned from the classic cel animation studio also on the NYIT campus. And, in a sense, we had access to character animators, like Johnny Gent, associated with Uncle Alex Schure’s Tubby the Tuba studio. We were surrounded with people who actually had made feature-length films—and were making another one. It wasn’t an unlikely possibility to us.
但是这种情况有几件事是错误的。最重要的是,我们很快了解到二维计算机动画对于真正的动画师来说太难了——也就是说,纽约理工学院受过经典训练的 cel 动画师。我们了解到,Alex Schure 的工作室作为制片人确实无法胜任这项任务。
But several things were wrong with this scenario. Most importantly, we quickly learned that two-dimensional computer animation was too hard for real animators—that is, the classically trained cel animators at NYIT. And we learned that Alex Schure’s studio really wasn’t up to the task as the producer.
此外,我们当时的电影概念并没有遵循计算机图形学的中心法则。这似乎令人惊讶,因为皮克斯成为以在中心法则“交响乐”形式中创作第一部长篇数字电影而闻名——基于 3D 欧几里得几何模型的角色动画,在牛顿物理学世界中运行,通过虚拟相机以文艺复兴时期的视角观看,并渲染成用于显示的像素。
Furthermore, our concept of The Movie at that point didn’t adhere to the Central Dogma of computer graphics. That might seem surprising because Pixar became famous for creating the first feature-length digital film inside the Central Dogma “symphonic” form—character animation based on three-dimensional Euclidean geometric models, operating in a world of Newtonian physics, viewed in Renaissance perspective by a virtual camera, and rendered into pixels for display.
交响乐形式在当时并不是一个陌生的概念,但一部尊重它的数字电影是遥不可及的。兰斯·威廉姆斯早在 1970 年代后期就曾提出将《作品》作为中央教条形式的电影。他和迪克·伦丁(Dick Lundin)和其他人在纽约理工学院工作,制作了几秒钟的壮观镜头。但 Ed 和我在The Works上运行了摩尔定律的数字,并意识到制作它需要花费数亿美元。换句话说,在当时是不可行的。
The symphonic form wasn’t a foreign concept back then, but a digital movie honoring it was unreachable. Lance Williams had early proposed The Works as a movie in Central Dogma form, in the late 1970s. He and Dick Lundin and others slaved at NYIT producing a few seconds of spectacular footage. But Ed and I ran the Moore’s Law numbers on The Works and realized it would cost hundreds of millions to produce. In other words, it wasn’t feasible at the time.
但是如果摩尔定律不是一个因素呢?假设总是有足够的计算能力以合理的成本制作一部长篇数字电影。进一步假设角色动画师一直都在。我们什么时候才有足够的技术专长来制作电影?
But what if Moore’s Law had not been a factor? Suppose there had always been enough computational power at a reasonable cost to make a feature-length digital movie. Further suppose that character animators had always been available. When would we have had enough technological expertise to make The Movie?
令人惊讶的答案是,我们总是准备好制作电影——除了一次技术飞跃。从根本上说,总是需要建模、动画和渲染程序,但这些程序的复杂性会并且确实会顺应摩尔定律的浪潮。艺术创意动画师的天才之处在于,他们可以随时将当前的技术水平变成引人入胜的故事。毕竟,迪士尼动画师在 1937 年将铅笔在纸上和在 cels 上的绘画变成了白雪公主。
The surprising answer is that we were always ready to make The Movie—except for one technological leap. Fundamentally, there always needed to be modeling, animation, and rendering programs, but the sophistication of these would and did ride the Moore’s Law wave. The genius of artistically creative animators is that they can turn the current level of technology into a compelling story at any time. After all, Disney animators turned pencil on paper and paint on cels into Snow White in 1937.
Central Dogmatic 数字电影的一项必要技术飞跃是运动模糊。我们理解了这一点——不知道如何解决它——在雷·哈里豪森 (Ray Harryhausen) 在杰森和阿尔戈英雄(1963) 中著名的定格格斗骷髅大战中作为观众遭受了不愉快的颤抖之后,我们明白了这一点。唯一的技术障碍,比如说,The Works,如果有足够的摩尔定律力量,当然是缺乏可行的运动模糊解决方案。但回到现实,直到 Cook、Carpenter 和 Porter Proletariat 三人组为André & Wally B. (1984) 解决了运动模糊问题——正如 Porter 1984 年壮观的图片中戏剧性地展示的那样(图 8.9)。但在 1985 年,我们做到了有一个很好的运动模糊解决方案。
The one necessary technological leap for Central Dogmatic digital movies was motion blur. We understood this—without knowing how to solve it—after suffering as spectators from the unpleasant judder of Ray Harryhausen’s famous stop-motion battling skeletons in Jason and the Argonauts (1963). The only technological barrier keeping, say, The Works, from being made—given enough Moore’s Law power, of course—was the lack of a feasible motion blur solution. But back to reality, motion blur wasn’t effectively solved until the Cook, Carpenter, and Porter Proletariat trio did so for André & Wally B. (1984)—as displayed dramatically in Porter’s spectacular picture 1984 (figure 8.9). But in 1985, we did have a good motion-blur solution.
我在这些页面中介绍了几种技术技术。采样器包括分形、粒子系统和建模中的补丁。以及渲染中的纹理贴图、凹凸贴图、Phong 着色和光线追踪。但声称是电影不需要这些(除了运动模糊)。沿着摩尔定律曲线向后思考和向前思考一样困难——除非你在那里。我们现在几乎不可能想象没有这些技术和摩尔定律计算能力的世界。
I’ve presented several technological techniques in these pages. A sampler includes fractals, particle systems, and patches in modeling. And texture mapping, bump mapping, Phong shading, and ray tracing in rendering. But the claim is that none of these—save motion blur—was required for The Movie. It’s as hard to think backward along the Moore’s Law curve as it is to think forward—unless you were there. It’s almost impossible for us now to imagine the world without these techniques and the concomitant level of Moore’s Law computational power.
我通过注意到摩尔定律每五年转动一次,就会有更多的技术成为可能,以此来论证这一点。它们经常被用来使对中心教条的坚持变得越来越引人注目。尽管这不是一项法律,但人们可以认为是在维持“生产守恒”。随着摩尔定律以指数方式缩短电影计算时间,改进建模、动画和渲染技术的计算需求扩大,以保持总制作时间不变,例如大约一年左右。这种“恒定性”有时被称为布林定律,归功于吉姆布林。
I argue this by noticing that with every five-year turn of the Moore’s Law crank many more techniques become possible. And they are often used to make adherence to the Central Dogma increasingly dramatic. Although it’s not a law, one can think of a “conservation of production” being maintained. As Moore’s Law exponentially contracts movie computation time, the computational demands of improved modeling, animation, and rendering techniques expand to keep the total production time constant, on the order of, say, a year or so. This “constancy” is sometimes known as Blinn’s Law, credited to Jim Blinn.
在实践中,这意味着计算机图形社区不断发明新算法并改进旧算法。他们以更有效的方式改进生产过程。在寻找电影的过程中,这意味着我们在等待摩尔定律实现的同时保持技术进步。
In practice this means that the computer graphics community unceasingly invents new algorithms and improves older ones. And they refine the production process in ever more efficient ways. On the quest for The Movie, it meant that we kept technological advance on a high burner while we waited for Moore’s Law to deliver.
X–10,000,000 X(1985–2000)X–10,000,000X (1985–2000)乔治和玛西娅卢卡斯于 1983 年离婚。由于加利福尼亚是一个社区财产州,乔治实际上在一夜之间失去了一半的财产。在接下来的几年里,这导致计算机部门被分成可以出售的不同单位。首先是 Digital Audio Group 及其产品 SoundDroid,以及 Video Editing Project 及其产品 EditDroid。它们是名为 The Droid Works 的衍生产品的一部分。乔治想要保留在卢卡斯影业中的唯一部分是游戏项目。它将成为 LucasArts。这只剩下计算机图形项目需要处理。
George and Marcia Lucas divorced in 1983. Since California is a community-property state, George effectively lost half his fortune overnight. Over the next couple of years this resulted in the Computer Division’s being split into distinct units that could be sold off. First to go was the Digital Audio Group and its product, SoundDroid, and the Video Editing Project and its product, EditDroid. They were made part of a spinoff called The Droid Works. The only part that George wanted to keep within Lucasfilm was the Games Project. It would become LucasArts. This left only the Computer Graphics Project to deal with.
我走进我附近的 Ed Catmull 的办公室,宣布:“我们将被解雇,Ed。乔治从来没有真正了解我们是谁,他再也负担不起我们了。” 然后我用了一个对我们俩都有意义的宗教词,“让这个世界级的集团分散是一种罪过。让我们开一家公司,给他们一个家。” 这是两个电脑书呆子在互相交谈。我们俩都没有中层经理的预算和资源意识,也没有任何关于筹集资金的详细概念。
I walked into Ed Catmull’s office near mine and announced, “We’re going to be fired, Ed. George has never really understood who we are, and he can no longer afford us.” Then I used a religious word meaningful to both of us, “It would be a sin to let this world-class group disperse. Let’s start a company to give them a home.” This was two computer nerds talking to one another. Neither of us had more than a middle manager’s sense of budgets and resources, nor any detailed notion about raising money.
埃德立即同意了,我们前往一个干净、光线充足的书店,这是一家位于拉克斯珀兰丁附近的受欢迎的书店,毗邻圣拉斐尔,前往旧金山的渡轮就是从那里出发的。我们每人买了两本关于如何创办公司的书。我买了图 8.16 中的两个苗条的。这正确地校准了我们当时的业务专业水平。33
Ed immediately agreed and we proceeded to A Clean Well-Lighted Place for Books, a popular bookstore in nearby Larkspur Landing, next door to San Rafael, where the ferries to San Francisco embark. We bought two books each on how to start companies. I bought the two slim ones in figure 8.16. This correctly calibrates our level of business expertise at the time.33
“公司会怎么做?” Ed 合理地问道,因为我们都知道计算机图形项目不能成为依赖于电影,还没有。或者更重要的是,很难利用我们公司的前景。美猴王项目让我们相信,我们需要另一个摩尔定律的曲柄,再过五年及其数量级的改进,才能以具有成本效益的方式制作电影。在此期间,我们必须做一些其他事情来将团队团结在一起。计算使我们确信,无论是软件公司还是数字效果和广告公司,都无法产生足以支持我们 40 人团队的收入。它必须是硬件。34
“What will the company do?” Ed asked reasonably, given that we both knew the Computer Graphics Project couldn’t become a separate company that depended on movies, not yet. Or more importantly that it would be difficult to capitalize our company on the prospect. The Monkey King project had convinced us that we needed another crank of Moore’s Law, another five years and its order-of-magnitude improvement, to produce a movie cost-effectively. We’d have to do something else in the meantime to hold the team together. Calculations convinced us that neither a software company nor a digital effects and commercials house would produce revenues enough to support our group of forty people. It had to be hardware.34
图 8.16
Figure 8.16
而且,我们有一台原型专用计算机,皮克斯图像计算机,这是该小组为乔治卢卡斯建造的,作为光学打印机数字化系统的一部分。我们认为,让我们遵循标准的硅谷做法,通过为原型筹集资金并将其投入生产。我们没有任何其他想法。这必须是它。硬件也许可以为我们的团队买单并保持五个几年我们等待摩尔定律。稍加思考就应该提醒我们,我们对市场营销、销售、硬件工程、制造、财务、人力资源等等知之甚少——无论如何,在研究部门之外。那四本小商业书籍大概会教给我们所有这些。我们不顾一切地想把团队聚在一起,去看第一部电影,然后在等待的时候拿到报酬。35
And, we had a prototype special-purpose computer, the Pixar Image Computer, which the group had built for George Lucas, as part of a system for digitizing the optical printer. Let’s follow standard Silicon Valley practice, we argued, by raising capital on the prototype and taking it into production. We didn’t have any other ideas. This had to be it. Hardware might be able to pay for our group and keep it together for five years while we waited for Moore’s Law. A moment’s reflection should have reminded us that we didn’t know much about marketing, sales, hardware engineering, manufacturing, finance, human resources, and so forth—not outside of a research department level anyway. Those four little business books were going to teach us all that, presumably. We were desperate to keep the group together, get to that first Movie, and get paid while we waited.35
所以 Ed 和我写了一个商业计划来建造和销售 Pixar Image Computers,“像素超级计算机”,并保留一个以 John Lasseter 和 Bill Reeves 为中心的计算机动画专家小组,假设他们会同意这个计划——在接下来的五年里,一旦接到电话,就准备好制作电影。现在我们必须把公司资本化。
So Ed and I wrote up a business plan to build and sell Pixar Image Computers, “supercomputers for pixels,” and to keep a small team of computer animation experts—centered on John Lasseter and Bill Reeves, assuming they would go along with the plan—alive for the next five years ready to make The Movie once the call came. Now we had to capitalize the company.
但首先,我们必须把它的想法卖给卢卡斯影业计算机图形组的其他 38 名成员。埃德和我带他们每个人,通常一次一个,去圣拉斐尔市中心一家最受欢迎的泰国餐厅。我们描述了这个计划,强调每个员工都将拥有新公司的一部分。直到最后,我们的意思是所有人,无论职位描述如何。
But first, we had to sell the idea of it to the 38 other members of the Lucasfilm computer graphics group. Ed and I took each of them out, usually one at a time, to a favorite Thai restaurant in downtown San Rafael. We described the plan, emphasizing that each employee would own a piece of the new company. Collegial to the end, we meant everybody, regardless of job description.
我们需要实体的名称。我们在那里也很平等。每个人都尝试创造一个名字并试图说服其他人。我们以前在这方面失败过一次。我们曾多次尝试将 Lucasfilm 计算机部门命名为“工业光魔”之类的酷东西。甚至乔治卢卡斯也尝试过。但没有两个人能达成一致,所以它仍然是计算机部门。我们又来了。我们在早期文档中使用占位符来表示名称。GFX(读作“graphics”)用了一段时间,但效果并不理想,一搜名字发现反正已经有人认领了。
And we needed a name for the entity. We were egalitarian there too. Everybody had a try at creating a name and trying to convince the others. We had failed once before on this front. We had tried repeatedly to name the Lucasfilm computer division something cool like Industrial Light & Magic. Even George Lucas had tried. But no two people could agree, so it remained Computer Division. Here we were again. We used a placeholder for a name in the early documents. GFX (pronounced “graphics”) lasted a while, but it was unsatisfactory, and a name search found that it was already claimed anyway.
最后,是时候向加利福尼亚州的国务卿提交公司注册文件了。此正式步骤需要一个名称。绝望中,我呼吁该组织,“你知道,现在每个人都将我们与‘皮克斯’这个词联系在一起,因为它已成为我们计算机的简称。我们为什么不直接使用 Pixar 作为我们的公司名称?” 人们普遍感到失望和不赞成,但我们没时间了,没有人有更好的建议。皮克斯由此得名。我已经解释了我们如何根据一个假的(或者我们说“创造的”)西班牙语动词pixar来命名计算机,意思是“制作照片”。所以皮克斯是一家制作图片的公司。想一想,它会制作假照片——就像不是基于现实或取自现实一样。但与其说是“假”图片,不如说是不真实的图片。
Finally, it came time to submit the incorporation papers to California’s secretary of state. A name was required for this formal step. In desperation I appealed to the group, “You know, everybody associates us with the word ‘Pixar’ now because it’s become the short name for our computer. Why don’t we just use Pixar as our company name?” There was a general groan of disappointment and disapproval, but we were out of time and nobody had a better suggestion. That’s how Pixar got its name. I’ve already explained how we named the computer based on a fake (or let’s say “coined”) Spanish verb, pixar, meaning “to make pictures.” So Pixar is a company that makes pictures. Come to think of it, it makes fake pictures—as in not based on, or taken from, reality. But rather than saying “fake” pictures, let’s instead call then unreal pictures.
1985 年年中,我和 Ed Catmull 开始为我们的新公司寻找资金。乔治卢卡斯的业务经理热衷于帮助我们,因为任何交易的一部分都会反弹到卢卡斯影业。但我们不知道在他们简单地拔掉我们的插头之前我们还有多久。
Ed Catmull and I began the grind of finding funds for our new company in mid-1985. George Lucas’s business managers were keen on helping us since part of any deal would rebound to Lucasfilm. But we didn’t know how long we had before they would simply pull the plug on us.
第一个想法是接触风险投资家,他们以资助硅谷的初创公司而闻名。在卢卡斯影业的影响力和卢卡斯影业业务经理的帮助下,我们接触了 36 家风险投资或投资银行公司。但我们不符合他们关于种子资本创业公司的想法——他们都拒绝了我们。36
The first idea was to approach the VCs, the venture capitalists, who famously funded startup companies in Silicon Valley. With the clout of Lucasfilm and the help of Lucasfilm business managers, we approached 36 VC or investment banking firms. But we didn’t fit their idea of a seed capital startup—and they all turned us down.36
然后我们转而与一家大公司建立“战略合作伙伴关系”。在我们认真交谈的 10 人中,有 8 人拒绝了我们。但我们几乎与通用汽车和飞利浦这两家大公司达成了一项联合交易——通用汽车当时是世界上最大的公司。37
Then we turned our minds to making a “strategic partnership” with a large corporation instead. Of the 10 we talked to seriously, 8 turned us down. But we almost closed a joint deal with two vast corporations, General Motors and Philips—GM was the largest in the world at the time.37
我们处理了 GM 部门,该部门以前是一家独立的公司,即由 H. Ross Perot 领导的 Electronic Data Systems。他就是几年后竞选美国总统的那个人。通用汽车将我们的技术视为一种替代其昂贵的粘土建模技术用于新车设计的方法。
We dealt with the GM division that had formerly been a separate company, Electronic Data Systems, headed by H. Ross Perot. He was the same man who would run for US president several years later. GM saw our technology as a way to replace their expensive clay modeling technique for new car designs.
随后飞利浦决定与通用汽车合作分担融资负担。我们拥有一种新的渲染技术,无需手术即可通过 CAT 扫描生成人体的 3D 内部视图,这是一项潜在的革命性医学成像进步。38
Then Philips decided to partner with GM to share the financing load. We had a new rendering technology that yielded three-dimensional internal views of human beings from CAT scans—without surgery—a potentially revolutionary medical imaging advance.38
它最终归结为在曼哈顿中城举行的一次重要会议,地点在中央车站上方飞利浦大楼的一个董事会会议室。我们与通用汽车、飞利浦和卢卡斯影业签署了一份意向书,日期为 1985 年 11 月 7 日。39
It came down finally to a crucial meeting in midtown Manhattan, in a boardroom at the Philips building high above Grand Central Station. We signed a letter of intent with GM, Philips, and Lucasfilm, dated November 7, 1985.39
但这笔交易从未发生。我们甚至可能在那个会议室里的每个人都不知道,H.罗斯佩罗三天前就通用汽车董事会斥资超过 50 亿美元收购了休斯工具。以前没有董事会成员在通用汽车董事会会议上反对过——自大萧条以来就没有!那不应该发生。佩罗花了一年时间才真正离开通用汽车,并用 7 亿美元鼓励他这样做。但当消息在《华尔街日报》上发布时,立即清楚的是,通用汽车公司任何涉及佩罗的事情都已经死了。我们的交易就在那个裂缝中。40
But the deal never happened. Unknown to us and perhaps to everybody in that boardroom, H. Ross Perot had three days earlier berated the GM board of directors about their purchase of Hughes Tools for over $5 billion. No board member had ever objected at a GM board meeting before—not since the Depression! That wasn’t supposed to happen. It took a year before Perot actually left GM, with $700 million to encourage him to do so. But it was immediately clear, when the news broke in the Wall Street Journal, that anything at GM that involved Perot was dead. Our deal fell right in that crack.40
这是一个很好的地方来记住这本书的更大的想法是数字光,而不仅仅是数字电影。请注意,通用汽车的车身模拟和飞利浦的医学成像都与数字电影无关。但两者都是 Digital Light 的一部分。车身模拟是计算机辅助设计 (CAD) 的一部分,尽管在我们的案例中,GM 对我们从内部计算机模型渲染的汽车图片比对物体本身更感兴趣。医学成像是图像处理的一部分——拍摄(人体)照片,而不是制作照片。我们还探索了 Digital Light 的其他几个部分,例如地质成像用于油井、智能卫星图像、机械部件的热应力测试、气体动力学。我们已准备好利用这些途径中的任何一种来获得资金,以使我们为实现电影的最终目标而活着。
This is a good place to remember that the larger idea of this book is Digital Light and not just digital movies. Notice that neither auto-body simulation for GM nor medical imaging for Philips had anything to do with digital movies. But both were parts of Digital Light. Auto-body simulation is part of computer-aided design (CAD), although in our case GM was more interested in pictures of autos we would render from internal computer models than with the objects themselves. And medical imaging is part of image processing—taking pictures (of the human body) rather than making them. We had explored several other parts of Digital Light as well, such as geological imaging for oil wells, intelligence satellite imagery, heat stress testing of mechanical parts, gas dynamics. We were ready to exploit any of these avenues to obtain funding to keep us alive for the ultimate goal of The Movie.
GM-Philips 是我们最后的希望,也是我们第四十六次尝试获得此类资金。埃德和我现在很疯狂。卢卡斯影业终于没有耐心了。在我们回加州的机场豪华轿车上,我们想出了一个冰雹玛丽——回到史蒂夫乔布斯。
GM-Philips had been our last hope, our forty-sixth attempt at such funding. Ed and I were frantic now. Lucasfilm had finally run out of patience. In the airport limo on our return trip to California, we came up with a Hail Mary—go back to Steve Jobs.
三个月前,即 1985 年 8 月 4 日,史蒂夫邀请埃德、我和我们的财务经理阿吉特·吉尔到他位于伍德赛德的豪宅,那里离帕洛阿尔托不远。史蒂夫刚刚被苹果公司赶下台。他提议从卢卡斯影业收购我们,并将我们作为他的下一家公司经营。我们说不,我们想自己经营公司,但我们会接受他的钱。他同意了。
Three months earlier, on August 4, 1985, Steve had invited Ed, me, and Ajit Gill, our financial manager, to his mansion at Woodside, not far from Palo Alto. Steve had just been ousted from Apple. He proposed that he buy us from Lucasfilm and run us as his next company. We said no, we wanted to run the company ourselves, but we would accept his money. And he agreed.
但是当史蒂夫向卢卡斯影业提出他的建议时,他们没有理会他。他的数字是 7 到 1400 万美元。通用汽车和飞利浦谈的是 20 到 3600 万美元。这笔交易进展顺利。
But when Steve presented his proposal to Lucasfilm, they paid him no heed. His number was $7 to $14 million. GM and Philips were talking $20 to $36 million. And that deal was proceeding nicely.
但现在通用飞利浦的交易失败了,我和埃德决定打电话给史蒂夫,要求他再次提出完全相同的报价,估值不到刚刚失败的交易的一半。我们相信卢卡斯影业最终可能会减少数量。史蒂夫正是这样做的,卢卡斯影业也确实做到了,这就是史蒂夫乔布斯成为资助皮克斯的风险投资家的原因。请注意,他并没有像经常误报的那样购买皮克斯。他资助了一家由员工部分拥有的衍生公司。
But now that the GM-Philips deal had fallen through, Ed and I decided to call Steve and ask him to make exactly the same offer again, the one with a valuation less than half of the deal that just went sour. We believed Lucasfilm, at the end of its tether, might go for the reduced amount. Steve did that very thing, Lucasfilm did go for it, and that’s how Steve Jobs became the venture capitalist who financed Pixar. Note that he did not buy Pixar as very often misreported. He financed a spinout corporation that was partially owned by the employees.
这笔交易与我们在 8 月份讨论过的差不多。Ed 和我将作为总裁和执行副总裁管理公司。史蒂夫将成为大股东,我们三个人将成为董事会。我们所有的员工都将获得公司的股份。史蒂夫拿走了 70%,员工拿了 30%。Ed 和我各拿了 4%,其他 38 名创始员工按比例拿了小块。史蒂夫以 1000 万美元为公司注资。我们在签约时从他那里拿到了 500 万美元的第一张支票,Ed 立即将其背书给卢卡斯影业,以购买我们在卢卡斯影业开发的技术的权利,包括皮克斯图像计算机。这是一项专有权利,但卢卡斯影业必须使用我们离开时已有的技术。41
The deal was much as we had discussed back in August. Ed and I would run the company as president and executive vice president. Steve would be majority shareholder, and the three of us would be the board. And all our employees would get a share of the company. Steve took 70 percent and the employees 30 percent. Ed and I took 4 percent each and all 38 other founding employees took smaller pieces on a graduated scale. Steve capitalized the company with $10 million. We took the first check from him at the signing for $5 million, and Ed immediately endorsed it over to Lucasfilm to purchase rights to the technology we had developed at Lucasfilm, including the Pixar Image Computer. It was an exclusive right except that Lucasfilm got to use the technology as it existed when we departed.41
皮克斯于 1986 年 2 月 3 日出生在旧金山北部的圣拉斐尔。我们设法让团队团结在一起,包括我们的动画单位。而且,正如所有初创企业家都必须相信的那样,我们认为皮克斯图像计算机是一款令人兴奋的产品。与此同时,史蒂夫正在运营另一家硬件公司 NeXT,距离旧金山南部大约一个半小时车程。这种身体上的分离原来是天赐之物。
Pixar was born February 3, 1986, in San Rafael, north of San Francisco. We had managed to keep the team together, including our nugget of an animation unit. And, as all startup entrepreneurs have to believe, we thought we had an exciting product in the Pixar Image Computer. Meanwhile Steve was running NeXT, yet another hardware company, about an hour and a half away, south of San Francisco. That physical separation turned out to be a godsend.
在接下来的五年里,我们通过由 Lasseter 和 Reeves 及其团队创作的一系列短片来保持电影的可能性。这磨练了他们的技能,让我们进一步发展我们的建模、动画和渲染算法,提升了我们的精神。这些短片中有Luxo Jr。(1986),自Le Faim ( Hunger) (1974) 以来第一部获得奥斯卡奖提名的电脑动画电影。这无疑是第一部获此殊荣的中央教条式三维动画电影。然后锡玩具(1988) 获得 1989 年奥斯卡最佳动画短片奖,不是因为它是电脑动画,而是因为它是一部出色的短片。拉塞特和里夫斯因这一成就分享了奥斯卡奖——这是皮克斯在许多人中的第一个奥斯卡奖。这一时期的其他皮克斯短裤是Red's Dream (1987) 和Knick Knack (1989)。在这些艰难的岁月中,这些是支撑我们的四颗闪闪发光的宝石。
We kept the possibility of The Movie alive during the next five years with a series of short films, created by Lasseter and Reeves and their team. This honed their skills, let us further develop our modeling, animation, and rendering algorithms, and elevated our spirits. Among these short pieces was Luxo Jr. (1986), the first computer-animated film since Le Faim (Hunger) (1974) to be nominated for an Academy Award. It was certainly the first Central-Dogmatic three-dimensional animated film to be so honored. Then Tin Toy (1988) won the 1989 Academy Award for Best Animated Short Film, not because it was computer-animated but because it was an excellent short film. Lasseter and Reeves shared the Oscar for this achievement—the first Oscar for Pixar of many to come. The other Pixar shorts from this period were Red’s Dream (1987) and Knick Knack (1989). These were four of the sparkling jewels that sustained us during these otherwise tough years.
每一件作品都代表了底层内部技术的持续改进。例如,Luxo Jr.结合了第一个来自多个光源的自我阴影的铰接物体。两个光源,两盏灯,在场景本身中,另一个在第一个。
Each one of these pieces represented continued improvements in the underlying in-house technologies. For example, Luxo Jr. incorporated the first articulated objects that self-shadowed themselves, from multiple light sources. Two of the light sources, the two lamps, were in the scene itself, another first.
在艺术上,小 Luxo是约翰·拉塞特试图说服他在其他地方的动画同事相信计算机不是一个硬、僵硬、线性的算术机器,在某种程度上与他们的艺术形式对立。在这方面,他取得了惊人的成功。每个人,尤其是其他动画师,都对两盏灯的个性做出了回应。迫在眉睫的问题不是他们还活着,而是他们的性别是什么?父子?母亲和女儿?观众可能不太关心底层的几何图形和自阴影。约翰故意没有指明性别。他们是你选择的任何人。
Artistically, Luxo Jr. was John Lasseter’s attempt to convince his animation colleagues elsewhere that the computer was not a hard, rigid, linear, arithmetic machine somehow antagonistic to their artform. In that he was spectacularly successful. Everyone, especially other animators, responded to the personalities of the two lamps. The looming question was not are they alive, but what is their gender? Father and son? Mother and daughter? Viewers could care less about the underlying geometry and self-shadowing. And John purposely didn’t specify the genders. They were whatever you chose them to be.
再举一个例子,第二颗宝石Red's Dream旨在展示我们的硬件产品 Pixar Image Computer。这件作品的主要背景是一家自行车店,是当时渲染的最复杂的计算机图形场景。
As another example, the second jewel, Red’s Dream, was designed to show off our hardware product, the Pixar Image Computer. The principal background for the piece, a bicycle shop, was the most complex computer graphics scene ever rendered at the time.
第五个宝石是 CAPS,我们为迪士尼创建的计算机动画制作系统。它使皮克斯和迪斯尼保持密切的相互钦佩的关系,并且是羽翼未丰的皮克斯的主要收入来源。多年来,每个迪斯尼 cel 动画都是在系统上执行的,使用皮克斯图像计算机运行皮克斯人编写的软件(以及迪斯尼人编写的逻辑软件)。迪士尼在小美人鱼(1989)中的一个场景中首次使用了 CAPS 。第一部使用该系统的完整电影是The Rescuers Down Under (1990)。CAPS 最终被用于总共 18 部迪士尼故事片。迪斯尼是皮克斯图像计算机的主要客户。这是CAPS交易的一部分。42
The fifth jewel was CAPS, the Computer Animation Production System we created for Disney. It kept Pixar and Disney close in a mutually admiring relationship and was a major source of income for the fledgling Pixar. Every Disney cel animation for years was executed on the system, using Pixar Image Computers running software written by Pixar people (and logistic software written by Disney people). Disney first used CAPS for one scene in The Little Mermaid (1989). The first complete movie using the system was The Rescuers Down Under (1990). CAPS was eventually used for a total of 18 Disney feature films. And Disney was a principal customer of Pixar Image Computers. That was part of the CAPS deal.42
但皮克斯是一家糟糕的硬件公司。硬件不差,但公司差。即使是著名的硬件制造商史蒂夫·乔布斯(Steve Jobs),持有公司多数股权并担任董事会成员,也不足以使其成功。在这五年里,我们失败了好几次。这是以通常的方式衡量的失败:我们用光了钱,无法支付账单或员工。如果我们有史蒂夫以外的任何其他投资者,我们就会死在水里。但在每次失败时——大概是因为史蒂夫无法忍受在苹果下台后他的下一个企业将是失败的尴尬——他会斥责我们这些管理人员。. . 然后再写一张支票。并有效地贬低员工权益。在几次这样的“再融资”之后,他将自己 1 亿美元的苹果财富的一半左右投入了皮克斯。在今天的金钱中,他向皮克斯投入了大约 1.15 亿美元。1991 年 3 月 6 日,在皮克斯的第五个年头,他终于确实购买了公司,但从员工那里购买,而不是后来描述的 1986 年从卢卡斯影业购买。现在他完全拥有了。我们的员工甚至不再拥有一份股份。43
But Pixar was a lousy hardware company. The hardware wasn’t lousy, but the company was. And even the famous hardware manufacturer Steve Jobs, holding a majority of the company and sitting on the board, wasn’t enough to make it a successful one. We failed several times over these five years. That’s failure measured the usual way: we ran out of money and couldn’t pay our bills or our employees. If we’d had any other investor than Steve, we would’ve been dead in the water. But at every failure—presumably because Steve couldn’t sustain the embarrassment that his next enterprise after the Apple ouster would be a failure—he’d berate those of us in management . . . then write another check. And effectively devalue employee equity. After several such “refinancings,” he had poured about half his $100 million Apple fortune into Pixar. In today’s money, he’d put about $115 million into Pixar. On March 6, 1991, in Pixar’s fifth year, he finally did buy the company, but from the employees, not from Lucasfilm in 1986 as later portrayed. Now he owned it completely. We employees no longer owned even a single share.43
该公司仍处于严重的财务困境中。我们尝试了各种小事情,比如基于约翰·拉塞特和比尔·里夫斯的小团队的电视广告业务。但这些想法都没有足够的创收能力来支付我们公司的费用。乔布斯探索了将我们纳入 NeXT 的想法,但他的联合创始人不想参与其中。真的只有一个出路。摩尔定律必须通过使电影最终在经济上可行来拯救我们。只有电影有足够的潜在回报来拯救我们。
And the company was still in serious financial trouble. We tried all sorts of small things, like a television commercial business based on John Lasseter and Bill Reeves’s small team. But none of these ideas had enough income-producing capacity to even hope to pay for our company. Jobs explored a notion of folding us into NeXT, but his cofounders there wanted nothing to do with it. There was really only one way out. Moore’s Law had to save us by making The Movie finally economically feasible. Only movies had enough potential reward to save us.
这是一次疯狂的旅程。. . . 我与皮克斯的合作是光荣而短暂的,但我认为这是我职业生涯中最富有成果和最愉快的时期之一。
It was a wild ride. . . . My involvement with Pixar was glorious and brief, but I consider it to be one of the most fruitful and enjoyable periods of my career.
——Jim Lawson,皮克斯 RenderMan 44的联合开发者
—Jim Lawson, co-developer of Pixar’s RenderMan44
皮克斯在电影前几年的第六颗也是皇冠上的宝石是RenderMan。它的名字是索尼随身听的双关语。45
Pixar’s sixth and crowning jewel during the pre-Movie years was RenderMan. Its name was a pun on the Sony Walkman.45
通往 RenderMan 的道路始于 1970 年代犹他大学的 Gouraud 着色或 Phong 着色等单独的着色技术。然后,正如我们所见,Rob Cook 在 1980 年代初期在卢卡斯影业将这一概念推广到了一种着色语言中。他将自己的系统编写为 Lucasfilm 内部渲染解决方案的前端,该解决方案是最初由 Loren Carpenter 编写的 Reyes 渲染器,然后由 Rob 进行了大幅改进。Reyes (发音为“Rays”)这个名字是 Loren 的巧妙首字母缩写词,意思是“渲染你所见的一切”,或“渲染你所见的一切”。雷耶斯表彰当地的雷耶斯角国家海岸,并被开发为在卢卡斯影业的特定硬件上运行。46
The path to RenderMan began with individual shading techniques, such as Gouraud shading or Phong shading from the 1970s at the University of Utah. Then, as we saw, Rob Cook generalized the notion into a shading language at Lucasfilm in the early 1980s. He wrote his system as a front end to Lucasfilm’s internal rendering solution, which was the Reyes renderer written initially by Loren Carpenter and then improved substantially by Rob. The name Reyes (pronounced “Rays”) was Loren’s clever acronym for Renders Everything You Ever Saw, or Renders Everything You’ll Ever See. Reyes honored the local Point Reyes National Seashore and was developed to run on Lucasfilm’s specific hardware.46
下一个重大飞跃是将着色语言从 Lucasfilm 硬件的特殊性中解放出来。这是从特定语言到标准语言的飞跃——从一家公司的硬件到任何公司的硬件。这是创建统一计算机图形行业的飞跃——因此 RenderMan 的重要性。
The next big leap was to free the shading language from the specificity of Lucasfilm’s hardware. This was the leap from a specific language to a standard language—from one company’s hardware to any company’s. This was the leap that created a unified computer graphics industry—hence the importance of RenderMan.
回忆计算章节中的名片通用图灵机。这台机器可以理解一种带有如下指令的语言:“3 : 4← [glyph],”意思是,“如果你在孔的胶带方块上看到 3,然后用 4 替换它,向左移动一个方块,然后旋转卡片,使其看起来像字形。” 每台计算机都有一种类似折磨人的机器语言,该语言是该特定计算机独有的。
Recall the business card universal Turing machine from the computation chapter. This machine understood a language with instructions like: “3 : 4 ← [glyph],” meaning, “if you see a 3 on the tape square in the hole, then replace it with a 4, move one square left, and rotate the card so it looks like the glyph.” Each computer has a similarly torturous machine language that is unique to that particular computer.
计算方面的突破是标准高级编程语言的开发,例如贝尔实验室的 C,可以在任何计算机上运行。用户用类似英语的语言编写程序。该程序通过一个程序员不必理解的特殊程序(称为编译器)传递,该程序将标准编程语言转换为特定计算机的机器语言。例如,当有人购买 Unix 系统时,它配备了高级 C 语言和一个将 C 编译成购买者拥有的机器的低级机器语言的编译器。从某种意义上说,不同的机器有不同的C。
A breakthrough in computation was the development of standard high-level programming languages, such as C from Bell Labs, that ran on any computer. A user writes a program in an English-like language. This program is passed through a special program that the programmer doesn’t have to understand, called a compiler, which converts the standard programming language into the machine language of a specific computer. When someone purchases the Unix system, for example, it comes complete with the high-level C language and a compiler for C into the low-level machine language for the machine that the purchaser owns. In a sense, there are different Cs for different machines.
同样,RenderMan 使图片制作者不必了解任何一家公司的渲染硬件的细节。当您购买 RenderMan 时,您将获得它的着色语言、该语言的编译器以及支持该语言的任何特定硬件的完整渲染系统。比如说,一个电影制作人只需要知道 RenderMan 的着色语言,而 RenderMan 系统会在幕后处理剩下的事情——像素的生成,可以这么说。
Similarly, RenderMan frees a picture maker from having to know the specifics of any one company’s rendering hardware. When you buy RenderMan, you get its shading language, a compiler of that language, and a complete rendering system for any specific hardware that supports the language. A moviemaker, say, has only to know RenderMan’s shading language, and the RenderMan system takes care of the rest—the generation of the pixels—behind the scenes, so to speak.
领导 RenderMan 标准的人是 Pat Hanrahan,他是皮克斯公司成立后的第一批员工之一。Pat 是一个温和的男人,他从蠕虫的世界来到计算机图形的世界。
The person who led the charge to the RenderMan standard was Pat Hanrahan, one of Pixar’s first hires after the founding of the company. Pat is a gentle man with a ready smile who came from a world of worms to the world of computer graphics.
作为威斯康星大学的研究生,他专门研究蛔虫的神经结构,蛔虫是世界上分布最广的寄生虫,可能感染了 10 亿人。这种大型蛔虫可以达到一英尺长,它们的菌落生活在肠道、肺部和血液中。是什么让帕特从恶心的蠕虫变成了漂亮的像素,这是一个谜,但这就是发生的事情。在卢卡斯影业团队离开后,他加入了纽约理工学院的实验室,开始了他的新方向。然后他找到了从纽约到加利福尼亚的路,成为皮克斯的另一个常驻天才。
As graduate work at the University of Wisconsin, he specialized in the neural structure of Ascaris lumbricoides, the most widespread parasitic worm in the world, infecting probably a billion people. This large roundworm can reach a foot in length, with colonies of them living in the intestines, lungs, and bloodstream. It’s a puzzle as to what led Pat from disgusting worms to beautiful pixels, but that’s what happened. He set out in his new direction by joining the Lab at NYIT, after the Lucasfilm contingent had departed. Then he found his way from New York to California to become yet another of Pixar’s resident geniuses.
将团队其他部分的人员引诱到计算机图形学领域的传统仍在继续。题词的吉姆劳森以前是卢卡斯影业数字音频项目的一部分。和 Pat Hanrahan 一样,他也在皮克斯成立后不久就加入了。Jim 和 Pat 合作将 Rob Cook 的内部着色语言强化为面向外部世界的 RenderMan 着色语言。Lawson 将为 RenderMan 编写“幕后”像素生成器。47
The tradition of seducing personnel from other parts of the group into computer graphics continued. Jim Lawson, of the epigraph, was formerly part of the digital audio project at Lucasfilm. Like Pat Hanrahan, he also joined Pixar shortly after its founding. Jim and Pat worked together to toughen up Rob Cook’s internal shading language into the RenderMan shading language that was intended for the outside world. Lawson would write the “behind the scenes” pixel generator for RenderMan.47
这里不是提供 RenderMan 详细信息的地方,但其现在标准着色语言中的一些官方术语的简短列表肯定不会让您感到惊讶:凹凸、深度、phong、折射和纹理。该语言允许您定义光源、阴影和像素散布器。以及更多。
This is not the place to give RenderMan details, but a short list of some of the official terms in its now-standard shading language surely won’t surprise you: bump, depth, phong, refract, and texture. The language lets you define light sources, shadows, and pixel spreaders. And much more.
RenderMan 将艺术家与工具分离。卢卡斯影业和皮克斯以外的任何人都很难使用 Carpenter 和 Cook 的渲染器 Reyes。RenderMan 将这项技术提供给皮克斯以外的一群新人——艺术家和技术人员。有了它,建模程序 A 可以与 RenderMan 渲染器 X 对话,建模程序 B 可以与 RenderMan 渲染器 Y 对话。尽管所有部分(A、B、X 和 Y)都是完全独立开发的,但一切正常。从某种意义上说,有不同的 RenderMen [ sic] 适用于不同的计算机。换句话说,人们可以使用该语言编写不同的 RenderMan 渲染器,这些渲染器可以与各种建模程序一起工作并在各种计算机上运行。从固定着色技术到着色语言(Cook)的转变是巨大的,从特定语言到标准语言(Hanrahan)的飞跃又是巨大的。
RenderMan decoupled the artist from the tool. It was difficult for anyone outside of Lucasfilm and Pixar to use Carpenter and Cook’s renderer Reyes. RenderMan made the technology available to a new group of people—both artists and technicians—outside of Pixar. With it, modeling program A could talk to RenderMan renderer X, and modeling program B could talk to RenderMan renderer Y. It all worked, even though all the pieces (A, B, X, and Y) were developed completely independently. In a sense, there are different RenderMen [sic] for different computers. In other words, people can use the language to write different RenderMan renderers that work with various modeling programs and run on various computers. Moving from fixed shading techniques to a shading language (Cook) was huge, and the leap from a specific language to a standard language (Hanrahan) was huge again.
创建一个好的标准很难——它必须设计得非常好才能普遍工作并随着时间的推移而保持不变。以前有许多图形标准,但 Hanrahan 是第一个包含可编程着色的标准。它所提供的灵活性是 RenderMan 能经受 30 年之久的原因。
Creating a good standard is hard—it must be very well designed in order to work universally and to hold up over time. There had been many previous graphics standards, but Hanrahan’s was the first to incorporate programmable shading. And the flexibility that it provided is why RenderMan has endured for 30 years.
RenderMan 于 1990 年出版,已成为好莱坞基于计算机图形学中心法则的视觉效果和动画的主打产品。RenderMan 不是一次创建一种算法来为三角形着色,每个算法都与其他算法不兼容,而是为所有此类算法建立了一个共同的基础。它是渲染过程的生产力增强器。48
RenderMan, published in 1990, has become a Hollywood staple for visual effects and animation based on the Central Dogma of computer graphics. Instead of creating one algorithm at a time for shading triangles, each incompatible with all the others, RenderMan established a common basis for all such algorithms. It’s a productivity enhancer for the process of rendering.48
该行业已经为开发者提供了丰厚的回报。Rob Cook、Loren Carpenter 和 Ed Catmull 因在 2001 年的贡献而获得奥斯卡奖,这是有史以来第一个授予计算机科学的奥斯卡奖。Pat Hanrahan 获得了三项技术奥斯卡奖,一项与 Loren、Rob、Ed 和其他人为 RenderMan 分享。Rob、Ed 和 Pat 都获得了 Siggraph 的 Coons 奖,这是它的最高奖项。而且,当我在 2020 年 3 月完成这份手稿时,我刚刚被告知 Ed Catmull 和 Pat Hanrahan 获得了图灵奖。49
And the industry has rewarded its developers richly. Rob Cook, Loren Carpenter, and Ed Catmull received an Academy Award for rendering contributions in 2001, the first Oscar ever awarded for computer science. Pat Hanrahan has won three technical Academy Awards, one shared with Loren, Rob, Ed, and others for RenderMan. Rob, Ed, and Pat have all been honored with Siggraph’s Coons Award, its highest award. And, as I complete this manuscript in March 2020, I’ve just been told that Ed Catmull and Pat Hanrahan have been presented the Turing Award.49
摩尔定律终于超过了另一个数量级——达到了 100,000X步。迪士尼于 1991 年(皮克斯创立五年后)挺身而出,并说:“让我们制作你一直想要的电影吧。” 他们资助了它,挽救了史蒂夫乔布斯的面子(和投资)和皮克斯公司。这部电影不是史蒂夫·乔布斯的主意,正如有时被误传的那样。乔布斯正在运行 NeXT。他从不谈论电影。这是迪士尼自 1970 年代以来的想法,也是我们的梦想和目标。
Moore’s Law finally ticked over another order of magnitude—to the 100,000X step. Disney stepped forward in 1991—five years after the creation of Pixar—and said, “Let’s make that movie you’ve always wanted.” They financed it, and saved Steve Jobs’s face (and investment) and Pixar the company. The Movie was not Steve Jobs’s idea, as sometimes misreported. Jobs was running NeXT. He never talked about movies. It was Disney’s idea and our dream and goal since the 1970s.
这就是电影,正是我们苦苦等待了五年的电影。但有一个问题。我们的首席动画师约翰·拉塞特拒绝与迪士尼合作。毕竟他们解雇了他。他坚信,时任迪士尼动画主管的杰弗里·卡岑伯格是一个他无法共事的暴君。所以,埃德和我又一次疯狂了。
This was The Movie, exactly what we’d been waiting for, for five painful years. But there was a problem. Our lead animator, John Lasseter, refused to work with Disney. They had fired him after all. And he was convinced that Jeffrey Katzenberg, then head of animation at Disney, was a tyrant he couldn’t work with. So, Ed and I were frantic yet again.
卡岑伯格明白了这个问题并陷入了困境。1991 年,他在迪斯尼伯班克总部召开了一次会议,旨在说服约翰他可以与迪斯尼合作,也可以与他自己合作。Ed 和我参加了这个重要的会议。约翰·拉塞特和比尔·里夫斯也是如此,我们紧密的动画师和程序员二人组。史蒂夫乔布斯的出现大概是为了评估暴君卡岑伯格。
Katzenberg understood the problem and stepped into the lurch. In 1991 he called a meeting at Disney’s Burbank headquarters designed to convince John that he could work with Disney and with himself. Ed and I attended this crucial meeting. So did John Lasseter and Bill Reeves, our tight animator-programmer duo. And Steve Jobs came along presumably to size up fellow tyrant Katzenberg.
卡岑伯格主持了会议。他首先让我们感到惊讶。“我试图从你那里雇佣约翰,但他很忠诚,不会离开。” 我们不知道。约翰没有告诉我们。“所以为了发挥他的才华,迪士尼将与皮克斯合作制作这部电影。” 我套用卡岑伯格的话说:“约翰,我知道你认为我是个暴君,所以我们今天要做的就是这个。我会离开房间,史蒂夫也会。然后,如果你愿意,其他人可以互相交流几个小时,并提出最棘手的问题,比如这里的真实情况,我的真实情况。” 这就是发生的事情。尤其是约翰,在下午剩下的时间里,他与迪士尼的动画师和导演进行了深入交谈。
Katzenberg ran the meeting. He started by surprising us. “I tried to hire John away from you, but he’s loyal and won’t leave.” We didn’t know that. John hadn’t told us. “So in order to get at his talent, Disney will work with Pixar to make this movie.” I paraphrase Katzenberg: “John, I know you think I’m a tyrant, so what we’re going to do today is this. I’ll leave the room, and Steve will too. Then the rest of you can mingle with one another for hours if you wish and ask the hardest questions you can about what it’s really like around here, what I’m really like.” And that’s what happened. John, in particular, talked deeply with animators and directors at Disney the rest of the afternoon.
一天结束时,约翰和我在其他人面前一起走一小段路,回到我们租来的汽车,开车去伯班克的机场。“你怎么看?” 我紧张地问道。“我能做到,”约翰说。我当时就知道这笔交易是出于所有实际目的。它仍然必须进行谈判和签订合同,但没有任何实质性内容。
At the end of the day, John and I were walking together a small distance in front of everybody else returning to our rental car for the drive to Burbank’s airport. “What do you think?” I asked nervously. “I can do it,” John said. I knew right then that the deal was on for all practical purposes. It still had to be negotiated and contracted, but there was nothing substantive in the way.
但我不得不离开。我不得不让史蒂夫乔布斯离开我的生活。大约一年前,他在臭名昭著的“白板事件”中以完全欺凌、专横的方式攻击了我。沃尔特·艾萨克森 (Walter Isaacson) 的著作史蒂夫·乔布斯 (Steve Jobs ) 对此进行了简要描述。50
But I had to leave. I had to get Steve Jobs out of my life. About a year earlier he had attacked me in full bullying, tyrannical mode in what is infamously known as “the whiteboard incident.” It’s described summarily in Walter Isaacson’s book Steve Jobs.50
现在,我知道电影 15 年前的愿景即将实现,我可以离开皮克斯了。因此,我与皮克斯协商离开,创办了一家新公司,Altamira Software(为洞穴,并使用另一个西班牙名称)。它基于一个像素编辑产品主要基于 Alpha 通道。该产品于 1994 年上市,几个月后微软收购了该公司。
Now, knowing that the 15-year-old vision of The Movie was about to be realized, I could leave Pixar. So I negotiated my departure from Pixar to start a new company, Altamira Software (for the cave, and with another Spanish name). It was based on a pixel-editing product heavily based on the alpha channel. The product hit the market in 1994, and Microsoft bought the company a couple of months later.
Ed Catmull 于 1991 年 7 月完成了与迪士尼的电影交易。我们在皮克斯用香槟庆祝它,我在那里一直维持着一个办公室,直到 1991 年 9 月。51
Ed Catmull closed the movie deal with Disney in July 1991. We celebrated it with champagne at Pixar where I maintained an office until September 1991.51
然后就发生了!在接下来的四年里,皮克斯在迪斯尼的帮助下完成了电影,并于 1995 年首映。该团队首次在纽约理工大学聚首已经 20 年,距离他们在卢卡斯影业扩张已有 15 年。皮克斯成立已经快 10 年了。玩具总动员汇集了我们在本章中遇到的天才们强大的技术和艺术创造力,而这些天才又建立在前几章中介绍的数十年的才华和成就之上。这部电影是数字大融合到来的恰当典范。虽然集中在 Digital Light 的数字电影部分,但它的技术很快就会影响到其他部分,如视频游戏和虚拟现实。几年之内,三维动画特征将取代二维 cel 动画。Digital Light 不止于此。它已经接管了。
Then it happened! During the next four years, Pixar completed The Movie with Disney’s help and it premiered in 1995. It had been 20 years since the group first got together at NYIT, and 15 years since they expanded at Lucasfilm. It was approaching 10 years since Pixar’s founding. Toy Story had brought together a powerful outpouring of technical and artistic creativity from the geniuses we’ve met in this chapter, who had in turn built atop the decades of talent and achievement presented in previous chapters. The movie was a fitting exemplar of the arrival of the Great Digital Convergence. Although concentrated in the digital-movies part of Digital Light, its technologies would soon influence other parts, like videogames and virtual reality. Within a few years, three-dimensional animated features would replace two-dimensional cel animation. Digital Light had more than arrived; it had taken over.
《玩具总动员》几乎在电影“装在罐子里”之后就大获成功。皮克斯和迪斯尼把它带到纽约市,让评论家们第一次看到,他们的热情是电动的。
And Toy Story was wildly successful almost as soon as the movie was “in the can.” Pixar and Disney took it to New York City for a first glimpse by critics, and their enthusiasm was electric.
乔布斯看到了这一点,做出了一个绝妙的举动,挽救了他的商业声誉,使他成为了亿万富翁。他决定将皮克斯公之于众,只不过是对玩具总动员的承诺。皮克斯几乎没有现金,除了出售公司失败的硬件部分的零碎,将我的公司 Altamira 出售给微软的百分比,以及微软和 Silicon Graphics 支付的运动模糊专利许可费。 ,吉姆克拉克的第一家公司。皮克斯的公开募股发生在 1995 年 11 月 29 日,进展顺利,是当年最大的一次,甚至超过了吉姆·克拉克的第二家公司网景。52
Jobs saw this and made a brilliant move that salvaged his business reputation and made him a billionaire. He decided to take Pixar public on nothing more than the promise of Toy Story. Pixar had little cash except what it had from selling off bits and pieces of the failing hardware part of the company, from its percentage of the sale of my company Altamira to Microsoft, and from motion-blur patent license fees paid by Microsoft and Silicon Graphics, Jim Clark’s first company. The public offering of Pixar occurred on November 29, 1995, and went very well, the biggest of the year, outstripping even that of Jim Clark’s second company, Netscape.52
从《玩具总动员》 (1995)开始,关于皮克斯的成功已经写了很多,我在这里只多说一点。到千禧年左右,皮克斯制作了另外三部成功的数字电影:虫虫的生活(1998)、玩具总动员 2 (1999) 和Monsters, Inc. (2001)。截至撰写本文时(2020 年),皮克斯已经制作了 23 部数字电影。迪士尼终于在 2006 年以超过 70 亿美元的价格收购了这家公司。考虑到 1970 年代我们弯着膝盖接近他们时,他们本可以免费获得我们,这是令人震惊的,在 1980 年代中期乔布斯是我们的最后机会,万福玛丽投资人时以 1000 万美元,在 1980 年代后期以 5000 万美元他会把我们卖给任何人,让自己变得完整和不尴尬。
So much has been written about Pixar’s successes starting with Toy Story (1995) that I will say only a little more here. By the millennium or thereabouts, Pixar had produced three other successful digital movies: A Bug’s Life (1998), Toy Story 2 (1999), and Monsters, Inc. (2001). As of this writing (2020), Pixar has produced 23 digital movies. Disney bought the company—finally!—in 2006 for over $7 billion. This is astounding considering they could have had us for free in the 1970s when we approached them on bended knee, for $10 million in the mid-1980s when Jobs was our last-chance, Hail Mary investor, and $50 million in the late 1980s when he would have sold us to anyone to make himself whole and unembarrassed.
Pacific Data Images 经营着一家聪明的公司。他们不是第一家计算机图形公司,但他们比 1970 年代末和 1980 年代初同时成立的所有其他公司都长寿。他们使用现成的计算机,从未犯过购买或租赁超级计算机的错误。他们通过制作数百个广播电视图形(例如飞行徽标)来自强不息。1985 年,他们提出了一部数字电影,但无法资助。考虑到我们大约在同一时间得出结论认为猴子电影不可行,这并不奇怪。但这也意味着皮克斯可能应该将它们视为电影的竞争对手。
Pacific Data Images ran a smart company. They weren’t the first computer graphics company, but they outlasted all the others founded about the same time in the late 1970s and early 1980s. They used off-the-shelf computers and never made the mistake of buying or leasing supercomputers. They bootstrapped themselves into longevity by producing hundreds of broadcast television graphics, such as flying logos. In 1985 they proposed a digital movie but were unable to fund it. This is not surprising considering that we were concluding about the same time that the Monkey movie was not feasible. But this also means that Pixar should have probably been considering them as a competitor for The Movie.
PDI 在 1980 年代后期创作了几部短片,就像皮克斯在同一时间制作的“珠宝”一样。一些 PDI 珠宝是Opéra Industriel (1986)、Burning Love (1988) 和Locomotion (1989)。53
PDI created several short films in the late 1980s, much as Pixar had with its “jewels” at about the same time. Some PDI jewels were Opéra Industriel (1986), Burning Love (1988), and Locomotion (1989).53
PDI 没有放弃电影的想法,于 1991 年成立了角色动画小组,以获得数字电影所需的技能和艺术家。埃里克·达内尔(Eric Darnell)当时加入了,他是一名动画师,刚从加州艺术学院毕业,这所迪斯尼创办的学校培养了约翰·拉塞特和布拉德·伯德(尽管达内尔毕业于实验动画而不是角色动画)。他很快创造了自己的一颗宝石,气体星球(1992)。54
Not giving up on the movie idea, PDI formed a Character Animation Group in 1991 to gain the skills and artists it needed for digital movies. Eric Darnell joined then, an animator just graduated from CalArts, the same Disney-founded school that trained John Lasseter and Brad Bird (though Darnell graduated in experimental animation rather than character animation). He soon created a jewel of his own, Gas Planet (1992).54
1994 年,杰弗里·卡岑伯格 (Jeffrey Katzenberg) 在与总裁迈克尔·艾斯纳 (Michael Eisner) 以及沃尔特 (Walt) 的侄子罗伊·E·迪斯尼 (Roy E. Disney) 的权力斗争中离开了迪士尼。然后,史蒂文·斯皮尔伯格、卡岑伯格和大卫·格芬在 1994 年末利用微软联合创始人保罗·艾伦的主要资助共同创立了梦工厂 SKG(代表三位联合创始人)。
In 1994 Jeffrey Katzenberg departed Disney in a power struggle with its president, Michael Eisner, and with Walt’s nephew, Roy E. Disney. Then Steven Spielberg, Katzenberg, and David Geffen cofounded DreamWorks SKG (for the three cofounders) in late 1994 using a major funding contribution from Microsoft cofounder, Paul Allen.
DreamWorks SKG 于 1995 年收购了 Pacific Data Images 的大部分但少数股权。新公司更名为 PDI/DreamWorks,后来当 PDI 的少数股权转变为多数股权时,DreamWorks Animation 更名为梦工厂动画。我将在这里使用梦工厂作为名称。它于 1998 年 10 月 2 日发行了其第一部数字电影《Antz》,由 Eric Darnell 联合导演。55
DreamWorks SKG bought a large but minority part of Pacific Data Images in 1995. The new outfit was renamed PDI/DreamWorks, and later DreamWorks Animation when the minority interest in PDI was converted to a majority. I’ll use DreamWorks as the name here. It released its first digital movie, Antz, on October 2, 1998, co-directed by Eric Darnell.55
在安兹之后,埃里克在梦工厂的第二部数字电影《怪物史莱克》(2001)中担任故事艺术家。2001 年为最佳动画长片设立了一个新的奥斯卡类别。史瑞克是第一部赢得该奖项的数字电影,击败了皮克斯的怪物公司(2001 年)。
After Antz, Eric worked as a story artist on Shrek (2001), DreamWorks’s second digital movie. A new Oscar category was created in 2001 for Best Animated Feature Film. Shrek was the first digital movie to win it, beating out Pixar’s Monsters, Inc. (2001).
梦工厂在本文中(2020 年)制作了许多数字电影,包括马达加斯加系列中的四部、史瑞克系列中的五部、功夫熊猫系列中的六部和驯龙高手系列中的三部。
DreamWorks has of this writing (2020) created many digital movies, including the four in the Madagascar franchise, five in the Shrek franchise, six in the Kung Fu Panda franchise, and three in the How to Train Your Dragon franchise.
PDI 和梦工厂应该得到比我在本章中更多的关注。我只讲述了与创建皮克斯的流程有关的故事。这个群体所取得的许多技术进步值得某人充分对待,而个人球员应该每个人都得到发展。MAGI和Blue Sky也应如此,总结如下。
PDI and DreamWorks deserve much more attention than I have room for in this chapter. I’ve only told their story in relation to the flows that created Pixar. The many technological advances made by this group deserve full treatment by someone, and the individual players should each be developed. The same should be said for MAGI and Blue Sky, summarized next.
他们将自己的想象力投射到其中并对其进行膨胀,所以看起来角色几乎就像从屏幕上伸出来一样。座位和屏幕之间的空间充满了这种非常明显的参与能量,而这种能量的波动——或者说它的强度——成为了我从那一刻开始关心的唯一衡量创意完整性的标准。
They were projecting their imaginations into it and inflating it, so it seemed almost as if the characters were reaching off the screen. The space between the seats and the screen was filled with this very palpable energy of engagement and the fluctuation of that—or the intensity of it—became the only measure of creative integrity that I’ve ever cared about from that moment forward.
——克里斯·韦奇,《冰河世纪》(2002 年)的导演,关于首映时的观众56
—Chris Wedge, director of Ice Age (2002), about the audience at its first screening56
MAGI 和 NYIT 在 1970 年代后期都是纽约州北部的计算机图形工作室,它们的位置相距约 20 英里,因为乌鸦飞了,但只有乌鸦飞了。纽约市介于两者之间。
MAGI and NYIT were both downstate New York computer graphics studios in the late 1970s, located about 20 miles apart as the crow flies—but only as the crow flies. New York City lay between.
Carl Ludwig 是 MAGI 的 Celco 顾问,他在 1970 年代后期与 NYIT 的 David DiFrancesco 合作,当时 David 正在考虑购买一台 Celco 电影录像机。MAGI 在迪斯尼的《创》(1982 年)中使用了 Celco 记录仪,随后聘请了路德维希,后者继续改进 MAGI 的光线追踪软件。
Carl Ludwig was the Celco consultant at MAGI who worked with NYIT’s David DiFrancesco in the late 1970s when David was considering the purchase of a Celco film recorder. MAGI used a Celco recorder for its part of Disney’s Tron (1982), and subsequently hired Ludwig, who proceeded to improve MAGI’s ray-tracing software.
Chris Wedge 是Tron的主要 MAGI 动画师。然后他和迪斯尼的约翰·拉塞特在 1983 年在那里合作进行了 Wild Things 测试,拉塞特负责二维前景,楔子负责三维背景。
Chris Wedge was the principal MAGI animator on Tron. Then he and Disney’s John Lasseter worked together on the Wild Things test there in 1983, Lasseter on the two-dimensional foregrounds and Wedge on the three-dimensional backgrounds.
1987 年 2 月,MAGI 关闭后,Wedge、Ludwig 和其他四人在东海岸共同创立了 Blue Sky Studios。这几乎是在 Ed 和我于 1986 年 2 月在西海岸共同创立皮克斯之后的一年。Blue Sky 在最初的几年里靠电视广告和故事片效果维持生计。
In February 1987 Wedge, Ludwig, and four others from MAGI cofounded Blue Sky Studios on the East Coast after MAGI shut down. This was almost exactly a year after Ed and I cofounded Pixar on the West Coast in February 1986. Blue Sky stayed afloat for the first few years with television commercials and feature-film effects.
他们也有他们的珠宝。两个早期的由 Chris Wedge 创建。第一个是在大部分真人电影乔的公寓(1996 年)中的一系列蟑螂电脑动画镜头。韦奇在 1997 年收购蓝天的贡献给 20 世纪福克斯留下了深刻印象。
And they had their jewels too. Two early ones were created by Chris Wedge. The first was a series of computer-animated shots of cockroaches in the mostly live-action movie Joe’s Apartment (1996). And 20th Century Fox was impressed enough by Wedge’s contribution to acquire Blue Sky in 1997.
与此同时,Wedge 还在创作他的第二颗宝石,一部名为Bunny的短电脑动画(1998 年)。它在 1998 年获得了奥斯卡最佳动画短片奖。蓝天已准备好迎接大时代。57
Meanwhile, Wedge was also working on his second jewel, a short computer animation called Bunny (1998). It won an Oscar for Best Animated Short Film in 1998. Blue Sky was ready for the big time.57
由韦奇执导的《冰河世纪》 (2002 年)是该公司在数字电影领域的处女航,是众多成功中的第一次。《冰河世纪》获得 2002 年奥斯卡最佳动画长片提名。截至撰写本文时(2020 年),该公司已经制作了 13 部数字电影,其中仅冰河世纪系列就有 5 部。
Ice Age (2002), with Wedge directing, was the company’s maiden voyage in digital movies, the first of many successes. Ice Age was nominated for an Oscar in 2002 for Best Animated Feature Film. As of this writing (2020) the company has produced 13 digital movies, including 5 in the Ice Age franchise alone.
正如我之前所说,这远远不能满足MAGI和Blue Sky应该得到的全部待遇。但这里不是地方。正确和真实的是,皮克斯、梦工厂和蓝天在很短的时间内用长篇数字电影在千禧年庆祝了伟大的数字融合。
As I’ve said before, this is far short of the full treatment that MAGI and Blue Sky should receive. But here is not the place. What is right and true is that Pixar, DreamWorks, and Blue Sky in short order celebrated the Great Digital Convergence with feature-length digital movies at the millennium.
在最后一章中,我重新对所有 Digital Light 进行了讨论。为了不让 The Movie 和它的同胞让我们眼花缭乱,我们需要重新建立真正巨大的 Digital Light 席卷,其中数字电影部门只是一个例子。
In the final chapter, I reopen the discussion to all Digital Light. Lest the dazzle of The Movie and its siblings blind us, we need to reestablish the truly gigantic sweep of Digital Light, of which the digital movie branch is a mere example.
从 1967 年的第一部彩色像素到千禧年的第一部数字电影,我们在 Epoch 2 计算机图形学的前 30 多年的快速旅程结束了。在那些年里,摩尔定律一直是不屈不挠的参与者。从 1965 年的 1 倍,到千禧年,它爆发到 10,000,000 倍——七个数量级!第一个彩色像素需要它,第一部数字电影更是如此。如果没有摩尔定律和它所代表的创造性工程胜利,这里就不会有故事。
This concludes our quick trip through the first 30-odd years of Epoch 2 computer graphics, from the first color pixels of 1967 to the first digital movies at the millennium. Moore’s Law was the unrelenting player throughout those years. From a factor of 1 in 1965, it exploded to a factor of 10,000,000 at the millennium—seven orders of magnitude! The first color pixels required it, and the first digital movies even more so. There would be no story here without Moore’s Law and the creative engineering triumphs it represents.
我们已经停在了千禧年,就在大型计算机动画工作室赚到数十亿美元之前。从那以后的近二十年里,我几乎没有提到摩尔定律因子已经达到 100,000,000,000 X- 四个数量级!这是正在进行的革命和工作室成功的原始燃料。它终于让 VR 变得实用了。
We’ve stopped at the millennium, just before the big computer animation studios made their many billions of dollars. I’ve barely touched on the almost two decades since then, during which the Moore’s Law factor has reached 100,000,000,000X—four more orders of magnitude! It’s the raw fuel of the ongoing revolution and the studio successes. It’s made VR practical at last.
数码电影只是数码光浩瀚海洋中的一滴水。然而,电影中的许多教训可以用来理解 Digital Light 的其余部分。例如,VR 的叙事形式本质上是两部实时计算的数字电影,每只眼睛一部用于立体效果。添加交互性以获得VR的游戏形式。你所知道的关于建模、渲染、像素、显示、抗锯齿、动画和中心法则的一切都直接从一个领域转移到另一个领域。
The digital movies are only a drop in the vast ocean that is Digital Light. Yet many lessons from the movies can be used to understand the rest of Digital Light. For example, the narrative form of VR is essentially two digital movies computed in real time, one for each eye for the stereo effect. Add interactivity to the mix to get the game form of VR. Everything you know about modeling, rendering, pixels, displays, antialiasing, animation, and the Central Dogma transfers directly from one realm to the other.
这本书的许多章节的主题是(1)一个想法,(2)驱动它的混乱,以及(3)一个暴君——或者不那么贬义地,一个赞助人——经常在不知不觉中提供足够的空间或保护实现的想法。在本章中,主要的想法是计算机可以制作长篇动画电影。推动他们创造的混乱是可怕的摩尔定律爆炸造成的宇宙破坏。理解七个数量级的破坏的唯一方法是简单地生活并驾驭波浪,因为它一次显示一个数量级。
The theme of many chapters of this book has been the schema of (1) an idea, (2) chaos that drives it, and (3) a tyrant—or less pejoratively, a patron—to provide, often unwittingly, enough space or protection to realize the idea. In this chapter, the driving idea was that a computer could make feature-length animated movies. The chaos that drove their creation was the disruption of the universe caused by the awesome Moore’s Law explosion. The only way to understand the disruption of seven orders of magnitude is simply to live it and ride the wave, as it reveals itself one order of magnitude at a time.
至于暴君和赞助人,皮克斯最初的赞助人是亚历山大·舒尔,他首先为我们提供了一个美丽的地方和合适的设备——当时世界上最好的——用于早期开发。亚历克斯叔叔是现在被称为皮克斯的集团的富有赞助人中最奇怪的一个。他是第一个——也是最勇敢的,或者最疯狂的——他们所有人,也是唯一一个失去一切的人。接下来是乔治卢卡斯和史蒂夫乔布斯,他们都成为了亿万富翁,乔布斯的第一个十亿直接来自他对皮克斯的投资。非正式地,在电影和动画章节中讨论了第四位无名赞助人,沃尔特的侄子罗伊迪斯尼。他凭借自己的影响力在两个关键时刻挺身而出。结果,迪士尼公司最终收购了皮克斯,现在拥有它,并从中赚取了数十亿美元。
As for tyrants and patrons, Pixar’s original patron was Alexander Schure, who first provided us a beautiful place and the right equipment—the best in the world at the time—for early development. Uncle Alex was the strangest of the wealthy patrons of the group now known as Pixar. He was the first—so the bravest, or the craziest—of them all, and the only one who lost everything. Next were George Lucas and Steve Jobs, who both became billionaires, with Jobs’s first billion coming directly from his Pixar investment. Informally, there was a fourth and unsung patron, Roy Disney, Walt’s nephew, discussed in the movies and animation chapter. He stepped forward at two crucial times with his influence. As a result, the Disney company eventually purchased Pixar, owns it now, and has made billions from it.
但我们的主导赞助人史蒂夫乔布斯也是我们的主导暴君。大概是为了挽救他的自尊心,他提供了金钱和时间,使我们有可能度过过去几年的地狱,以实现电影的伟大创意。
But our dominant patron, Steve Jobs, was also our dominant tyrant. He provided, presumably to salvage his ego, the money and the time that made it possible for us to ride through the last several years of hell to implement the great idea of The Movie.
史蒂夫与玩具总动员没有任何创造性的关系。拉尔夫·古根海姆(Ralph Guggenheim)在纽约理工学院与卢卡斯影业首次接触并成为皮克斯的《玩具总动员》联合制片人,他在最近的一本书中说:“我会说,在 86 年到 95 年之间,当《玩具总动员》问世时,史蒂夫可能——我没有夸大其词——我不要以为他在九年内来我们大楼的次数不超过九次。” 史蒂夫确实喜欢约翰·拉塞特拜访他并向他展示部分电影结果,这样他就可以畅所欲言了。但就像我和埃德如果可以避免的话,永远不会让史蒂夫进入皮克斯的建筑一样,拉塞特也不会让乔布斯参加皮克斯的故事会。这几乎无关紧要。史蒂夫当时正在经营 NeXT,距离一个半小时路程,严重的财务问题让他忙得不可开交。58
Steve had nothing creatively to do with Toy Story. Ralph Guggenheim, who made first contact with Lucasfilm at NYIT and became Pixar’s coproducer for Toy Story, stated in a recent book, “I would say between ’86 and ’95 when Toy Story came out Steve probably—I’m not exaggerating—I don’t think he was in our building more than nine times in nine years.” Steve did like to have John Lasseter visit him and show him partial movie results so he could talk the talk. But just as Ed and I never let Steve in Pixar’s buildings if we could avoid it, Lasseter never let Jobs into a Pixar story meeting. It hardly mattered. Steve was running NeXT at the time, an hour and a half away, and its serious financial problems kept him busy.58
但乔布斯在对已完成的《玩具总动员》的批评反应中跃跃欲试,并出色地让皮克斯上市。乔布斯的公开募股营销故事的一部分是他的新神话,即他与人共同创立了皮克斯并从一开始就担任首席执行官。这两种说法都不是真的,这是有据可查的。在《玩具总动员》上映时,他确保自己站在镜头前,而不是 Ed Catmull。59
But Jobs leapt at the critical response to the completed Toy Story and—brilliantly—took Pixar public. Part of Jobs’s marketing story for the public offering was his new myth that he had cofounded Pixar and run it as CEO from inception. Neither claim was true, as is well documented. And he made sure he was standing before the cameras at the release of Toy Story, not Ed Catmull.59
我不指望你在读完这些章节后能够渲染电影,但我确实希望从计算机中提取电影的神秘感已经大大降低。该过程本质上是这样的:计算正确代表每个像素位置的平均颜色。这可能是并且通常是复杂的计算。但它是一个计算——一个包含许多步骤的明确定义的过程。这就是计算机所做的。它在每个像素上重复这种计算,对于电影的一帧,它会重复数百万次。然后它再次重复计算,每帧数百万次,超过十万帧。正是 Amplification 的荣耀使得如此多的计算步骤在合理的时间内发生——比如长片的几个月到一年。
I don’t expect you to be able to render a movie after reading these chapters, but I do hope that the mystery of extracting a movie from a computer has been greatly reduced. The process is essentially this: compute what average color properly represents each pixel location. This can be, and often is, a complicated computation. But it’s a computation—a well-defined process of many steps. That’s what a computer does. It repeats this computation at each pixel, millions of times for a frame of a movie. Then it repeats the computations again, millions of times per frame, for over a hundred thousand frames. It’s the glory of Amplification that makes this astonishingly large number of computational steps happen in a reasonable amount of time—say several months to a year for a feature-length movie.
但我无法解释存在于几个人类贡献中的压倒一切的谜团:艺术家创作带有感人情感的故事。动画师启发了那些由几何构造的角色。程序员将数百万个无意义的计算机步骤组织成有意义的计算,以将故事和角色渲染成电影帧。工程师改进了底层芯片技术,以达到前所未有的摩尔定律速度。所有这些都是纯粹的莫名其妙的人类创造力。
But I cannot explain the overriding mystery that resides in the several human contributions: Artists create stories with emotion-provoking characters. Animators inspirit those characters constructed from geometry. Programmers organize millions of meaningless computer steps into meaningful computations to render the stories and characters into movie frames. Engineers improve the underlying chip technology to reach ever more awesome Moore’s Law speeds. All those are pure inexplicable human creativity.
在接下来的最后一章中,我重新审视了理念-混沌-暴君的主题,因为它已被所研究的每一种技术所指导或修改。我还回顾了从各个章节中得出的其他几个一致的教训:简单叙述的不足,技术的谱系,定义每一个的令人惊讶的流程,技术思想的实际简单性——以及它们的美丽——以及真正魔法的存在,至少我们今天(不)理解它,由人类提供。
In the next, closing chapter, I revisit the idea–chaos–tyrant theme as it’s been instructed or modified by each technology studied. And I also review several other consistent lessons derived from the various chapters: the insufficiency of simple narrative, the genealogy of technology, the surprising flows that define each, the actual simplicity of technological ideas—and their beauty—and the existence of true magic, at least as we (don’t) understand it today, provided by human beings.
经典被定义为“被接受为真实的神圣书籍的集合或清单” 。我希望通过这本书确立基于神圣事实而非神话的数字光经典的开端。现在开始这项任务还为时不晚。我们距离新千年只有 20 年,而 Digital Light 将无限期地延伸到未来。60
A canon is defined as “a collection or list of sacred books accepted as genuine.” I hope to establish with this book the beginnings of a canon for Digital Light, based on sacred facts not myths. It’s not too late to begin this task. We’re only two decades into the new millennium, and Digital Light extends indefinitely into the future.60
在引言中,我承诺解释图片是如何与媒体分离的——一头野猪是如何在几千年后从阿尔塔米拉的洞穴壁上小跑的,或者雅克-路易·大卫的英雄传记拿破仑是如何骑着他的骏马离开欧洲的皇家城墙的并进入本书的开篇。
In the introduction I promised to explain how pictures became separated from their media—how a wild boar trotted off the cave wall in Altamira after dozens of millennia, or how Jacques-Louis David’s heroically hagiographic Napoleon rode his mighty steed off the royal walls of Europe and into the opening pages of this book.
这种解释要求我提出一个被低估的关键想法——像素。这直接导致了数字光,这是一个由像素介导的广阔图像领域,主宰着现代视觉世界。事实上,它是如此之大,以至于我有选择地修剪了 Digital Light 部分以适应书中的内容,同时忠实地代表了整个主题。出乎意料的复杂像素将它们全部绑定在一起,并可以将所选部分的细节推广到整个域。
That explanation required me to develop an underappreciated key idea—the pixel. And that led directly to Digital Light, the vast pictorial domain mediated by pixels which dominates the modern visual world. It’s so vast, in fact, that I selectively pruned the Digital Light parts to fit inside the book while faithfully representing the topic as a whole. The unexpectedly sophisticated pixel binds it all together and makes it possible to generalize the specifics of the chosen parts to the entire domain.
在最后一章中,我将镜头拉远到足以让我们再次看到所有数码灯。我讨论了自从我选择故事的终点以来的两年内发生的事情,即千年。根据摩尔定律,这是四个数量级之前的数据,而X在此期间计算机的功能已经提高了 10,000 倍——符合“定律”。
In this final chapter I zoom out far enough for us to see all Digital Light again. I discuss what’s happened in the two decades since my chosen end point for the story, at the millennium. That was four orders of magnitude ago, by Moore’s Law, and computers have become 10,000X more powerful in the interim—compliant with the “Law.”
革命在继续,所以我也尝试做“数量级”这个短语所暗示的不可能的事情:预测随着摩尔定律放大因子在 2025 年达到 1万亿倍时接下来会发生什么,然后...... X. . 它不是无穷大,但数字仍然大得令人难以置信。那未来会怎样?
The revolution proceeds, so I also attempt to do what the phrase “orders of magnitude” suggests is impossible: predict what might happen next as the Moore’s Law Amplification factor races for 1 trillion X in 2025, and then . . . it’s not quite infinity and beyond, but the numbers are nevertheless mindbogglingly big. What might that future hold?
但首先,让我们回顾和评论关键的基本技术点。
But first, let’s review and comment on the key fundamental technological points.
数码灯是由像素组成的任何图片。这是一个非常广泛的类。它包括当今世界上几乎所有的图片。事实上,由于数字爆炸,Digital Light 包含了几乎所有曾经存在的图片。但这只是成为现实最近,从 2000 年左右开始,即千禧年——在一个我称之为大数字融合的不为人知的事件中。这种变化悄无声息地悄悄袭来——而且很快——似乎是一夜之间。所有媒体类型都融合为一个通用数字媒体,比特。图片与其显示的分离变得完整。但是,融合怎么可能是分离呢?
Digital Light is any picture composed of pixels. It’s a very broad class. It includes almost all the pictures in the world today. In fact, because of the digital explosion, Digital Light includes nearly all the pictures that have ever existed. But that became true only recently, beginning around the year 2000, the millennium—in an unheralded event I call the Great Digital Convergence. The change crept upon us quietly and unremarked—and quickly—seemingly overnight. All media types converged into one—the universal digital medium, bits. The separation of pictures from their display became complete. But how could a convergence be a separation?
答案恰恰在于像素(图片元素的缩写)和显示元素之间的区别。这些不同类型的混为一谈仍然是当今世界上最普遍的技术混淆之一。两者通常都被称为“像素”,但事实并非如此。像素是视觉场景中某一点的数字化样本。我们看不到一个点,因此我们看不到一个像素。我们可以看到的显示器上的小发光区域是从底层看不见的像素进行的模拟重建。我们称这样一个微小的发光点为显示元件。
The answer lies exactly in the difference between a pixel—short for picture element—and a display element. The conflation of these distinct kinds remains one of the most prevalent technical confusions in the world today. Both are often called “pixels,” but that just cannot be. A pixel is a digitized sample of a visual scene at a point. We can’t see a point, hence we can’t see a pixel. The little glowing area on a display that we can see is an analog reconstruction from an underlying, unseen pixel. We call such a tiny glowing spot a display element.
显示元件将数字像素作为输入并输出模拟色光斑点。我们说一个像素必须被一个显示元素散布才能被看到。那些颜色的斑点——顺便说一句,它们几乎不是小方块——重叠形成一个平滑的连续图片。
A display element takes a digital pixel as input and outputs an analog blob of colored light. We say that a pixel must be spread by a display element to be seen. Those blobs of color—which, by the way, are hardly ever little squares—overlap to form a smooth continuous picture.
像素是离散的、尖锐的、分离的、数字的和不可见的。显示元素(散布像素)发出平滑、连续、重叠、模拟,当然还有可见光。
Pixels are discrete, spiky, separated, digital, and invisible. Display elements—spread pixels—emit smooth, continuous, overlapping, analog, and of course visible glows.
像素是普遍有效的,但显示元素远非普遍。显示元素因设备和制造商而异。
Pixels are universally valid, but display elements are far from universal. Display elements differ from device to device and manufacturer to manufacturer.
像素简洁地代表一张图片。由这些像素驱动的显示元素显示它。这正是改变现代图片世界的图片与其显示的分离。. . 并呼吁我在本书中努力澄清像素/显示混淆。
Pixels succinctly represent a picture. Display elements, driven by those pixels, display it. That’s exactly the separation of a picture from its display that has changed the modern picture world . . . and called for my efforts in this book to clarify the pixel/display confusion.
当所有图片都可以用像素表示时,对其他媒体类型的需求就消失了。这是大数字融合的时刻。因此,数字像素与模拟显示元素的分离使许多模拟媒体类型能够融合到一种数字或通用媒体中。
When all pictures could be represented by pixels, the need for other media types disappeared. This was the moment of the Great Digital Convergence. Thus, the separation of digital pixels from analog display elements enabled the convergence of many analog media types into the one digital, or universal, medium.
像素是通用的这一事实是大数字融合起作用的原因。我可以将手机中的任何像素发送到我的笔记本电脑、台式机、喷墨打印机、电视机、任意酒店房间的电视机、我妻子的手机或她的笔记本电脑的显示器上,任意演讲厅中的 PowerPoint 投影仪等。或通过互联网连接到您和您的设备。这些设备的显示元素差异很大,但在所有情况下,像素都是相同的。
The fact that pixels are universal is why the Great Digital Convergence works. I can take any of the pixels in my cellphone and send them to the display of my laptop, my desktop, my inkjet printer, my television set, the television set in an arbitrary hotel room, to my wife’s phone, or her laptop, to a PowerPoint projector in an arbitrary lecture hall, etc. Or over the internet to you and your devices. The display elements of these devices vary considerably, but in all cases, the pixels are the same.
我的手机包含数千张图片,每张都有数百万像素。我怀疑你的差不多。显然,这些图片“在里面”某处,但你看不到他们。如果我要求看其中一张图片,那么在那一刻——似乎是瞬间的——像素的扩散发生了,图片显示是从它的像素表示中重建的。
My cellphone contains thousands of pictures, each with millions of pixels. I suspect yours is much the same. Clearly, the pictures are “in there” somewhere but you can’t see them. If I ask to see one of the pictures, then at that moment—seemingly instantaneously—the spreading of the pixels occurs, and the picture display is reconstructed from its pixel representation.
这个方案有效是伟大的采样定理的礼物——数学上的胜利。它发生得如此之快且分辨率如此之高的事实是伟大的摩尔定律的礼物——一个工程奇迹。
That this scheme works is a gift of the great Sampling Theorem—a mathematical triumph. The fact that it happens so fast and at such high resolution is a gift of the great Moore’s Law—an engineering miracle.
这一计划的安静但革命性的转变恰巧发生在千禧年。不久前,它成为标准假设我们可以随时随地看到我们的像素。总会有一种显示设备,一种理解通用媒体的设备,可供我们使用,以供我们观赏。这就是数字大融合的意义所在。
The quiet but revolutionary changeover to this scheme happened coincidentally at the millennium. It became standard then—not very long ago—to assume we could see our pixels whenever and wherever we wanted. There would always be a display device, one that understood the universal medium, available to us for our viewing pleasure. That’s the meaning of the Great Digital Convergence.
但究竟什么是像素?它们的离散网格——一个尖尖的钉床——如何准确地代表一个平滑的视野?Digital Light 的基本定理(对“真理”的幻想)回答了这一切。这是采样定理,由 Vladimir Kotelnikov 在 1933 年以完整的现代形式带给我们。他令人惊讶的数学结果是所有现代视觉媒体(以及音频)的支柱。该定理说,要准确地表示一个视野,请在规则间隔的点网格(因此是钉床)上对其进行采样,其中间隔必须满足某个标准:样本间隔的频率必须超过最高频率的两倍场景中的傅立叶频率。
But what exactly is a pixel? And how could a discrete grid of them—a spiky bed of nails—represent a smooth visual field accurately? The fundamental theorem (fancy for “truth”) of Digital Light answers all this. It’s the Sampling Theorem, brought to us in full modern form by Vladimir Kotelnikov in 1933. His surprising mathematical result is the backbone of all modern visual media (and audio too). The theorem says that to accurately represent a visual field, take samples of it on a regularly spaced grid of points—hence the bed of nails—where the spacing must meet a certain criterion: the frequency of spacing of the samples must exceed twice the highest Fourier frequency in the scene.
这足够抽象和不直观,足以解释为什么我们大多数人还不知道像素是什么。让我简明扼要地说明定义,在括号中稍作调整以确保准确性:像素是在(大于)其中最高傅立叶频率的两倍处拍摄的视野的(数字化)样本。只要您记得括号中的位,您就可以在以令人难忘的方式陈述定义时省略它们:像素是在其最高频率的两倍处拍摄的视野样本。
That’s abstract and unintuitive enough to explain why most of us don’t yet know what a pixel is. Let me state the definition succinctly, putting slight adjustments in parentheses for accuracy: A pixel is a (digitized) sample of a visual field taken at (greater than) twice the highest Fourier frequency in it. So long as you recall the parenthetical bits, you’re free to omit them in stating the definition in a memorable way: A pixel is a sample of a visual field taken at twice its highest frequency.
这个奇怪的词频支配着定义,就像采样定理一样。所以我用本书的第一章来解释什么是(傅里叶)频率。Joseph Fourier 的伟大想法是:视野可以表示为不同频率和幅度的波的总和。是音乐。大多数人都明白,音乐是不同频率(音高)和不同幅度(响度)的声波的总和。傅立叶告诉我们,视觉场景也是如此。它是不同频率和幅度的颜色亮度波的总和。
That curious word frequency dominates the definition, as it does the Sampling Theorem. So I devote the first chapter of this book to explaining what a (Fourier) frequency is. Joseph Fourier’s great idea is this: A visual field can be represented as a sum of waves of different frequencies and amplitudes. It’s music. Most people understand that music is a sum of sound waves of different frequencies (pitches) and different amplitudes (loudnesses). Fourier teaches us that the same is true of a visual scene. It’s a sum of color brightness waves of different frequencies and amplitudes.
我正在苏格兰的一座城堡里写这最后一章。在附近的商店出售的薯片产品(图 9.1)将帮助您在下面的解释中想象出沟槽与波纹的关系。
I’m writing this final chapter in a castle in Scotland. A potato chip product (figure 9.1), for sale in a nearby shop, will help you visualize the relationship of furrows to corrugations in my explanation below.
亮度波可以被描绘成一块宽大的波纹金属板或带沟的薯片。它的频率是它在空间上上下摆动的速度(比如芯片每英寸摆动四次),它的幅度是它摆动的最大高度(亮度)。令人惊讶的是,将不同摆动率和亮度高度的波纹或沟纹加在一起,可以为您提供例如您的孩子或宠物、大峡谷或银河系的照片。亮度波是空间的,响度波是时间的,但数学并不能区分两者。对一个人有用的东西也对另一个人有用。这就是傅立叶教给我们的。
A brightness wave can be pictured as an extensive piece of corrugated sheet metal or furrowed potato chip. Its frequency is how fast it wiggles up and down spatially (say four wiggles per inch for the chip), and its amplitude is the maximum height (brightness) of its wiggles. The surprise is that adding together corrugations or furrows of different wiggle rates and brightness heights gives you a picture of, say, your child or pet, or the Grand Canyon, or the Milky Way. Brightness waves are spatial, and loudness waves are temporal, but the math doesn’t distinguish between the two. Whatever works for one also works for the other. That’s what Fourier taught us.
我希望你会开始看到视觉世界的音乐结构——它的频率。它们无处不在,可以迅速成为一种新的观看方式。
I hope you’ll start to see the musical structure of the visual world—its frequencies. They’re everywhere and can quickly become a new way of seeing.
傅立叶的想法是表示模拟视觉场景的另一种模拟方式。Kotelnikov 的想法是用数字方式来表示模拟视觉场景。他的采样定理从傅立叶表示开始,告诉我们如何从中获取像素,然后在我们需要时如何从中查看原始场景。正是采样定理使像素定义的后半部分——最高傅里叶频率位的两倍——如此重要。第二章解释了这种魔法是如何运作的,这证明了将第一章专门用于傅里叶波是合理的。
Fourier’s idea is an alternative analog way to represent an analog visual scene. Kotelnikov’s idea is a digital way to represent an analog visual scene. His Sampling Theorem starts with the Fourier representation and tells us how to take pixels from it, and then how to view the original scene from them when we so desire. It’s the Sampling Theorem that makes the second half of the pixel definition—the twice the highest Fourier frequency bit—so important. The second chapter explains how this magic works, which justifies devoting the first chapter to Fourier’s waves.
第二章的另一个目的是表明数字并不比模拟少。采样似乎意味着样本之间无限量的信息丢失了——数字只是一个近似值——但事实并非如此。如果正确应用采样定理,则证明数字不会丢弃任何东西。相反,它是对无穷大的极其巧妙的重新包装。
Another purpose of the second chapter is to show that digital is not somehow less than analog. Taking samples seems to imply that the infinite amount of information between samples is lost—that digital is only an approximation—but it’s not so. The Sampling Theorem, if correctly applied, proves that digital discards nothing. Instead, it’s an extremely clever repackaging of infinity.
Digital Light 的一半——制作部分(相对于拍摄部分)——源自计算机。所以在第三章中,我解释了数字光的第三个伟大的基本思想:计算,以及使计算快速进行的称为计算机的机器。. . 和电脑动画电影成为可能。
Half of Digital Light—the make part (as opposed to the take part)—originates in computers. So in the third chapter I explain the third great foundational idea of Digital Light: computation, and the machines called computers that make computations go fast . . . and computer-animated movies possible.
中心思想很容易理解:计算是一个仔细的过程,通过将其分解为一系列更小、更简单的步骤来完成。但那句无伤大雅的句子并不像看起来那样平淡无奇。它包含众多。
The central idea is easy to understand: a computation is a careful process accomplished by breaking it into a sequence of smaller, simpler steps. But that innocuous sentence is not nearly as pedestrian as it might seem. It contains multitudes.
1936 年年轻的剑桥学生艾伦·图灵是第一个完全掌握它、命名它并发现其中的惊喜的人。有前人看过计算的承诺——莱布尼茨、巴贝奇、洛夫莱斯——但最终并完全掌握了计算的是图灵,他以惊人的天才一击。他用一台简单的机器解决了一个困难的数学问题——这里称为 eProblem。他的解决方案——使用我们现在所说的“图灵机”——彻底改变了世界。这是一台简单得惊人的造纸机,以至于他的导师马克斯·纽曼起初认为它只是一个玩具。
The young Cambridge student Alan Turing in 1936 was the first to fully grasp it, name it, and discover the surprises in it. There were predecessors who glimpsed the promise of computation—Leibniz, Babbage, Lovelace—but it was Turing who finally and completely captured it, in a stroke of amazing genius. He solved a difficult mathematical problem—called the eProblem here—with a simple machine. His solution—using what we now call “a Turing machine”—revolutionized the world. It was a paper machine of such astonishing simplicity that his mentor Max Newman at first thought it only a toy.
图 9.1
Figure 9.1
我用一张名片和一些纸带设计了一个图灵机,以在第 3 章中演示它们是多么简单。它可以在四个方向之一“操作”,它使用六个符号的字母表。而已。但是这台机器可以计算世界上任何可计算的东西。这是图灵最深刻的结果的一个例子:有一台机器可以计算任何其他此类机器可以计算的东西。我们称之为通用图灵机。这就是现代计算机直接产生的想法,也使图灵与他的思想先辈们区分开来。
I designed a Turing machine out of a business card and some paper tape to demonstrate in chapter 3 just how simple they are. It can be “operated” in one of four orientations, and it uses an alphabet of six symbols. That’s it. But this machine can compute anything that is computable in the world. It’s an example of Turing’s most profound result: there is one machine that can compute what any other such machine can compute. We call it a universal Turing machine. That’s the idea from which the modern computer directly springs, and which sets Turing apart from his intellectual forebearers.
但他发现的细节很重要。他表明,任何一台特定图灵机的计算都可以编码成一串符号。我们今天称其为程序,我们通常称程序员为编码员。图灵表明,如果一个程序像数据一样存储在通用机器中,那么该机器可以模拟程序中编码的特定机器。换句话说,它可以计算与特定机器相同的东西。因此,只需更改程序,通用机器就可以计算任何东西。图灵不仅第一次彻底地描述了计算,而且还发明了存储程序计算机。所有现代计算机都是通用存储程序计算机。它们是图灵的想法,旨在快速发展。
But the details of his discovery matter. He showed that the computation of any one specific Turing machine could be encoded into a string of symbols. We call this a program today, and we often call programmers coders. Turing showed that if a program is stored as if it were data in the universal machine, then that machine can simulate the specific machine encoded in the program. In other words, it can compute the same thing that the specific machine does. So, by simply changing the program, the universal machine can compute anything. Not only had Turing thoroughly described computation for the first time, but he had invented the stored-program computer. All modern computers are universal stored-program computers. They are Turing’s idea made to go fast.
但在探讨这意味着什么之前,让我强调计算的奇迹,这是有史以来最深刻的思想之一,但现在却如此普通。图灵的想法曾经而且非常庞大,以至于它包含了所有已知的执行谨慎过程的方法。另一种说法是:计算机是人类制造的最具延展性的工具。可能的计算数量是无法理解的。从来没有人发现过使用存储程序计算机无法完成的细致过程。因此,经过大约 80 年的经验,我们现在认为,仔细处理和计算这两个想法是等价的。
But before exploring what that means, let me stress the marvels of computation, one of the most profound ideas of all time, yet now so ordinary. Turing’s idea was and is so large that it encompasses all known ways of executing careful process. Another way to put it is this: The computer is the most malleable tool that humankind has ever made. The number of possible computations is beyond understanding. Nobody has ever discovered a careful process that cannot be accomplished with a stored-program computer. So, after about 80 years of experience, we now believe that the two ideas, careful process and computation, are equivalent.
计算机有时被认为是一个锋利的、僵化的、确定性的、非常复杂的数字运算机器。有些人认为,这样的机器肯定与微妙、神秘、艺术、优雅或智慧无关。关于人们可以用计算机制作什么样的图片的假设常常被这种误解所影响。这就是为什么在第 3 章中,我打破了五个神话来揭示计算的真正美。
A computer is sometimes thought to be a hard-edged, rigid, deterministic, very complex, number-crunching machine. Such a machine certainly could have nothing to do, some think, with subtlety, mystery, art, grace, or intelligence. Assumptions about what kinds of pictures people can produce with computers are all too often colored by such misperceptions. That’s why, in chapter 3, I bust open five myths to reveal the true beauty of computation.
首先,计算不仅仅是数字运算。它们是关于模式操作的。可以肯定的是,我们经常操纵的流行模式之一是数字,但认为计算机受数字约束是错误的,并且会妨碍我们的想象力。这种特殊误解的部分原因可以追溯到计算机基本上是 0 和 1 的概念,因此本质上是基于数字的。但是计算机中没有小的 0 和 1。0 和 1 都是两种状态的简单名称,通常是现代计算机中的两种电压。我们也可以,但不那么方便,称他们为 Mutt 和 Jeff。计算机是关于改变状态模式的,而不是在做算术。
First, computations are about much more than number crunching. They’re about pattern manipulation. To be sure, one of the popular patterns we often manipulate are numbers, but to think computers are bound by numbers is wrong and hampers our imaginations. Part of this particular misunderstanding can be traced to the notion that computers are basically 0s and 1s and therefore intrinsically based on numbers. But there are no little 0s and 1s in a computer. Both 0 and 1 are simply names for two states, usually two voltages in a modern computer. We could just as well, but not so conveniently, call them Mutt and Jeff. Computers are about changing patterns of states, not doing arithmetic.
其次,认为计算机必须由位组成(当然,有两个状态分别称为 0 和 1)的信念是错误的。我们“操作”的名片机由四种状态组成,而不是两种状态。它是 4 进制的,而不是二进制的。这些状态是名片的方向,而不是数字。但是,正如我在第四章中解释的那样,所有现代计算机都是由比特构成的。事实证明,这个选择是我们通往惊人速度的道路——通往称为放大的第二个计算奇迹——但这不是必需的。
Second, the belief that computers must be made of bits (with two states named 0 and 1, of course) is wrong. The business-card machine we “operate” is made of four states, not two. It’s 4-ary, not binary. And those states are orientations of the business card, not numbers. But, as I explain in the fourth chapter, all modern computers are made of bits. That choice turned out to be our path to awesome speed—to the second miracle of computation called Amplification—but it’s not required.
第三,计算机不一定是电子的。然而,再一次,由于我们对速度的无法抑制的渴望,所有的计算机都是电子的。就像使用比特的选择一样,电子产品最终成为我们实现惊人放大的途径。但这也不是必需的。
Third, computers don’t have to be electronic. Again, however, because of our unquenchable thirst for speed, all computers are electronic. Like the choice of using bits, electronics turned out to be our path to astonishing Amplification. But it’s also not required.
第四,计算机是确定性的,但这并不意味着它看起来的样子。确定性可能是计算中最容易被误解的方面。我以这种方式陈述艾伦·图灵的发现:在小处确定并不意味着在大处预先确定。确实,计算机执行的每一步都很简单且完全确定。确实,必须完全确定任何此类步骤序列的最终结果。但这并不意味着我们可以预测或预先确定结果将是什么。尽管每个步骤都已确定,但通常计算可能无法预测。通常,确定计算将做什么的唯一方法是执行它。
Fourth, computers are deterministic, but that doesn’t mean what it might seem to. Determinism is perhaps the most misunderstood aspect of computation. I state what Alan Turing discovered this way: determined in the small does not imply predetermined in the large. It’s true that each step a computer takes is simple and completely deterministic. And it’s true that the ultimate outcome of any sequence of such steps must be completely determined. But it doesn’t follow that we can predict, or predetermine, what that outcome will be. A computation, in general, may not be predictable despite the fact that every step is determined. In general, the only way to know for sure what a computation will do is to perform it.
这通常不会影响 Digital Light——我们通常知道我们的计算将要做什么——但它可以用来校准我们的计算概念。假设计算机是刚性的和确定性的并不能保证计算公正。有些人认为,由于这种僵化和确定性,计算机不可能成为人脑的模型。但科学家们正在努力研究人工智能 (AI),这是艾伦·图灵首先追求的另一个想法。将以下句子与上一段中关于计算的类似句子进行比较。一般而言,确定人类会做什么的唯一方法是退后一步,看着他们过自己的生活。
This doesn’t normally affect Digital Light—we usually know what our computations are going to do—but it’s offered to calibrate our notions of computation. Assuming computers are rigid and deterministic doesn’t do computation justice. Some have thought that computers couldn’t possibly be a model for the human brain because of that rigidity and determinism. But scientists are hard at work on artificial intelligence (AI), another idea first pursued by Alan Turing. Compare the following sentence to the similar one about computation in the preceding paragraph. The only way to know for sure what human beings will do, in general, is to stand back and watch them live their lives.
第五个也是最后一个神话是计算机很复杂,而我们真正的意思是它们可以非常快地完成许多简单的事情。计算机执行的每一步都很简单且毫无意义,就像“将位左移(或右移)一个位置”之类的操作。这里有一个复杂性的奥秘,但它不是计算机的复杂性。我们无法解释一个人如何创建一个包含数千甚至数百万个愚蠢步骤的列表,这些步骤可以做一些有意义的事情,比如计算一部电影。这是人类创造力的复杂性——甚至是谜团。
The fifth and final myth is that computers are complex, when what we really mean is that they do lots of simple things very fast. Each step a computer takes is simple and meaningless, an operation like “shift the bits left (or perhaps right) by one position.” There is a mystery of complexity here, but it’s not complexity of the computer. It’s our inability to explain how a person creates a list of thousands, even millions, of dumb steps that does something meaningful, like compute a movie. It’s the complexity—mystery even—of human creativity.
在数码光的早期,这些误解导致人们认为计算机只能产生有限种类的图片。例如,最初假设计算机只能制作块状图片,或者动画运动必须沿着不优美的直线。但实际上并不存在这样的限制。令人信服的人类化身在微妙的运动和复杂的情感中,已经被计算并投射到大屏幕上。
In the early days of Digital Light these misconceptions led people to think that a computer could only produce limited kinds of pictures. For example, it was originally assumed that computers could make only blocky pictures, or that animated movement had to be along graceless straight lines. But no such limits actually existed. Convincing avatars of human beings in subtle motion, and complex emotion, have been computed and projected on the big screen.
基本思想为我们提供了足够的机制来呈现数字光的分类,以帮助我们讨论本书中采用和未采用的道路。
The foundational ideas give us enough machinery to present a taxonomy of Digital Light, to help us talk about roads taken and not taken in this book.
构造:区分。
Construction: Draw a distinction.
内容:称其为第一区别。
Content: Call it the first distinction.
-G。斯宾塞布朗,表格1的法律
—G. Spencer Brown, Laws of Form1
Digital Light 世界中的第一个区别在于像素的起源。如果它是现实世界的样本,那么我们说它是被采取的。我们通过对现实世界进行采样并将结果数字化来从现实世界中获取这些像素。获取此类像素的一种常见方法是使用数码相机——例如手机中的相机。我们说我们拍摄这样的像素。无论我们是在拍摄快照、静态照片还是视频序列(对时间和空间进行采样),都是如此。
The first distinction in the world of Digital Light turns on the origin of a pixel. If it’s a sample of the real world, then we say it is taken. We take such pixels from the real world by sampling the real world and digitizing the results. A common way to obtain such pixels is with a digital camera—the one in your cellphone, for example. We say we shoot such pixels. This is true whether we’re taking snapshots, or still photographs, or a video sequence (which samples time as well as space).
如果一个像素是从头开始创建的,那么我们就说它是制造的。制作像素的常用方法是使用数字计算机执行计算,并用计算结果填充像素。我们计算的像素与现实世界之间没有必要的联系。事实上,这些像素通常与奇幻世界相关联。
If a pixel is created from scratch, then we say it is made. The usual way to make a pixel is by performing a computation with a digital computer and filling the pixel with the results of that computation. There is no necessary connection between a pixel we compute and the real world. In fact, these pixels are often associated with fantastical worlds.
take 与 make 的区别与analytic和synthesis的区别相同。拍摄与计算的区别也是如此。
The take versus make distinction is the same as the difference between analytic and synthetic. So is the shoot versus compute distinction.
第一个区别将广阔的数字光世界分为两个主要子领域。分析部分有各种名称,我们将它们集中在一起,统称为图像处理。同样,合成的一半通常被称为计算机图形学。事实上,该领域的早期学术期刊被称为计算机图形和图像处理。为了站得住脚,这本书主要致力于计算机图形的“一半”。除了偶尔提及,它省略了图像处理。要了解在 Digital Light 中创建的空白有多大,请考虑以下省略一半的示例:所有使用手机拍摄的照片,任何您为您的孩子或宠物制作的视频、所有空间站和火星探测器视频、所有飓风和恶劣天气视频、所有在现实世界中拍摄的现场演员的现代电影、所有有线电视新闻节目(不包括高度合成的广告和徽标) ,所有间谍卫星图像,现代汽车倒车时的所有后视镜显示等等,都是分析数字光的例子。
This first distinction divides the vast world of Digital Light into its two major subfields. The analytic half goes by various names, which we clump together and generically call image processing. Similarly, the synthetic half is generically called computer graphics. Indeed, an early academic journal of the field was called Computer Graphics and Image Processing. To be tenable, this book is devoted mostly to just the computer graphics “half.” Except for the occasional mention, it omits image processing. To understand how massive a lacuna that creates in the body of Digital Light, consider the following examples from the omitted half: all photos made with your cellphone, any video you make of your child or pet, all space station and Mars rover videos, all hurricane and severe weather videos, all modern movies of live actors shot in the real world, all cable television news shows (excluding the highly synthetic commercials and logos), all spy satellite imagery, all rearview mirror displays in modern cars when in reverse, and so forth on and on, are examples of analytic Digital Light.
但是数字光的这个分析(或拍摄)一半的像素遵循与合成(或制作)一半相同的规则。傅里叶的频率思想适用。Kotelnikov 的采样定理适用。像素和显示元素的区别是一样的。图像文件格式相同。显示设备相同。像素就是像素。数码灯是一回事。只有用于用有意义的位填充像素的方法不同。如果您了解像素的工作原理,那么您就掌握了ALL Digital Light。
But the pixels of this analytic (or take) half of Digital Light obey the same rules as those of the synthetic (or make) half. Fourier’s frequency idea applies. Kotelnikov’s Sampling Theorem applies. The distinction between pixels and display elements is the same. The image file formats are the same. The display devices are the same. Pixels are pixels. Digital Light is one thing. Only the methods used to fill the pixels with meaningful bits differ. If you understand how pixels work, then you have a handle on ALL Digital Light.
由于实际书籍的空间有限,我进一步细分了合成计算机图形。区别是基于意图。如果主要目的是在现实世界中生成一个对象(例如汽车、房屋或烤面包机),我们将其称为计算机辅助设计(CAD)。如果意图是一张图片,而不是一个对象,那么我们就进入了面向图片的计算机图形学的世界(当很明显只有图片是意图时,通常简称为计算机图形学。)
Because of the finite amount of space in an actual book, I have further subdivided synthetic computer graphics. The distinction is based on intent. If the main purpose is to generate an object in the real world—a car, house, or toaster, say—we’ll call it computer-aided design (CAD). If the intent is a picture, not an object, then we enter the world of picture-oriented computer graphics (often shortened to computer graphics when it’s clear that only pictures are intended.)
正如我在第六章中所解释的那样,这两个子领域——CAD 和面向图片的计算机图形学——的历史高度交织在一起,并且有着共同的创始人。在考虑了这段重叠的早期历史之后,我不会在本书中进一步讨论 CAD,而是将这项任务留给其他人。但是,我们在本书中所说的关于像素的所有内容也同样适用于 CAD 像素。
The histories of the two subfields—CAD and picture-oriented computer graphics—are highly intertwined and share originators, as I explain in the sixth chapter. After considering this overlapping early history, I don’t further treat CAD in this book and leave that task to others. But, again, everything we say about pixels in this book applies to CAD pixels too.
随时间变化的视觉场景称为视觉流。这是一个平滑的模拟流程,因此需要同时使用傅立叶和 Kotelnikov 技术。这样我们就可以在时间和空间上对其进行采样。我们都熟悉常规时间样本:在电影和电视中,我们称它们为帧。
A visual scene that changes through time is called a visual flow. It’s a smooth analog flow and therefore subject to both Fourier and Kotelnikov techniques. Thus we can sample it in both time and space. We’re all familiar with regular time samples: in movies and television we call them frames.
本书中整个数字光的主要路径是通过面向图片的计算机图形学的非实时分支。所以,定义“实时”很重要,即使只是为了限制它的表现。有两个概念向我们传达实时信息,因此我们必须区分它们。
The main path through the entirety of Digital Light in this book is via the non-real-time branch of picture-oriented computer graphics. So, defining “real time” is important, if only to confine its presentation. There are two notions that convey real time to us, so we must distinguish them.
第一个概念是时变视觉流中的下一帧是在单帧时间(时间样本之间的时间)内计算的。计算速度足够快,可以在时钟的下一个滴答声中渲染下一帧——例如,对于实时数字视频,每六十分之一秒。这是实时计时的。时钟实时计算机图形最常见的用途是视频游戏,或众所周知的电子游戏。稍后我会详细介绍它们。
The first notion is that the next frame in a time-varying visual flow is computed during a single frame time—the time between temporal samples. The computation is fast enough to render the next frame at the next tick of the clock—for example, every one sixtieth of a second for real-time digital video. This is clocked real time. The most common use of clocked real-time computer graphics is videogames, or electronic games as they are also known. I’ll say more about them in a moment.
实时的第二个概念是它的速度足以让与不断变化的图像交互的人看起来是瞬间的。这是交互式实时. 一个简单的例子是游标。用户在桌面上拖动鼠标,或在触摸板上拖动手指,同时观察光标在屏幕上的移动。只要人移动,屏幕就会通过将光标从其先前位置移开并将其置于其当前位置来更新。实时速度足以让我们相信光标与我们的鼠标或手指紧密相连。它完全由用户的动作解锁和控制。如果用户不移动,则不执行图像计算。交互式实时计算机图形的常见用途是在任何手机、平板电脑、笔记本电脑或台式计算机上的几乎任何应用程序的用户界面中。以及操作系统本身——比如 Windows 或 MacOS。当然,所有这些接口都是合成数字光的一部分。
The second notion of real time is that it’s fast enough to seem instantaneous to a person interacting with the changing images. This is interactive real time. An easy example is cursoring. A user drags a mouse across a desktop, or a finger across a touchpad, while watching a cursor move on a screen. As fast as the person moves, the screen is updated by removing the cursor from its previous position and placing it at its current position. Real time is fast enough to convince us that the cursor is rigidly tied to our mouse or finger. It’s unclocked and controlled entirely by the user’s movements. If the user doesn’t move, then no picturing computations are performed. A common use of interactive real-time computer graphics is in the user interface to almost any app on any cellphone, tablet, laptop, or desktop computer. And to the operating system itself—say Windows or MacOS. All of these interfaces are, of course, parts of synthetic Digital Light.
数字电影是本书的主要范例。这是非实时计算机图形的一部分,机器可以根据需要进行计算以创建图片。实时计算电影需要在 24 秒内计算每一帧。而整部电影在90分钟左右。为了展示当今电影行业的不切实际,皮克斯电影需要几个月的时间来计算,并且单帧需要长达 30 小时。一年大约有 50 万分钟。将一年的计算量减少到 90 分钟的实时电影将需要四个数量级的加速 - 10,000 X。假设摩尔定律继续成立——这是一个非常大的假设——我们可以期待在 2040 年左右会有一部实时电影。
A digital movie is the principal exemplar in this book. That’s the part of non-real-time computer graphics in which the machine can compute as long as necessary to create a picture. To compute a movie in real time would require that each frame be computed in a twenty-fourth of a second. And the entire movie in 90 minutes or so. To show how unrealistic that is today in the movie industry, Pixar movies take months to compute and have taken as long as 30 hours for a single frame. A year has about a half million minutes. To reduce a year’s computation to a 90-minute real-time movie would take a speedup by four orders of magnitude—10,000X. Assuming that Moore’s Law continues to hold—and that’s a very big assumption—we could expect a real-time movie in about 2040.
另一方面,计算机现在速度如此之快,以至于它们可以生成实时图片。这就是许多现代电子游戏所做的。此外,他们会根据游戏玩家在游戏时的输入来改变计算的内容。所以他们同时利用实时、时钟和交互式类型。这些图像不像电影那样逼真和复杂,但本书所追求的数字电影与视频游戏之间唯一真正的技术区别是可用的马力。关键是本书涵盖的内容也适用于游戏,尽管我并不专注于它们或它们特定的历史和英雄。
On the other hand, computers are now so fast that they can generate real-time pictures. That’s what many modern videogames do. Furthermore, they change what they compute depending on input from the game player while gaming. So they utilize both types of real time, clocked and interactive. The images aren’t as photoreal and complex as a movie’s, but the only real technical difference between the digital movies pursued in this book and videogames is how much horsepower is available. The point is that what this book covers applies to games too, although I don’t concentrate on them or their particular history and heroes.
这本书中的一个特殊主题——称之为贯穿始终的主题和弦——涉及一种困扰技术突破的理念-混乱-暴君三重奏。我们首先在第一部分的三个“基本伟大创意”章节中了解主题是如何发挥作用的,其中每个三合会也与一个人联系在一起。然后是第二个主题,当我们发现接收到的技术历史经常充满错误时。在后面的部分中,我们将这两个主题应用于其他技术,因为它们与人群相关。
One particular motif in this book—call it a thematic chord sounding throughout—involves an idea–chaos–tyrant triad that haunts technological breakthroughs. We first learn how the motif plays out in the three “foundational great idea” chapters of part I, where each triad is also tied to a single person. Then comes a second motif, when we discover that received histories of technologies are often riddled with error. In later sections, we pursue both motifs into other technologies as they are tied to groups of people.
故事从法国革命家约瑟夫·傅立叶开始。在这种情况下,这个想法是傅立叶的伟大概念,即所有自然都是音乐。推动他的世界的混乱是法国大革命以及他随后与皇帝和国王的战斗。拿破仑是将傅立叶流放到以格勒诺布尔为中心的偏远部门的暴君,因此在不知不觉中为他提供了发展他的革命思想的空间。
The story begins with a French revolutionary, Joseph Fourier. In this case, the idea was Fourier’s great notion that all nature is music. The chaos that drove his world was the French Revolution and his subsequent battles with emperor and king. Napoleon was the tyrant who exiled Fourier to a remote department centered at Grenoble and thus unknowingly provided him space to develop his revolutionary idea.
在基本思想的第二章中,我们遇到了大多数美国人都不知道的俄罗斯人弗拉基米尔·科捷尔尼科夫。他采纳了傅立叶的伟大想法并在其上建立了自己的想法:伟大的采样定理是使数字光成为可能的微妙而美丽的想法。
In the second chapter of fundamental ideas we meet a Russian unknown to most Americans, Vladimir Kotelnikov. He took Fourier’s great idea and erected his own atop it: the great Sampling Theorem is the subtle and beautiful idea that made Digital Light possible.
这里的想法,在想法-混沌-暴君三元组中,是 Kotelnikov 的高度不明显的采样概念,即离散的、尖峰的样本可以准确地表示平滑的模拟连续体。他的混乱是影响世界历史进程的一系列战争,尤其是在俄罗斯——俄国革命、随后的内战、世界大战和冷战。他的暴君是斯大林的继任者马林科夫、克格勃的贝利亚,以及拥有古拉格集中营的苏联秘密机构。在 Kotelnikov 的案例中,他的保护者、Malenkov 的妻子 Valeriya Golubtsova 故意并一再保护他免受混乱,并在她的大学里给了他一个家。
The idea here, in the idea–chaos–tyrant triad, is Kotelnikov’s highly nonobvious sampling notion that discrete, spiky samples can accurately represent a smooth, analog continuum. His chaos was the sequence of wars that so affected the course of world history, especially in Russia—the Russian Revolution, the civil wars that followed, both World Wars, and the Cold War. His tyrants were Stalin’s successor Malenkov, the KGB’s Beria, and the Soviet secrecy apparatus with its Gulag of prison camps. In Kotelnikov’s case, his protectress, Valeriya Golubtsova, Malenkov’s wife, knowingly and repeatedly protected him from the chaos and gave him a home in her university.
采样定理是Kotelnikov 的想法。美国人被教导——我被教导——这是克劳德香农或哈里奈奎斯特的,但香农从未声称它和奈奎斯特从未说过。因此,我们看到流传下来的关于技术的故事往往是错误的,但仍然是我们所接受知识的一部分。在这种情况下,腐败的错误几乎可以肯定是民族主义,或者更普遍的政治。在冷战时期的美国,这么重要的想法怎么可能归功于苏联共产党?!尽可能准确地讲述每种技术的正确历史不仅可以检查而且还可以说明为什么存在“替代”版本。
And the Sampling Theorem was Kotelnikov’s idea. Americans are taught—I was taught—that it was Claude Shannon’s or Harry Nyquist’s, but Shannon never claimed it and Nyquist never stated it. Thus we see how stories handed down about technology are often erroneous but nevertheless part of our received knowledge. In this case, the corrupting error is almost certainly nationalism, or politics more generally. In Cold-War America, how could such an important idea be credited to a Soviet Communist?! Told with as much accuracy as possible, a proper history of each technology not only examines but also suggests why “alternative” versions exist.
数字光的第三个伟大的基本理念来自于数字世界著名的同性恋烈士艾伦·图灵。他独自创造了我们现在所知道的存储程序计算机、计算和编程的概念。他的混乱是二战,他的暴君是英国的《官方保密法》,一方面,当他因同性恋入狱时,他无法解释他在拯救国家方面的作用。(但错误有时会得到部分纠正。英国新发行的 50 英镑纸币将以图灵为特色,并于 2021 年进入发行阶段。)
The third great foundational idea of Digital Light comes from the digital world’s famous gay martyr, Alan Turing. He singlehandedly created the concepts of the stored-program computer, computation, and programming as we now know them. His chaos was World War II, and his tyrant was the Official Secrets Act of Great Britain, which for one thing wouldn’t allow him to explain his role in saving the country when he was jailed for homosexuality. (But wrongs are sometimes partially righted. The new £50 note of Great Britain will feature Turing and enter distribution in 2021.)
图灵的故事与约翰·冯·诺依曼的故事相反。约翰尼惊人的智力使他成为世界上为数不多的了解和欣赏图灵所取得的成就的天才之一——存储程序计算机的发明。他把在世界上建造硬件计算机作为自己的职责——让图灵的想法快速发展——使用一种主导计算机工程数十年的简单架构。
Turing’s story unfolds in counterpoint to that of John von Neumann. Johnny’s awesome intellectual powers made him one of the mere handful of geniuses in the world who understood and appreciated what Turing had accomplished—the invention of the stored-program computer. And he made it his duty to get hardware computers built in the world—to make Turing’s idea go fast—with a simple architecture that has dominated computer engineering for decades.
图灵发明了编程的概念,冯诺依曼参与命名。他们都注意到编程或软件,而不是硬件,是计算的挑战。
Turing invented the concept of programming, and von Neumann participated in naming it. They both noticed that programming, or software, more than hardware, was the challenge for computation.
计算机和电影这两种技术促成了数码光的发展。在本书的第二部分,我们将探讨其中包含的两种技术:计算机中的数字光本身和电影中的动画。计算机显然对 Digital Light 至关重要,我们发现它们与 Digital Light 的诞生密切相关。但电影也为 Digital Light 贡献了重要的结构和术语,尤其是数字电影。更重要的是,电影依赖于与 Digital Light 相同的基本采样理念。电影将采样从空间扩展到时间,并支持我们的论点,即采样是对现代世界的一项关键技术贡献。一种理论有助于解释这一切。
Two technologies—computers and movies—contributed to the evolution of Digital Light. In the second part of this book we look at two technologies subsumed within them: Digital Light itself in computers, and animation in movies. Computers are obviously crucial to Digital Light, and we find them linked intimately with Digital Light at its birth. But movies have contributed crucial structure and terminology to Digital Light too, especially digital movies. More importantly, movies depend on the same fundamental great idea of sampling as does Digital Light. Movies extend sampling from space into time and bolster our argument that sampling is a key technological contribution to the modern world. One theory helps explain it all.
这两种高科技独立地展示了本书的“接受的历史是错误的”主题,尤其是通过它们奇怪的有缺陷的历史来呈现,并由每种技术的理念-混乱-暴君三元组所概述,并延伸到人群。
These two high technologies independently demonstrate the received-history-is-wrong motif of the book, especially as presented by their strangely flawed histories and outlined by the idea–chaos–tyrant triad for each technology, which extends to groups of people.
图灵发明的计算机有一个主要缺点:速度慢得令人难以忍受。他的机器可以计算皮克斯的玩具总动员,但这样做可能需要整个宇宙的生命。因此,图灵启动了一个项目来构建他的通用存储程序计算机的电子版本,以使其运行得更快。他引用了现在熟悉的经验法则:让软件快速运行,在硬件中实现它。换句话说,如果忽略速度,硬件和软件本质上是等价的。我强调这一点是因为现代历史学家在 1940 年代后期仍然将存储程序计算机的功劳归于硬件工程师,而图灵已经在他 1936 年的著名论文中描述并使用了这个概念。这是他证明普遍性的关键,因为我在第 3 章中展示了他的证明草图。
There was one major drawback to Turing’s invention of the computer: it was insufferably slow. His machine could have computed Pixar’s Toy Story, but it might have taken the lifetime of the universe to do so. So Turing launched a project to build an electronic version of his universal stored-program computer to make it go fast. He invoked what is by now a familiar rule of thumb: to make software go fast, implement it in hardware. In other words, hardware and software are fundamentally equivalent if speed is ignored. I emphasize this because modern historians are still assigning credit for the stored-program computer to hardware engineers in the late 1940s, whereas Turing had already described and used the concept in his famous paper of 1936. It was key to his proof of universality, as I show in a sketch of his proof in chapter 3.
我们今天所说的计算机一词的含义正是:电子存储程序计算机。图灵走出数学界,在 1940 年代加入了一个名为 Pilot Ace 的项目,以建造第一台这样的计算机。他失败了,原因我在第四章中解释过,但其他人接受了这个想法。事实上,比赛正在进行中。几个团队争先恐后地制造了第一台机器,尤其是在美国和英国。
What we mean by the word computer today is exactly this: an electronic stored-program computer. Turing stepped out of mathematics and joined a project in the 1940s, called Pilot Ace, to build the first such computer. He failed, for reasons I explain in the fourth chapter, but others picked up on the idea. In fact, the race was on. Several teams rushed to create the first machines, especially in the United States and United Kingdom.
显而易见的是,第一台计算机的许多索赔人不符合条件。再一次,收到的故事是错误的。它当然不是美国的 Eniac,它不是存储程序计算机,也不是英国早期的 Colossus,也不是存储程序。通过仔细定义计算机,实际上可以列出前 10 台左右的计算机。根据电子存储程序计算机的定义,英国曼彻斯特的 Baby 是第一台计算机。它赢了,因为它拥有第一个成功的电子存储器。memory 和 Baby 是由英国工程师 Freddie Williams 和 Tom Kilburn 使用通常称为 Williams 管的解决方案创建的。尽管他没有设计或制造机器,但图灵很快就找到了通往 Baby 的道路。
What becomes clear is that many claimants for first computer don’t qualify. Once again, the received stories are wrong. It certainly wasn’t America’s Eniac, which wasn’t a stored-program computer, or England’s earlier Colossus, also not stored-program. By following a careful definition of computer, it’s possible to actually list the first 10 or so computers. According to that definition of an electronic, stored-program computer, Baby at Manchester in England was the first computer. It won because it had the first successful electronic memory. The memory and Baby were created by English engineers Freddie Williams and Tom Kilburn with a solution usually called a Williams tube. Turing soon found his way to Baby although he did not design or build the machine.
与此同时,天才约翰·冯·诺依曼打算在美国制造一台计算机。他的团队与 RCA 实验室的 Vladimir Zworykin(已经以电视闻名)和他的团队签订了合同,以构建电子存储器。这段历史的简短版本是 Zworykin 团队未能及时让他们的记忆发挥作用。冯Neumann 团队听说了 Baby 的记忆解决方案 Williams 管,并立即采用了它。
Meanwhile genius John von Neumann was intent on building a computer in America. His team contracted with Vladimir Zworykin (already famous for television) and his group at RCA Labs to build an electronic memory. The short version of this history is that the Zworykin team failed to get their memory working in time. The von Neumann team got word of Baby’s memory solution, the Williams tube, and immediately adopted it.
冯·诺依曼分析了他能找到的每一台计算机或类似计算机的机器。他注意到,通过添加一些简单的硬件使其成为存储程序计算机,可以将 Eniac 转换为计算机。我将由此产生的新改进的 Eniac 称为 Eniac+。正如我所写,关于 Eniac+ 是否确实赢得了“第一台计算机”称号,存在学术争论。根据几乎任何“完整”的定义,这两台机器都是在几周之内诞生的,而记录的日期不同,让历史学家争论不休。
Von Neumann analyzed every computer or computer-like machine he could find. He noticed that Eniac could be converted into a computer by adding some simple hardware to make it a stored-program computer. I call the resulting new improved Eniac by the name Eniac+. There’s scholarly argument, as I write, about whether Eniac+ did indeed win the “first computer” title. The two machines were born within a few weeks of one another by almost any definition of “complete,” while recorded dates differ and keep the historians arguing.
我在这本书中强调 Baby,因为它显示了第一个像素。威廉姆斯管在阴极射线管 (CRT) 的表面上存储位,一个短划线表示 1,一个点表示 0。这些是 Baby 的显示元素(或扩展像素)。它们排列成一个阵列。Kilburn 在 1947 年拍摄了这张我称之为 First Light 的照片,就在 Baby 于 1948 年完成之前。
I emphasize Baby in this book because it displayed the first pixels. The Williams tube stored bits on the surface of a cathode-ray tube (CRT), a dash for 1 and a dot for 0. Those were Baby’s display elements (or spread pixels). They were arranged in an array. Kilburn made the picture I’ve called First Light in 1947, just slightly before Baby was completed in 1948.
由于这种第一台计算机/第一台光的巧合,第 4 章不仅是计算机的历史,也是早期数字光的历史。在那一章中,我开始阐述本书的另一个主题,即高科技几乎不会简化为对单个创造性天才的叙述。即使是对早期少数计算机的解释也需要引入我所谓的流程图或谱系图,即参与创建这些重要机器的人们的“家庭”。
Because of this first-computer / first-light coincidence, chapter 4 is not only a history of computers but also of early Digital Light. In that chapter I begin to elaborate another theme of the book, that a high technology hardly ever reduces to a narrative about a single creative genius. Even an explanation of the early handful of computers requires the introduction of what I call a flow chart, or genealogy, of the “family” of people involved in the creation of these important machines.
但是,计算机的这段特殊历史是本书中唯一几乎符合单一创意天才模式的历史。图表的最顶端是艾伦·图灵。从图灵到第一台计算机 Baby 没有单一的直接路径。冯诺依曼和其他一些人也接近榜首。该图表显示了谁影响了谁,或多或少以正确的时间顺序显示。它展示了这些想法如何扩散并影响了早期的计算机。总结是图灵发明了计算机的概念——意思是存储程序计算机——而冯诺依曼帮助创建了允许工程师在硬件中实现图灵想法的架构。宝贝,事实上,尽管是在英国建造的,但它使用了冯诺依曼建筑。而冯诺依曼的美国团队采用了英国的记忆解决方案,威廉姆斯管,
But this particular history—of computers—is the only one in the book that almost does fit the single-creative-genius mold. At the very top of the chart is Alan Turing. There is no single direct path from Turing to Baby, the first computer. Von Neumann is also near the top of the chart, as are a few others. The chart shows who influenced whom, more-or-less in correct time order. It shows how the ideas proliferated and affected the early computers. The summary is that Turing invented the concept of computer—meaning stored-program computer—while von Neumann helped to create the architecture that allowed engineers to implement Turing’s idea in hardware. Baby, in fact, despite being built in England, used a von Neumann architecture. And von Neumann’s American team adopted the British memory solution, the Williams tube, to make its breakthrough with Edvac and Edvac’s numerous progeny.
在本章中介绍摩尔定律会带来一个易于在本书其余部分应用的公式:计算机的所有优点每五年会提高一个数量级。这使得摩尔定律的革命性意义,作为数字革命中令人敬畏的超新星发电站,比集成电路元件密度方面的通常表述更为明显。我建议这个神秘的“定律”衡量一个大在竞争中,当技术的改进没有最终的物理障碍并且技术必须按自己的方式付费时,一群,比如说成千上万的有创造力的人可以继续改进一项技术。
Introducing Moore’s Law in this chapter brings into play a formulation that is easy to apply throughout the remainder of the book: everything good about computers gets better by an order of magnitude every five years. This makes the revolutionary implications of Moore’s Law, as the awesome supernova powerhouse of the Digital Revolution, more obvious than does the usual formulation in terms of integrated-circuit component density. I suggest that this mysterious “Law” measures the ultimate speed at which a large group, say thousands, of creative people can proceed to improve a technology, under competition, when there is no ultimate physical barrier to its improvement and when the technology must pay its own way.
同时,流程图机制使早期计算机历史中的国际互动和竞争变得容易可视化。同一张图表让我们可视化了 Digital Light 的最早发展,因为所有第一次突破都发生在第一台计算机上。对本书特别重要的是,第一个流程图的一个分支自然而然地引出了第 6 章中的流程图。通过麻省理工学院的 Whirlwind 计算机,这个分支最终导致了现代计算机图形学。 Digital Light 中最早的图片——可能包括第一批动画。然后我们沿着这条线进入第 7 章及其流程图。
Meanwhile the flow chart mechanism makes it easy to visualize the international interactions, and competitions, in early computer history. The same chart lets us visualize the earliest developments in Digital Light because all the first breakthroughs occurred on the first computers. Of particular importance to this book, one of the branches of this first flow chart leads naturally to the flow chart in chapter 6. That’s the branch that eventually leads to modern computer graphics, via the Whirlwind computer at MIT, a source of many of the earliest pictures in Digital Light—including probably the first animations. Then we follow that line into chapter 7 and its flow chart.
但首先我打断了 Digital Light 的流畅故事,介绍另一项影响数字电影的高科技。第 5 章是关于传统模拟电影的旧技术的简短总结。
But first I interrupt the flowing story of Digital Light to introduce another high technology that influenced digital movies. Chapter 5, missing so far from this short summary, is about the old technology of traditional analog movies.
当我准备写这本书时,我沮丧地注意到,我自己拥有 50 多年的电脑电影制作经验,无法告诉你是谁制造了第一台电脑或是谁发明了电影。我以为其他人也不能。在讲述技术历史时存在系统性缺陷,我开始理解这一点。我对这两种技术历史的解决方案是相同的:首先,仔细定义术语。其次,使用家谱方法而不是简单的叙述。
As I prepared to write this book, I noticed with dismay that I myself, with over 50 years of experience in making computer movies, couldn’t tell you who built the first computer or who invented the movies. I assumed that nobody else could either. There was a systemic flaw in the telling of technological history, which I set out to understand. My solution for both technological histories is the same: First, define terms carefully. And second, use a genealogical approach rather than simple narrative.
我刚刚讨论了这种方法对第一台计算机历史的影响。随着对计算机一词的良好定义,那里的大部分问题都消失了。当民族主义主张被打折以支持互动的创作者家庭时,剩下的问题就消失了。结果是一个易于理解的历史,其中包括主要参与者和地区。它还可以直接将数字光的突破分配给早期计算机创建的适当中心。当然,我不能声称绝对正确,但我确实声称这种方法为历史提供了一个易于纠正的结构。因此,在第 5 章中,我将同样的方法应用于电影。
I’ve just discussed the results of this approach to the history of the first computers. Much of the problem there disappeared with a good definition of the word computer. The rest of the problem vanished when nationalistic claims were discounted in favor of interacting families of creators. The result is an easy-to-follow history which includes the principal players and locales. It also makes it straightforward to assign breakthroughs in Digital Light to appropriate centers of early computer creation. I cannot claim infallibility, of course, but I do claim that this approach gives an easily correctible structure to the history. So, in chapter 5, I apply the same approach to movies.
就像我问过的几乎每个人一样,我认为电影是由托马斯·爱迪生、埃德沃德·迈布里奇或卢米埃尔兄弟创作的。但我不能告诉你是哪个。事实上,定义和流程图分析技术表明,电影不是由他们制作的。正确地说,他们都影响了正确的故事,但一些主要的创新者只是从流行的历史中消失了,或者从未被包括在内。对于美国的威廉·肯尼迪·劳里·迪克森来说尤其如此和法国的 Georges Demenÿ。但他们也不是单独行动的单身英雄。它需要流程图来表明谁与谁合作,谁偷了谁,谁背叛了谁,等等。它还可以透视不同的玩家。爱迪生在这些灯光下,给人的印象是一个从他支持的发明家那里窃取信用的暴君。迈布里奇被揭露为一个他没有实施的想法的优秀推销员。Lumière 兄弟的传奇圣徒身份因他们实际所做的细节的披露而受到影响。这是一个比我想象的要复杂得多的故事。
Like almost everybody I’ve quizzed, I assumed that movies were created by Thomas Edison, Eadweard Muybridge, or the Lumière brothers. But I couldn’t tell you which. In fact, the definition and flow-chart analysis techniques show that movies weren’t created by any of them. Stated correctly, all of them influenced the proper story, but some of the main innovators have simply disappeared from popular histories or have never been included. This is particularly true for William Kennedy Laurie Dickson in America and Georges Demenÿ in France. But they weren’t single heroes acting alone either. It takes the flow chart to indicate who worked with whom, who stole from whom, who backstabbed whom, and so forth. It also makes it possible to see the various players in perspective. Edison, under these lights, comes across as a tyrant who stole credit from the inventors he supported. Muybridge is revealed as an excellent salesman of an idea that he didn’t implement. And the legendary sainthood of the Lumière brothers suffers from revelation of the details of what they actually did. It’s a much more complex story than I would’ve ever guessed.
与计算机一样,将电影机器定义为相机、胶卷和投影仪的仔细定义是明确的概念。仅发明这三部曲中的一部分不足以作为电影发明的权利。看一下本章的流程图可以看出,不可能有简单的叙述来捕捉电影机器的历史。几乎没有什么可以有意义地简化。
As with computers, a careful definition—of a movie machine as camera, film, and projector—served as the clarifying concept. Invention of only one part of this trio is insufficient as a claim to the invention of movies. A look at the flow chart for this chapter shows that there can be no simple narrative that captures movie machine history. There is little that could be meaningfully simplified.
从技术上讲,电影和动画章节允许我们在三维时间中练习采样定理,其中帧就是我们所说的视觉流样本。我开始这一章时相信我可以使用采样定理解释电影为什么会移动。但是我发现采样定理的解释并不完全正确。我们可以使用该定理制作一部理想的电影,但显然该解决方案尚未实施。我称之为“瞳孔外”的解释,即在光进入人眼之前传播样本(帧)。
Technologically, the movie and animation chapter allows us to exercise the Sampling Theorem in a third dimension, time, where the frame is what we call the sample of visual flow. I began the chapter believing I could explain why movies move using the Sampling Theorem. But I discovered that the Sampling Theorem explanation is not precisely the right one. We could make an ideal movie using the theorem, but apparently that solution hasn’t been implemented. I call it an “outside the pupil” explanation, where spreading the samples (frames) occurs before light enters the human eye.
相反,电影,甚至是数字电影,都使用将连续“帧”呈现给人眼的技术。这似乎可以通过“在瞳孔内”锻炼人脑的感知机制来发挥作用。也就是说,分离的帧直接提供给视网膜和大脑,后者将重建为平滑运动。我不想解释大脑的机制,但指出,从证据来看,它似乎在做类似于从样本中重建采样定理的事情。
Instead movies, even digital movies, use the technique of presenting successive “frames” to a human eye. This seems to work by exercising the perceptual mechanisms of the human brain “inside the pupil.” That is, separated frames are supplied directly to the retina and brain, which does the reconstruction into smooth motion. I don’t attempt to explain the brain’s mechanism but point out that it seems, from the evidence, to be doing something akin to Sampling Theorem reconstruction from samples.
电影章节还包括动画——尤其是角色动画——以及技术和人。沃尔特迪斯尼和经常被忽视的 Ub Iwerks 在本节中出现。建议是,经典动画师的挤压和拉伸、预期和夸张技巧是采样问题的直观解决方案。再次因为我在该领域工作了 50 多年,了解到早期考虑的替代二维动画系统,这让我个人感到非常惊讶。只有著名的 cel 动画系统才能进入现代世界。所以 cel 动画是 1980 年代中期“现称为皮克斯的团队”为迪士尼的计算机动画制作系统 (CAPS) 实施的动画技术。这是我们所知道的唯一技术。
The movie chapter also covers animation—particularly character animation—as well as technology and people. Walt Disney and the often overlooked Ub Iwerks feature in this section. The suggestion is that the classic animators’ tricks of squash and stretch, anticipation and exaggeration are intuitive solutions to sampling problems. What a personal surprise it was, again because I’ve been in the field for more than 50 years, to learn of alternative two-dimensional animation systems that were considered in the early days. Only the well-known cel animation system made it into the modern world. So cel animation was the animation technology that the “group now known as Pixar” implemented for Disney’s Computer Animation Production System (CAPS) in the mid-1980s. It was the only technology we knew.
这里的好主意是,如果在硬件中实现,图灵 1936 年的存储程序计算机想法可以快速运行。比赛开始了,从 1940 年代初开始。推动第一台计算机生产的混乱是希特勒和纳粹德国的崛起,以及对他们会在英国或美国之前达到生产原子弹的巨大恐惧。事实上,第一台计算机 Baby 是在希特勒和纳粹灭亡后的 1948 年完成的。但混乱仍在继续,因为苏俄迅速取代了德国作为生存敌人的角色,氢弹取代了原子弹成为最可怕的武器。早期的计算机用于武器计算和炸弹爆炸的模拟。
The great idea here was that Turing’s 1936 idea of stored-program computer could be made to go fast if implemented in hardware. And the race was on, starting in the early 1940s. The chaos driving production of the first computers was the rise of Hitler and Nazi Germany and the tremendous fear that they would reach the production of an atomic bomb before the United Kingdom or United States did. In fact, the first computer, Baby, was completed in 1948 after the destruction of Hitler and the Nazis. But the chaos continued because Soviet Russia quickly replaced the German role as existential enemy, and the hydrogen bomb replaced the atomic bomb as the most feared weapon. Early computers were used in weapon calculations and simulations of bomb explosions.
直接影响图灵和冯诺依曼的暴政是英国和美国各自的国家安全体系。特别是,英国的《官方保密法》实际上对追捕艾伦·图灵(Alan Turing),甚至可能导致他的死亡负责。
The tyrannies that directly affected Turing and von Neumann were the respective state security systems of the United Kingdom and United States. In particular, the UK’s Official Secrets Act was responsible in effect for the hounding of Alan Turing, perhaps even to his death.
这项高科技的好主意是,在付费观众之前及时复制视觉流程是一件好事。这个想法本质上取决于一系列照片作为呈现视觉流动的方法。因此,它建立在 19 世纪中叶相对较新的静态摄影领域的基础上,并在其结束时,即 1895 年取得了第一个成果。
The great idea for this high technology was that replicating a visual flow in time before a paying audience was good business. The idea inherently hinged on a sequence of photographs as the method of presenting visual flow. Thus it built on the relatively new field of still photography from the middle of the nineteenth century and bore first fruit just at the end of it, in 1895.
没有明显的外部混乱驱动电影的发展。如果我们希望将某些东西推广到那个水平,那么混乱就是纯粹的资本主义竞争冲向被认为是有利可图的新市场。
There was no obvious external source of chaos driving the development of movies. The chaos, if we wish to promote something to that level, was the pure capitalistic competitive rush to what was presumed to be a lucrative new market.
但是有一个明显的暴君,至少在美国方面。托马斯爱迪生很好地填补了这个角色。他建立了一个设备齐全的实验室,并邀请了热情的年轻发明家。他给了他们一个家和鼓励。麻烦的是,爱迪生随后声称他们所有的发明都是他自己的,他把所有的钱和名声都收入囊中。本书中最明显的例子是威廉·肯尼迪·劳里·迪克森的案例。迪克森今天鲜为人知,尽管他为爱迪生制造了相机,为传记制造了投影仪,并完善了成为电影界标准的 35 毫米穿孔胶片格式。
But there was a clear tyrant, at least on the American side. Thomas Edison fills the role nicely. He famously set up a well-furnished laboratory to which he invited enthusiastic young inventors. He gave them a home and encouragement. The trouble was that Edison then claimed all their inventions as his own, and he pocketed all the money and fame. The clearest example in this book is the case of William Kennedy Laurie Dickson. Dickson is hardly known today although he was the one who built the camera for Edison and the projector for Biograph, as well as perfecting the 35 mm perforated film format that became the standard of the movie world.
在法国方面,没有这么明显的暴君。但是关于卢米埃尔兄弟不仅相爱而且还一起发明电影的错误神话有一个专横地控制着法国人的想象力。事实是,兄弟俩互相刺伤对方,从乔治斯·德梅尼(Georges Demenÿ)等其他人那里汲取灵感,并在电影格式之战中输给了迪克森。
On the French side, there was no such obvious tyrant. But the false myth that the Lumière brothers not only loved each other but also invented movies together has a tyrannical hold on the French imagination. The truth is that the brothers stabbed each other’s backs, took ideas from others such as Georges Demenÿ, and lost the film format battle to Dickson.
被称为动画电影的电影子领域是那些与现实世界时间脱节或精神错乱的电影。最初的想法是手绘框架可以形成娱乐的视觉流。如果我们再次愿意将竞争性资本主义提升为混乱,那么它的混乱与一般电影的混乱相同。暴君的角色由沃尔特·迪斯尼本人担任,他从热心的企业家转变为声称自己是公司和米老鼠的唯一发明者,或者至少让这种看法在公众心目中获得了未经纠正的基础。
The subfield of movies called animated films are those divorced, or unhinged, from real-world time. The original idea was that hand-drawn frames could form visual flow for entertainment. Its chaos was the same as that for movies in general, if we are again willing to elevate competitive capitalism to chaos. And the role of tyrant is filled by Walt Disney himself, who went from eager entrepreneur to claiming he was the sole inventor of the company and of Mickey Mouse, or at least letting that perception gain uncorrected ground in the public mind.
本书的第三部分专门讨论数字光。我在三个章节(6、7 和 8)中使用面向图片的计算机图形作为骨架来讲述它的故事,涵盖摩尔定律之前(时期 1)和之后(时期 2)的发展。暂时,让我们回到第 4 章和 Digital Light 的黎明时刻,回忆一下我们在那里发现的东西。
The third part of this book is devoted to Digital Light proper. I tell its story using picture-oriented computer graphics as an armature in three chapters (6, 7, and 8) that cover developments preceding Moore’s Law (Epoch 1) and after (Epoch 2). For just a moment, though let’s go back to chapter 4 and the dawning moments of Digital Light, to recall what we discovered there.
第一个像素是在 70 多年前的 1947 年末,在注定要成为第一台显示设备的 CRT 上显示的。我称那第一张数码照片为 First Light。我们在第一台计算机 Baby 上找到它的像素,即第一个像素。黎明章节 (4) 涵盖了像素和计算机的起源。我已经总结了关于计算机的部分,所以现在我转到像素和图片部分。
The first pixels were displayed in late 1947, 70-plus years ago, on a CRT destined to be the first display device. I call that first digital picture First Light. We find its pixels, the first pixels, on the first computer, Baby. The Dawn chapter (4) covers the origins of both pixels and computers. I’ve already summarized the part about computers, so now I move on to the pixels and pictures part.
1940年代后期出现了几张数码图片,1950年代初期出现了最早的互动游戏和动画。在这个早期阶段,用珍贵的计算机拍照通常被认为是轻浮的,不像核弹计算那样严肃。但不可能阻止对机器图片的推动。给定一个显示设备,人们只需要制作图片。即使花费数百万美元。
Several digital pictures appeared in the late 1940s, and the early 1950s saw the earliest interactive games and animations. During this early stage, making pictures with the precious computers was generally considered frivolous, not serious like nuclear bomb calculations. But it was impossible to stop the push toward pictures on machines. Given a display device, people just have to make pictures. Even if it cost millions of dollars.
1950 年代初,麻省理工学院的 Whirlwind 发生了第一次与图片无关的时代的一致背离。许多早期的图片出现在这台电脑的版本上,可能包括第一个数字动画和早期的互动游戏,以及第一个 3D 图片(但没有透视图)。第 4 章的流程图将我们直接带入第 6 章的图表和 Digital Light 的兴起。
The first concerted departure from the pictures-are-frivolous era occurred on Whirlwind at MIT in the early 1950s. Many early pictures appeared on versions of this computer, including perhaps the first digital animations and early interactive games, and the first three-dimensional pictures (but without perspective). The flow chart for chapter 4 carries us directly into the chart for chapter 6 and the rise of Digital Light.
我们从计算机图形学中最可爱的形状之一——样条曲线开始第 6 章。这是一个优美的形状,掩盖了早期错误的信念,即计算机只能绘制刚性、块状、棱角分明的线性物体。事实证明,样条曲线可以用采样定理来解释!实际上,与采样定理相反。这让我们介绍另一位采样定理的发明者,英国人 Edmund Taylor Whittaker 爵士,他的工作比 Kotelnikov 的工作早了 18 年。他几乎拥有(相反的)采样定理,但“几乎”使他无法获得首要地位。因为他使用了与 Kotelnikov 不同的观点,所以他错过了完整定理的一个重要点(工程师称之为“带通”版本)。Kotelnikov 的观点是这样的:给定一个平滑、连续的信号,将其采样为离散样本,然后将样本重建——我们说,将它们传播——回到原始的连续实体中。Whittaker 的观点正好相反:给定一组离散数据点,找到一条通过它们的平滑连续曲线,准确预测哪些点可能合理地落在给定点之间。Whittaker 在给定数据点之间插入值的技术与我们所说的扩展样本并添加它们没有区别。但是,当科捷尔尼科夫正在重建一条给定的曲线时,惠特克正在构建或发明一条曲线。构建曲线上的点对他来说很重要,而不是曲线本身——数据而不是形状。给定一组离散数据点,找到一条通过它们的平滑连续曲线,准确预测哪些点可能合理地落在给定点之间。Whittaker 在给定数据点之间插入值的技术与我们所说的扩展样本并添加它们没有区别。但是,当科捷尔尼科夫正在重建一条给定的曲线时,惠特克正在构建或发明一条曲线。构建曲线上的点对他来说很重要,而不是曲线本身——数据而不是形状。给定一组离散数据点,找到一条通过它们的平滑连续曲线,准确预测哪些点可能合理地落在给定点之间。Whittaker 在给定数据点之间插入值的技术与我们所说的扩展样本并添加它们没有区别。但是,当科捷尔尼科夫正在重建一条给定的曲线时,惠特克正在构建或发明一条曲线。构建曲线上的点对他来说很重要,而不是曲线本身——数据而不是形状。但是,当科捷尔尼科夫正在重建一条给定的曲线时,惠特克正在构建或发明一条曲线。构建曲线上的点对他来说很重要,而不是曲线本身——数据而不是形状。但是,当科捷尔尼科夫正在重建一条给定的曲线时,惠特克正在构建或发明一条曲线。构建曲线上的点对他来说很重要,而不是曲线本身——数据而不是形状。
We begin chapter 6 with one of the loveliest shapes in computer graphics—the spline. It’s a graceful shape that belies the early mistaken belief that computers could draw only rigid, blocky, angular, linear things. The spline, it turns out, can be explained by the Sampling Theorem! Actually, the reverse of the Sampling Theorem. This lets us introduce another claimant to the invention of the Sampling Theorem, the Englishman Sir Edmund Taylor Whittaker, whose work preceded Kotelnikov’s by 18 years. He almost had (the reverse of) the Sampling Theorem, but that “almost” keeps him from primacy. Because he used a different point of view from that of Kotelnikov, he missed one of the important points of the full theorem (what engineers call the “bandpass” version). Kotelnikov’s point of view was this: given a smooth, continuous signal, sample it into discrete samples, then later reconstruct the samples—spread them, we say—back into the original continuous entity. Whittaker’s point of view was the reverse: given a set of discrete data points, find a smooth continuous curve through them that accurately predicts what points might rationally fall between the given points. Whittaker’s technique for interpolating values between his given data points is indistinguishable from what we call spreading the samples and adding them. But whereas Kotelnikov was reconstructing a given curve, Whittaker was constructing, or inventing, one. And points on the constructed curve were important to him, not the curve itself—data not shapes.
第 6 章剩下的大部分内容是关于用三角形建模 3D 形状。我讲述了一些最早的研究人员在后来成为计算机图形学方面的故事。最早的玩家,例如 Steven Coons 和 Pierre Bézier——以及几乎被遗忘的 Paul de Casteljau——对图片并不特别感兴趣。他们使用计算机雕刻木头或泡沫,或以其他方式计算实际物体——例如汽车车身或飞机机翼。因此,严格来说,他们是计算机辅助设计或 CAD 的先驱。但是在这个早期阶段,面向对象的 CAD 和面向图片的计算机图形学是一回事。两者的起点都是计算机内存中的几何模型。
Much of the rest of chapter 6 is about modeling three-dimensional shapes with triangles. I recount the stories of some of the earliest researchers in what would become computer graphics. The earliest players, such as Steven Coons and Pierre Bézier—and the almost forgotten Paul de Casteljau—weren’t particularly interested in pictures. They used computers to carve wood or foam, or otherwise compute an actual object—such as an automobile body or airplane wing. So they were, strictly speaking, pioneers of computer-aided design, or CAD. But object-oriented CAD and picture-oriented computer graphics were one and the same at this early stage. The starting point for both was a geometric model inside a computer’s memory.
计算机图形技术的故事通常以叙述方式讲述,其中有一个人 Ivan Sutherland,同时不连贯地向其他开国元勋致敬——以 Steven Coons 的名字命名该领域的最高奖项,或者命名一个特定的皮埃尔·贝塞尔之后的曲线。所以再一次,如果没有错误,收到的故事是不充分的。我在这里尝试使用另一个系谱流程图来尝试更令人信服和综合的历史,正如我所提到的,该流程图连接到第 4 章(黎明)的流程图。
The story of computer graphics technology has usually been told in the narrative way by featuring one man, Ivan Sutherland, while at the same time honoring other founding fathers incoherently—by naming the highest award in the field after Steven Coons, or by naming a particular curve after Pierre Bézier. So once again, the received stories are inadequate if not in error. I attempt a more convincing and integrative history here using yet another genealogical flow chart that connects, as I mentioned, to the flow chart of chapter 4 (Dawn).
使用这种技术,我取代了简单的叙述,即计算机图形始于 Sutherland 在 1962 年编写的 Sketchpad,具有更强大的网络Coons、Bézier 和来自汽车和飞机行业的被遗忘的 de Casteljau,以及三个经常被忽视的玩家,他们都逃脱了纳粹恐怖的贡献:被阿尔伯特·爱因斯坦救下的赫伯·弗里曼;Bertram Herzog,被 Kindertransport 计划拯救;还有马塞利·韦恩,他的父亲在辛德勒的名单上。
With this technique I replace the simple narrative, that computer graphics began with Sketchpad written by Sutherland in 1962, with a more robust network featuring Coons, Bézier, and the forgotten de Casteljau from the automobile and aircraft industries, and three often overlooked players who all escaped the Nazi horror to contribute: Herb Freeman, who was saved by Albert Einstein; Bertram Herzog, saved by the Kindertransport program; and Marceli Wein whose father was on Schindler’s list.
伊万·萨瑟兰仍然是一个主要参与者,但与由他自己、蒂姆·约翰逊和拉里·罗伯茨组成的 MIT 同学三巨头共同担任创始角色。事实上,萨瑟兰给了我们第一个交互式渲染二维图形系统,称为Sketchpad。大约在同一时间,Sutherland 的同学(也很像)Tim Johnson 为我们提供了第一个交互式渲染的三维系统,称为 Sketchpad III——三维的 III,而不是版本号。这显然是任何类型的第一个交互式三维系统,尽管通用汽车公司的三维 DAC-1 系统大约在同一时间可用。Sketchpad III 在透视的使用上绝对超过了 DAC-1,它采用了 Triumvirate 中的第三位同学拉里·罗伯茨 (Larry Roberts) 设计的方法,这种方法至今仍在使用。
Ivan Sutherland continues to be a major player but shares the founding role with a Triumvirate of MIT classmates consisting of himself, Tim Johnson, and Larry Roberts. Indeed, Sutherland gave us the first interactively rendered two-dimensional graphics system, called Sketchpad. At about the same time Sutherland’s classmate (and lookalike) Tim Johnson gave us the first interactively rendered three-dimensional system, called Sketchpad III—the III for three dimensions, not version number. This was apparently the first interactive three-dimensional system of any sort, although the three-dimensional DAC-1 system from General Motors was available at approximately the same time. Sketchpad III definitely exceeded DAC-1 in its use of perspective, employing a method devised by the third classmate in the Triumvirate, Larry Roberts, a method that’s still used today.
Sutherland 和 Roberts 以及来自新机构 NASA 的 Robert Taylor 成为另一个新机构 ARPA(现称为 DARPA)的连续资助者。该行业的大部分早期资金来自 NASA 和 ARPA。Sutherland 随后与 David Evans 一起创立了 Evans & Sutherland 计算机图形设备供应商,同时也是犹他大学著名的计算机图形系,该领域的许多未来领导者都在那里接受了培训。泰勒随后创立了著名的计算机实验室施乐帕洛阿尔托研究中心(PARC)。罗伯茨继续帮助启动互联网。
Sutherland and Roberts, along with Robert Taylor from the new agency NASA, became successive funders at another new agency ARPA (now known as DARPA). Much of the early funding of the industry came from NASA and ARPA. Sutherland then joined David Evans to found Evans & Sutherland computer graphics equipment supplier and also the famed computer graphics department at the University of Utah, where many future leaders of the field got their training. Taylor then founded the famous computer laboratory Xerox Palo Alto Research Center (PARC). Roberts went on to help kickstart the internet.
本章的想法是,由虚构对象构成的虚构世界的内部模型可以渲染成二维图片。这一时期的破坏性混乱是苏联的核威胁和太空竞赛。暴政_是国家安全系统。这一时期的辉煌是美国完全放弃了资本主义原则,以便更快地为可能的核攻击做好准备。有远见的年轻天才们在没有竞标的情况下迅速发放了大量资金——尤其是来自两个新成立的机构,ARPA 和 NASA。这是一场豪赌,但收获颇丰。它这样做的一种方法是加速数字光的发展,这两个机构都做出了贡献——这一章中的 ARPA,下一章(阴影)中的 NASA。
The idea of this chapter is that internal models of fictional worlds made of fictional objects can be rendered into two-dimensional pictures. The disruptive chaos of the period was the Soviet nuclear threat and the space race. The tyranny was the national security system. The glory of the period was the complete abeyance of capitalistic principles in the United States to more quickly prepare it for possible nuclear attack. Vast amounts of money were handed out quickly, without competitive bidding, by visionary young geniuses—especially from the two newly created agencies, ARPA and NASA. It was a big gamble, but it paid off handsomely. One way it did so was to accelerate development of Digital Light, to which both agencies contributed—ARPA in this Shapes chapter, NASA in the next chapter (Shades).
另一种完全的力量,即艺术界,开始出现在这里的数码之光故事中。本章强调 Digital Light 贡献者与开创性艺术世界事件之间的密切联系,例如著名的Cybernetic Serendipity书籍和展览。艺术界和科技界都小心翼翼地互相关注从这里开始,两人都意识到了绘画艺术中的一些新事物。他们的联系一直持续到今天。
Another kind of force entirely, namely the art world, begins to figure in the Digital Light story here. This chapter emphasizes the close connections between Digital Light contributors and seminal art-world events, like the famous Cybernetic Serendipity book and exhibit. Both the art world and the tech world took careful note of one another starting here, both aware of something new in the pictorial arts. Their connection continues to this day.
第 6 章中的黑白线条图在第 7 章中推进到彩色表面渲染——从形状到阴影。事实上,摩尔定律以及 Epoch 2 计算机和电路实现的计算机放大技术的爆炸式增长使所有这些颜色成为可能:从 1967 年的第一个彩色像素到电影——第一部完全数字电影——在1970年代后期。和以前一样,本章的流程图是上一章图表的延续。这一章的复杂性促使我将其分为三个步骤或部分,由相应的摩尔定律功率因数命名,从 1X到 10X到 100 X。
The black-and-white line drawings in chapter 6 advance in chapter 7 to colored surface renderings—from shapes to shades. Indeed, Moore’s Law, and the explosive growth in computer Amplification enabled by Epoch 2 computers and circuitry made all this color possible: from the first color pixels in 1967 to the first articulation of the vision of The Movie—the first completely digital movie—in the late 1970s. As before, the flow chart of this chapter is a continuation of the previous chapter’s chart. The complexity of the chapter spurred me to break it into three steps, or sections, named by the corresponding Moore’s-Law power factor, from 1X to 10X to 100X.
第 1 步(摩尔定律 1 X)是关于第一个颜色像素的创建。它们出现在何时何地?Gene Youngblood 于 1970 年撰写的媒体艺术经典著作Expanded Cinema意外地为解开这个谜团提供了线索。滋生地原来是阿波罗登月。我们确定通用电气工程师 Rod Rougelot 和 Bob Schumacker 在设计 NASA Apollo 模拟器时展示了第一个渲染颜色。那是 1967 年,他们利用摩尔定律的第一批成果来做到这一点。我们了解将几何图形渲染为彩色像素的含义以及如何做到这一点。
Step 1 (Moore’s Law 1X) is about the creation of the first color pixels. Where and when did they appear? The media-arts classic written by Gene Youngblood in 1970, Expanded Cinema, serves as an unexpected lead to the solution of this mystery. The breeding ground turns out to be the Apollo Moon shot. We establish that General Electric engineers Rod Rougelot and Bob Schumacker displayed the first rendered color while designing a NASA Apollo simulator. This was 1967, and they used the first fruits of Moore’s Law to do so. We learn what it means to render geometry into color pixels and how to do it.
第 2 步(摩尔定律 10 X)涵盖 Xerox PARC、犹他大学和康奈尔大学的早期数字光。PARC 是 ARPA 和 NASA 的后裔。犹他大学计算机图形学起源于 ARPA。康奈尔大学是通用电气的鲁杰洛特和舒马克的后裔,是在帐篷里与唐格林伯格的一次偶然相遇。PARC 拥有世界上第一个通用彩色像素和第一个完全抗锯齿的像素渲染。但施乐决定不追求色彩。来自犹他州和康奈尔大学的学生负责第一个 3D 渲染计算机动画——康奈尔大学的彩色动画。在本节中,我将介绍元素渲染技术:纹理映射、着色模型和部分透明度等。
Step 2 (Moore’s Law 10X) covers early Digital Light at Xerox PARC, the University of Utah, and Cornell University. PARC descended from both ARPA and NASA. University of Utah computer graphics descended from ARPA. And Cornell’s descended from Rougelot and Schumacker at GE via a chance encounter in a tent with Don Greenberg. PARC had the first general-purpose color pixels available in the world and the first fully antialiased pixel renderings. But Xerox decided not to pursue color. Students from Utah and Cornell were responsible for the first three-dimensional rendered computer animations—Cornell’s in color. In this section I introduce elemental rendering techniques: texture mapping, shading models, and partial transparency, among others.
第 3 步(摩尔定律 100 X)介绍了纽约理工学院 (NYIT),该学院由长岛的特殊亚历山大·舒尔 (Alexander Schure) 领导。他幻想自己是沃尔特迪斯尼的继承人,并且是第一个在数字电影上投入巨资的金融家。他失去了一切,但在施乐 PARC 的“毕业生”和犹他大学的毕业生聚集在一起并组成后来成为皮克斯的团队之前,他失去了一切。电影——第一部完全由计算机生成的故事片——的愿景在这里首次形成。我在本节中解释了二维动画比三维动画更难,并介绍了最重要的 Alpha 通道。
Step 3 (Moore’s Law 100X) introduces the New York Institute of Technology (NYIT) headed by the idiosyncratic Alexander Schure on Long Island. He fancied himself heir to Walt Disney and was the first financier to invest heavily in the digital movie. He lost everything, but not before Xerox PARC “graduates” and University of Utah graduates came together there and formed the group later to become Pixar. Here is where the vision of The Movie—the first completely computer-generated feature film—first forms. I explain in this section that two-dimensional animation is harder than three-dimensional and introduce the all-important alpha channel.
摩尔定律的持续爆发驱使我们进入第 8 章,了解千禧年的电影本身——以及电影所象征的数字大融合。计算机图形现在让位于数字电影。当我介绍摩尔定律从 1,000X到 10,000,000的改进时X,我再次将它们细分为摩尔定律数量级的步骤。
The continued explosion of Moore’s Law drives us on into chapter 8 to The Movie itself at the millennium—and to the Great Digital Convergence that The Movie symbolizes. Computer graphics now gives way to just digital movies. As I cover Moore’s Law improvements from 1,000X to 10,000,000X, I again subdivide them into Moore’s Law order-of-magnitude steps.
第 4 步(摩尔定律 1,000 X)是关于卢卡斯影业的,由乔治卢卡斯在加利福尼亚州马林县创立。纽约理工学院的小组目睹了 Schure 与Tubby the Tuba (1975) 的失败。另一方面,卢卡斯是突破性特效电影《星球大战》的成功制片人(1977 年)。因此,1980 年,当他向他招手时,其中一些人高兴地跳到加利福尼亚与他一起工作。在这里,该团队首次在大银幕上曝光,与迪士尼公司签订合同,将经典的 cel 动画数字化,并聘请了第一位伟大的动画师。一家日本公司接洽该团队制作第一部电影,但众所周知,由于摩尔定律的力量不足,Monkey 项目未能实现。然后乔治和玛西娅卢卡斯离婚了,这让卢卡斯无法支持这个团队,并导致了皮克斯的衍生公司。一项主要的技术进步是从一堆渲染技术飞跃到一种用于表达无限量的语言——一种着色语言。另一种是有效处理运动模糊的突破性方法,对三维动画的发展至关重要。事实上,第一个 3D 角色动画出现了。几乎与 Lucasfilm 集团同时,Pacific Data Images (PDI) 和 Mathematical Applications Group Inc. (MAGI) 也开发了角色动画。
Step 4 (Moore’s Law 1,000X) is about Lucasfilm, founded by George Lucas in Marin County, California. The group at NYIT watched Schure fail with Tubby the Tuba (1975). Lucas, on the other hand, was a successful producer of the breakthrough special-effects movie Star Wars (1977). So some of the group happily leapt to California in 1980 to work with him when he beckoned. Here the group got its first big-screen exposure, worked on contract with the Disney company to digitize classic cel animation, and hired its first great animator. The group was approached by a Japanese company to make the first movie, but the Monkey project, as it was known, failed to materialize because of insufficient Moore’s Law power. Then George and Marcia Lucas divorced, making the group too expensive for Lucas to support and leading to the spin-out company Pixar. A principal technological advance was the leap from a grab bag of rendering techniques to a language for expressing an infinity of them—a shading language. Another was a breakthrough method for efficiently handling motion blur, crucial to the advancement of three-dimensional animation. In fact, the first three-dimensional character animations appeared. Almost in parallel with the Lucasfilm group, Pacific Data Images (PDI) and Mathematical Applications Group Inc. (MAGI) arrived at character animation.
第 5 步(摩尔定律 10,000 X–10,000,000 X)是关于第一部数字电影的创作。第一个是皮克斯的玩具总动员(1995 年),该公司于 1986 年从卢卡斯影业分拆出来。第二个是梦工厂动画公司,从 PDI 中分离出来,名为Antz(1998 年)。蓝天,第一批数字电影公司中的第三家,出自 MAGI,很快制作了冰河世纪(2002)。这三部电影是千禧年的多彩标记,也是数字大融合终于发生的标志。相应的流程图显示了这些早期数字工作室如何共享许多通用流程。
Step 5 (Moore’s Law 10,000X–10,000,000X) is about the creation of the first digital movies. The first was Toy Story (1995) by Pixar, the company spun out of Lucasfilm in 1986. The second was by DreamWorks Animation, out of PDI, called Antz (1998). Blue Sky, the third of the first digital movie companies, out of MAGI, soon produced Ice Age (2002). These three movies served as colorful markers of the millennium and a sign that the Great Digital Convergence had finally happened. The corresponding flow chart shows how these early digital studios shared many common flows.
这本书的最后一个想法-混乱-暴君三合会始于创造第一部数字电影的好主意。推动它的混乱是摩尔定律造成的巨大破坏。有几个暴君,最明显的是皮克斯的史蒂夫乔布斯。他的钱使公司得以存在,但实际上,他后来声称皮克斯和电影是他的想法,并拿走了大部分钱,更不用说功劳了。出于所有错误的以自我为中心的原因,他继续支持皮克斯度过了最艰难的日子,但效果与他分享了我们的愿景一样。忠实于暴虐的形式,他无意中创造了一个财务保护的空间,我们可以在其中生存以实现我们的愿景。
The final idea–chaos–tyrant triad of the book starts with the great idea being to create the first digital movies. The chaos driving it was the tremendous disruption created by Moore’s Law. There were several tyrants, the most obvious being Steve Jobs for Pixar. His money enabled the company to exist, but true to form, he subsequently claimed Pixar and The Movie were his ideas and took most of the money, never mind the credit. For all the wrong egocentric reasons, he continued to support Pixar through its most difficult days, but the effect was the same as if he had shared our vision. True to tyrannical form, he unintentionally created a financially protected space in which we could survive to realize our vision.
在没有评论或通知的情况下,1960 年代的计算机图形学社区采用了 Triumvirate 隐含实践的中心法则——蒂姆·约翰逊和拉里·罗伯茨在 1963 年的 Sketchpad III 中使用它,1968 年伊万·萨瑟兰 (Ivan Sutherland) 加入了他的头戴式显示器。正如最初的中心法则所规定的那样:图片应基于由欧几里得几何构建的三维模型,并以文艺复兴时期的视角在二维中观察。这是一个教条,因为计算机或计算并没有强迫这些选择。从抽象的几何图案到表现主义的飞溅,整个绘画世界都可以在计算机上实现。然而,计算机图形学主线尊重教条。
Without comment or notice, the 1960s computer graphics community adopted the Central Dogma as implicitly practiced by the Triumvirate—Tim Johnson and Larry Roberts using it in 1963 in Sketchpad III, joined by Ivan Sutherland in 1968 with his head-mounted display. As the original Central Dogma dictated: pictures shall be based on models built from Euclidean geometry in three dimensions and viewed in two dimensions with Renaissance perspective. It’s a dogma because there is nothing about computers or computation that forces these choices. The entire world of picture making, from abstract geometric patterns to expressionist splatters, is possible for computers. Nevertheless, the computer graphics mainline honors the dogma.
在 1960 年代后期,当彩色计算机图形成为可能时,中心法则悄悄地扩展到包括牛顿物理学,这也是计算机不需要的。这种完整的“交响乐形式”是当今数字电影、VR(虚拟现实)、视频游戏、飞行模拟器等领域中的一种。这里是简明扼要的总结:
In the late 1960s when color computer graphics became possible, the Central Dogma was silently extended to include Newtonian physics, also not required by computers. This full “symphonic form” is the one honored today in digital movies, VR (virtual reality), videogames, flight simulators, and so forth. Here it is in succinct summary:
中心法则=欧几里得模型、文艺复兴观点、牛顿物理学。
Central Dogma = Euclidean models, Renaissance perspective, Newtonian physics.
尽管高度结构化,但这种形式承认惊人的奇幻创造力,这从千禧年和千禧年以来制作的任何数字电影列表中都可以清楚地看出。但是中央教条形式之外的数字光的巨大子空间需要探索。绘画程序是早期不受中心法则约束的最明显的数码光创意工具。
Although highly structured, this form admits of astonishing fantastical creativity as is clear from any list of the digital movies made at and since the millennium. But the awesomely large subspaces of Digital Light outside the Central Dogmatic form beg to be explored. Paint programs are the most obvious Digital Light creative tools from the early days that were not subject to the Central Dogma.
请注意,在 Digital Light 的分析、图像处理部分,中心法则不是教条。就是这样。这就是现实世界的实际运作方式。至少它代表了人类规模的正常现实世界的最佳模型。
Notice that in the analytic, image processing half of Digital Light, the Central Dogma isn’t dogma. It just is. It’s how the real world actually works. At least it represents our best models for the normal real world at human scale.
另请注意,根据定义,CAD 受制于中心法则。它的对象必须存在于现实世界中并经受住物理测试才能在那个牛顿世界中使用。正是计算机图形学与 CAD 的共同历史根源使得中心法则对于面向图片的计算机图形学也显得如此自然且不言而喻。
Notice also that CAD is subject to the Central Dogma by definition. Its objects must exist in the real world and withstand physical testing for use in that Newtonian world. It’s the shared historical roots of computer graphics with CAD that has made the Central Dogma seem so natural—and unspoken—for picture-oriented computer graphics too.
计算机视觉人员喜欢说他们所做的与计算机图形学相反。他们的意思是,大脑从二维视网膜输入中生成我们感知的三维内部模型。他们实际上的意思是,大脑做的与受中心法则支配的计算机图形部分相反。
Computer vision people like to state that what they do is the inverse of computer graphics. What they mean is that the brain generates, from two-dimensional retinal input, three-dimensional internal models of what we perceive. What they actually mean is that brains do the inverse of that part of computer graphics subject to the Central Dogma.
到目前为止,我在这个结局中所写的内容总结了这本书以及 Digital Light 到千年的发展。但现在已经过去了 20 年,在此期间,不断爆发的摩尔定律推动了数字光领域更令人惊叹的进步。我在以下几节中只勾勒出其中的一些发展。
What I’ve written so far in this finale summarizes the book and the development of Digital Light up to the millennium. But two decades have now passed during which the always-exploding Moore’s Law has fueled ever more awesome advances in Digital Light. I sketch in the following sections only some of those developments.
在现代虚拟现实 (VR) 中,根据用户输入(例如头部位置)实时生成一对立体图像(每只眼睛一个)。用户佩戴一副特殊的护目镜或眼镜。实时执行大量计算并不容易,需要付出很多特别的努力。但回想一下经验法则:如果您希望计算速度更快,请使用专用硬件。算法相同,但由硬件加速。换句话说,在硬件的帮助下,与制作电影相同的技术正在被用于创建 VR。理解电影像素在很大程度上解释了 VR 像素。硬件支持有时只不过是您的手机提供的。(就上下文而言,iPhone 于 2007 年推出,Android 系统于 2008 年推出,就在昨天。)
In modern virtual reality (VR), a stereo pair of images—one for each eye—is generated in real time and according to user input, such as head position. The user wears a special pair of goggles or glasses. Performing massive computations in real time is not easy and requires much special effort. But recall the rule of thumb: if you want a computation to go faster, use special-purpose hardware. The algorithms are the same but sped up by the hardware. In other words, the same techniques used to make movies are being used, with hardware help, to create VR. Understanding movie pixels explains VR pixels to a large degree. And the hardware assist is sometimes nothing more than what your cellphone provides. (For context, the iPhone was introduced in 2007 and the Android system in 2008, just yesterday in the grand scheme of things.)
阴影章节中的流程图自然地延伸到了对 VR 的讨论中。梦工厂动画公司的动画师 Eric Darnell 与 Maureen Fan(作为 CEO)在硅谷共同创立了一家 VR 公司 Baobab Studios。公司中的一些人,例如拉里·卡特勒(作为首席技术官),是梦工厂和皮克斯的毕业生。梦工厂的格伦恩蒂斯、迪士尼的格伦基恩和皮克斯的我都是这家初创公司的顾问。Baobab 已经在 VR 中创建并制作了多个获奖角色动画。同样,来自视觉效果工作室和游戏公司的许多人现在都在创建 VR 内容。
The flow chart from the Shades chapter extends naturally into this discussion of VR. Eric Darnell, animator at DreamWorks Animation, cofounded with Maureen Fan (as CEO) a VR company, Baobab Studios, in Silicon Valley. Some in the company, such as Larry Cutler (as CTO), are graduates of DreamWorks and Pixar. Glenn Entis from DreamWorks, Glen Keane from Disney, and I from Pixar are advisers to the startup. Baobab has already created and produced several prize-winning character animations in VR. Similarly, many people from visual effects studios and game companies are now creating VR content.
目前对数字光感兴趣的是增强现实 (AR),其中合成图片与现实世界实时结合。一般来说,这是拍摄和制作数码光的组合。现实世界是实时数字化的。AR设备实时合成一个虚构的世界,并将其像素与现实世界的像素相结合,创造一种全新的视觉体验。在最简单的情况下,这只是合成场景在真实场景上的简单叠加,使用 Alpha 通道。现实世界只是合成前景的二维背景。事实上,有时现实世界根本没有数字化。它只是简单地通过并与护目镜或眼镜内的合成图像进行光学组合。
Of current interest in Digital Light is augmented reality (AR), where a synthesized picture is combined with the real world in real time. In general, this is a combination of take and make Digital Light. The real world is digitized in real time. The AR device synthesizes a fictitious world in real time and combines its pixels with the real-world pixels to create a new kind of visual experience. In the simplest cases, this is just a simple superposition, using an alpha channel, of the synthetic scene over the real scene. The real world is simply a two-dimensional background to the synthetic foreground. In fact, sometimes the real world is not digitized at all. It’s simply passed through and combined optically with the synthetic images inside the goggles or glasses.
艺术家 Darcy Gerbarg 最近一直在使用 AR 探索 Digital Light 的边缘。她的作品说明了本书的类别。她的主要工具是 Google 的 TiltBrush,一款 VR 应用程序,以及 Adobe 的 Photoshop,一款经典的二维像素应用程序。倾斜画笔允许画家使用符合中心教条的笔触在三个维度上进行绘画。它们以欧几里得几何建模,凹凸贴图看起来像笔画,根据牛顿物理学投射阴影,并以文艺复兴时期的视角观看。但随后她使用手机中的特殊程序将 VR 绘画笔触与来自现实世界的图像结合起来。换句话说,她在移动时从选定的视点看到她的 3D VR 绘画笔触,叠加在她工作室的二维手机图像上。然后她将这些 AR 场景的选择带入 Photoshop,并按照她的艺术意愿创造性地改变像素的内容。她的作品以一种全新而有力的方式将你拉入二维空间,2
The artist Darcy Gerbarg has recently been exploring the edges of Digital Light using AR. Her work illustrates the categories of this book. Her principal tools are Google’s Tilt Brush, a VR app, and Adobe’s Photoshop, the classic two-dimensional pixel app. Tilt Brush allows a painter to paint in three dimensions with strokes of paint that honor the Central Dogma. They are modeled in Euclidean geometry, are bumpmapped to look like paint strokes, cast shadows according to Newtonian physics, and are viewed in Renaissance perspective. But then she combines the VR paint strokes with images from the real world using a special program in her cellphone. In other words, she sees her three-dimensional VR paint strokes, from selected viewpoints as she moves, superimposed over two-dimensional cellphone images of, say, her studio. Then she brings selections of these AR scenes into Photoshop and creatively changes the content of pixels at her artistic will. Her work pulls you into two-dimensional space in a new and powerful way, not subject to the Central Dogma but using it (figure 9.2).2
在数字光的当前极端是一个更复杂的案例——通常称为混合现实 (MR),以强调它与简单 AR 的区别:计算机从现实世界中推导出三维结构,因此合成世界似乎与它——比如说,一种合成动物在现实世界的桌面上令人信服地行走。这类似于我们的大脑必须做的事情——计算机图形学的反面,当然受制于中心法则。在 AR 中,只有真实世界和合成世界相结合。在 MR 中,创意空间结合在一起——两个世界的内部模型交织在一起。
At the current extreme of Digital Light is a more complex case—often called mixed reality (MR) to emphasize how it differs from simple AR: a computer derives three-dimensional structure from the real world so that the synthetic world appears to interact meaningfully with it—a synthetic animal walks convincingly on a real-world tabletop, say. This resembles what our brains must be doing—the inverse of computer graphics, subject to the Central Dogma of course. In AR only the Display Spaces of the real and synthetic worlds combine. In MR the Creative Spaces combine—the internal models of the two worlds intertwine.
图 9.2
Figure 9.2
充满活力的乐队-TL2-205552D2eC2,© Darcy Gerbarg,2018。
Vibrant band-TL2-205552D2eC2, © Darcy Gerbarg, 2018.
正如我所写(在 2020 年),MR 有几种技术方法:微软正在追求其 HoloLens 设备,而 Magic Leap 是一种直接到视网膜的方法。我们等待这些非凡的设备和其他设备的成熟。请注意,它们似乎分别代表了瞳孔外和瞳孔内的解决方案,使用了本书电影和动画章节中的术语。瞳孔代表了我们大脑外部和内部发生的事情之间的硬边界。3
As I write (in 2020), there are several technological approaches toward MR: Microsoft is pursuing its HoloLens device and Magic Leap a direct-to-retina approach. We await the maturity of these extraordinary devices and others. Note that they appear to represent, respectively, outside-the-pupil and inside-the-pupil solutions, utilizing the terminology from the movie and animation chapter of this book. The pupil represents the hard boundary between what happens external to and internal to our brains.3
在我们等待期间,有关 MR 的技术问题比比皆是。现实世界的对象会隐藏计算对象吗?并在他们身上投下阴影?计算对象会通过透明的现实世界对象显示吗?现实世界的光源会改变计算对象的阴影吗?我在 Siggraph 2019 上问过的专家向我保证,其中一些问题已经得到解答,但仍然是商业机密。两个世界的真正混合似乎是一个令人生畏的问题。它是拍摄和制作、拍摄和计算的完全整合,是计算机图形学和逆向计算机图形学的综合,两者都受制于中心法则。当然,这是一个足以激发一代计算机图形学家(如果不是神经科学家和科幻小说作者)和艺术家的问题。
Technical questions about MR abound while we wait. Will real-world objects hide computed objects? And cast shadows on them? Will computed objects show through transparent real-world objects? Will real-world light sources change the shading of the computed objects? Experts I quizzed at Siggraph 2019 assured me that some of these questions have already been answered but are still trade secrets. True mixture of the two worlds seems a daunting problem. It’s a full integration of take and make, of shoot and compute, a synthesis of computer graphics and inverse computer graphics both subject to the Central Dogma. Surely it’s a big enough problem to fuel a generation of computer graphicists (if not neuroscientists and science-fiction authors)—and artists.
一个新术语刚刚演变为容纳这可能发生的许多可能方向。它被称为扩展现实的 XR,适用于真实和虚拟环境的任何混合。
And a new term has just evolved to house the many possible directions this might go. It’s called XR for extended reality, for any mixture of real and virtual environments.
皮克斯人在 1996 年获得了技术学院奖,这是多年来的众多奖项之一。技术奖项在与电视转播的奥斯卡颁奖典礼一样迷人的颁奖典礼上颁发——同样的燕尾服和礼服、豪华轿车和电影明星、华丽的宴会和限时的获奖感言。但没有广播电视工作人员,也没有红地毯采访。电影艺术与科学学院理所当然地感觉到,公众可能对地面烟雾机或蜘蛛网发生器不感兴趣,这是我多年来亲眼目睹的两项技术奖项。
Pixar people won a technical Academy Award in 1996, one of many over the years. The technical awards are handed out at a ceremony that’s just as glamorous as the televised Academy Awards—the same tuxedos and gowns, limousines and movie stars, fancy banquet, and time-limited acceptance speeches. But no broadcast television crews and no red-carpet interviews. The Academy of Motion Picture Arts and Sciences senses, justifiably, that the general public might not be interested in ground-hugging fog machines or spider-web generators, two technical awards I’ve personally witnessed over the years.
该活动总是由电影明星主持。1996 年是理查德·德莱福斯(Richard Dreyfuss),他因许多角色而闻名,尤其是乔治·卢卡斯 (George Lucas) 的美国涂鸦(1973) 中的柯特。Ed Catmull 和我与 Pixarians 坐在一张桌子旁,等待获奖。几个月前, 《玩具总动员》的首次亮相就轰动一时。4
The event is always hosted by a movie star. In 1996 it was Richard Dreyfuss, famous to us for many roles, but especially as Curt in George Lucas’s American Graffiti (1973). Ed Catmull and I were seated at a table with the Pixarians to be awarded. Toy Story had had its smashing debut just a few months earlier.4
Dreyfuss 从关于演员和技术人员如何相互依赖以及另一个非电视奥斯卡颁奖典礼对像他这样的演员的重要性的礼仪演讲开始。“我们演员和技术人员正在共同迈向未来,”他说。但随后他又增加了一个转折点。他看着我们的桌子并说:“请注意,皮克斯的人,我一起说的!” 观众席间传来一阵紧张的窃笑声。那里的演员显然一直在听我所在行业的同事过于油嘴滑舌的说法,“现在任何一天,我们都会用模拟代替演员。”
Dreyfuss began with the de rigueur speech about how actors and technologists depend on one another and how important this other, non-televised Academy Award ceremony is to actors such as himself. “We actors and technologists are marching together into the future,” he said. But then he added a twist. He looked at our table and said, “Notice, Pixar people, that I said together!” A nervous titter slid through the audience. The actors there had obviously been listening to overly glib statements from colleagues in my industry that “any day now, we’ll replace actors with simulations.”
2000 年,我受邀为《科学美国人》杂志写一篇关于这个主题的文章——更换演员的可能性。然后我写的东西强调了一些我们还无法解释的人的特别之处——甚至一点也解释不了。5
In 2000 I was invited to write an article for Scientific American magazine about that very subject—the possibility of replacing actors. What I wrote then emphasized the something special about people that we can’t yet explain—not even a little.5
我在这里称其为创造力,但这是一个不精确的术语。我想到的是图灵、科特尔尼科夫和傅立叶所做的,程序员、工程师和建模师所做的,以及动画师和演员所做的。
I’ll call it creativity here, but that’s an imprecise term. What I have in mind is what Turing and Kotelnikov and Fourier did, what programmers and engineers and modelers do, and what animators and actors do.
这就是图灵在发明计算和存储程序计算机时所做的,看似无中生有。这是创造力的惊人飞跃,是有史以来最伟大的飞跃之一。这是理论多样性的技术创造力——来自象牙塔。Kotelnikov 也用采样定理做到了这一点,这是另一个伟大的创造性飞跃。而且,当然,傅立叶的好主意是科捷尔尼科夫跳出来建造他的。
It’s what Turing did when he invented computation and the stored-program computer, seemingly out of nothing. It was an astonishing leap of creativity, one of the greatest ever. That’s technical creativity of the theoretical variety—from the ivory tower. Kotelnikov did it too with the Sampling Theorem, another of the great creative leaps. And, of course, Fourier’s great idea was the one Kotelnikov leapt from to build his.
当程序员从一长串无意义的计算机指令中构建一个程序来做一些有意义的事情——比如计算玩具总动员时,这就是程序员所做的,或者使他们能够做到这一点的原因。那是技术创造力,工程多样性——来自我在这里所说的臭味。正如摩尔定律所描述的,不断创造出速度极快的计算机是这种多样性的另一个例子。另一个是使用几何和着色语言构建复杂的角色内部模型。
It’s what programmers do, or what enables them to do it, when they build from a very long list of meaningless computer instructions a program that does something meaningful—like compute Toy Story. That’s technical creativity, of the engineering variety—from the stinks as I’ve called it here. The constant creation of awesomely faster computers, as described by Moore’s Law, is another example of this variety. And another is building elaborate internal models, of characters say, using geometry and a shading language.
当动画师让我们相信一堆三角形是有意识的并且感到痛苦时,动画师会这样做——这是对精心制作的角色的启发。这就是艺术创造力。演员们也有它,让我们相信他们的身体所承载的思想属于与他们完全不同的人。事实上,演员和动画师认为这是相同的技能。如前所述,皮克斯根据动画师的表现来雇佣动画师。
And it’s what animators do when they convince us that a stack of triangles is conscious and feels pain—the inspiriting of crafted characters. That’s artistic creativity. Actors have it too, convincing us that their bodies house minds belonging to people completely distinct from themselves. In fact, actors and animators believe it’s the same skill. As previously stated, Pixar hires animators by how well they act.
我在 2000 年写的内容在 20 年后的今天仍然有效:我们不知道如何更换演员。但是我们可以替换演员的外表。代表演员的屏幕外观称为头像。我们可以用令人信服的化身代替银幕上的演员——即使是情感特写。我知道这一点,因为它已经完成了。在《本杰明·巴顿奇事》 (2008 年)中有布拉德·皮特的镜头,其中布拉德·皮特不是布拉德·皮特,而是他的化身——他外表的数字表示。关键是化身是由一位伟大的演员“驱动”的,即布拉德皮特本人。他和他的技能没有被取代。只有他的屏幕外观是。令人信服的细微差别是他的,而不是某些计算机程序的。6
What I wrote in 2000 still holds today two decades later: we don’t have a clue about how to replace actors. But we can replace the appearance of an actor. A screen appearance that represents an actor is called an avatar. We can replace an actor onscreen with a convincing avatar—even in emotional closeup. I know this because it’s been done. There are shots of Brad Pitt in The Curious Case of Benjamin Button (2008) where Brad Pitt is not Brad Pitt but an avatar of him—a digital representation of his appearance. The point is that the avatar is “driven by” a great actor, namely Brad Pitt himself. He and his skill were not replaced. Only his screen appearance was. The convincing nuance was his, not some computer program’s.6
这是我在 2000 年的预测——只要人类演员的化身被那些特殊的人叫做演员。我在Benjamin Button的存在证明之前八年通过计算机动画的持续发展进行推断,做出了预测。
That was my prediction in 2000—that we would be able to make a “cameraless” live-action movie so long as the avatars of the human actors were controlled by those special people called actors. I made the prediction eight years before the existence proof of Benjamin Button by extrapolating from the continued advancement of computer animation.
动画师的技能与演员的技能基本上没有区别,除了用于表达的媒介——演员的人体或动画师的三角形。它们都让我们相信内心的生活,事实上,不是演员或动画师在实践他或她的艺术。正如我们在第 8 章中看到的那样,到千禧年为止,至少有三部电脑动画电影向我们展示了动画三角形在被称为动画师的创作者操纵时具有内在生命。那一年我实现的飞跃是,根据摩尔定律的奇迹,人物的真实感将无情地增加,达到令人信服地代表人类外表的程度。卡通化身将向现实化身发展。让我们相信他们的内心生活仍然是动画师和演员“驱使他们”的独特工作。
Animators have a skill that’s essentially indistinguishable from that of actors except by the medium used for expression—the human body for actors or triangles for animators. They both convince us of an inner life that is, in fact, not that of the actor or animator practicing his or her art. As we saw in chapter 8, by the millennium at least three computer-animated movies had shown us that animated triangles had inner lives when they were manipulated by the creators called animators. The leap I made that year was that the realism of the characters would inexorably increase, by the Moore’s Law miracle, to a point where they would convincingly represent the appearance of human beings. Cartoon avatars would evolve toward realistic avatars. It would remain the unique job of animators and actors “driving them” to convince us of their inner life.
我在 2000 年挥手建议,因为我们花了 20 年的时间从 1975 年的电脑动画电影的想法到 1995 年的真实电影,也许还需要 20 年才能实现第一部无相机——但不是无演员——电影。所以 2020 年实际上已经到来,因为我对本章进行了最后的编辑,这清楚地表明我的挥手只是那个。没有证据表明一部情感上有效的无相机电影,只有人类化身,没有可见的人类。当然,没有证据表明演员或动画师被计算机模拟所取代。Richard Dreyfuss 可以在可预见的未来放松一下。
I waved my hands in 2000 and suggested that since it took us 20 years to get from the idea of a computer-animated movie in 1975 to a real movie in 1995, perhaps it would take 20 more to arrive at the first cameraless—but not actorless—movie. So 2020 is actually here as I make final edits to this chapter, which makes it clear that my handwave was only that. There’s no evidence in sight of an emotionally effective cameraless movie, with only human avatars and without visible humans. And certainly no evidence of actors, or animators, being replaced by computer simulations. Richard Dreyfuss can relax for the foreseeable future.
但 。. . 2020 年的进步暗示了一些不同的事情。考虑最近的电影《爱尔兰人》(2019)。每个伟大的七十多岁的人罗伯特·德尼罗、乔·佩西和阿尔·帕西诺都扮演着年轻的自己。这种“去老化”介于使用数码相机拍摄电影和使用计算机图形制作电影之间。而且它远非无摄像头。取而代之的是一个精心制作的摄像机(实际上是三个摄像机)用于记录演员的表演,就像在经典电影制作中一样。它们不受早期尝试渲染演员化身时使用的点或其他特殊标记的影响。然后数字艺术家使用复杂的、最先进的软件接管,仔细地将每个演员的真实面孔转换成令人信服的年轻自我代表。德尼罗的化身是年轻的德尼罗。它是由德尼罗本人推动的。数字艺术家将渲染复杂头像的缓慢过程称为“烘焙”。所以,7
But . . . 2020 has advances that hint at something different. Consider a recent movie, The Irishman (2019). Each of the great septuagenarians Robert De Niro, Joe Pesci, and Al Pacino acts in it as his younger self. This “de-aging” lies somewhere between taking a movie with a digital camera and making one with computer graphics. And it’s far from cameraless. Instead an elaborate camera (actually three cameras) is used to record the actors’ performances as in classical filmmaking. They are unencumbered by dots or other special markers used in earlier attempts at rendering an actor’s avatar. Then digital artists, using sophisticated, state-of-the-art software, take over to carefully convert each actor’s actual face into a convincing representation of his younger self. The avatar of De Niro is a younger De Niro. It’s driven by De Niro himself. Digital artists refer to the slow process of rendering a complex avatar as “baking.” So, to bake a movie is to both take and make one—an amalgam of analytic and synthetic Digital Light.7
不过,请注意:这些奇妙的欺骗性艺术进步可能会被不择手段的人用来对付我们。这种对人的虚假陈述被称为深度伪造,并且已经被部署。8
A word of caution, though: These wonderfully deceptive artistic advances can be used against us by the unscrupulous. Such misrepresentations of people are called deepfakes and are already being deployed.8
像素,一种看似简单但微妙的设备,将所有数字图片制作和拍摄结合到一个领域,即数字光,其中几乎包含所有现代图片。只需直观地介绍三个伟大的基本思想即可轻松理解数字光:傅里叶波、Kotelnikov 样本和图灵计算。
The pixel, a seemingly simple but subtle device, unites all digital picture making and taking into one realm, Digital Light, which comprises nearly all of modern pictures. Digital Light can be easily understood by the intuitive presentation of just three great foundational ideas: Fourier waves, Kotelnikov samples, and Turing computations.
与数字光相关的两项基础高科技——计算机和电影——都在直观的层面上进行了处理。计算机显然是任何“数字”的基础。电影也是因为它们运用了采样定理,而 Digital Light 从它们那里继承了术语和概念。在本书中,我直接记录了这两种技术的历史。显示这种历史的更好方法是作为许多人的家谱流程图。这与以一个英雄人物为主角的引人入胜的叙述大不相同,后者非常受欢迎,但经常歪曲事实。这本书的灵魂在于这些图表所代表的“家庭”故事,包括所有通常的庆祝和争吵、合作和竞争、高尚和邪恶的人际关系。
Two foundational high technologies are relevant to Digital Light—computers and movies—both treated at an intuitive level. Computers are obviously foundational to anything “digital.” Movies are too because they exercise the Sampling Theorem, and from them Digital Light inherited terminology and concepts. In this book I set the record straight on the histories of these two technologies. The better way to show such history is as a genealogical flow chart of many people. This is very different from the seductive narrative, featuring one heroic person, that is so popular but so often corrupts the facts. The soul of the book is in the “family” stories represented by these charts, with all the usual celebrations and quarrels, collaborations and competitions, high-mindedness and deviltry of human relationships. The flow-charting techniques are then applied to the history of Digital Light technology itself, particularly the path through it that yielded the first digital movies.
在所有这些基础思想和高科技的历史中,一个重复的主题是思想-混乱-暴君三元组:一个伟大的想法,一个需要或推动其实施的混乱或破坏,以及一个暴君或其他形式的暴政,通常为错误的原因,创作者们为实现这个想法而苦苦挣扎。
A repeating motif resounding in all these histories of foundational ideas and high technologies is an idea–chaos–tyrant triad: a great idea, a chaos or disruption demanding or driving its implementation, and a tyrant or other form of tyranny that protects, often for the wrong reasons, the creators as they struggle to realize the idea.
随着本书的进行,鼓声变得越来越响亮,然后随着它到达最后一章而变得震耳欲聋和确定。这是摩尔定律所描述的每五年一次的常规数量级的额外功率爆发。我密切关注这颗爆炸的超新星,这是我们几乎无法理解的革命性发展。它扩展了我们作为人类的数量级限制。它放大了我们。Digital Light 只是其耀眼的成就之一。
A drumbeat becomes louder and louder as the book proceeds and then booms as it reaches the last chapter where it becomes deafening and definitive. It’s the regular order-of-magnitude burst of additional power every five years, described by Moore’s Law. I pay close attention to this exploding supernova, a revolutionary development that we barely comprehend. It stretches our order-of-magnitude limitations as human beings. It Amplifies us. Digital Light is but one of its shining achievements.
任何简单到可以理解的系统都不会复杂到可以智能地运行,而任何复杂到可以智能地运行的系统将太复杂而无法理解。
Any system simple enough to be understandable will not be complicated enough to behave intelligently, while any system complicated enough to behave intelligently will be too complicated to understand.
——乔治·戴森,人工智能第三定律,Analogia 9
—George Dyson, third law of AI, Analogia9
几年前,我妻子在剑桥大学国王学院休假期间,约翰·布朗斯基尔(John Bronskill)找到了我——艾伦·图灵(Alan Turing)在那里完成了他的开创性的工作。Bronskill 让我大吃一惊:“Alvy,我们不必再编程了!” 他因为 Adobe Photoshop 编写扩展而出名,这可能是专业领域中最受欢迎的像素应用程序。
John Bronskill, an old pixel-packing colleague, approached me a couple of years ago during my wife’s sabbatical at King’s College, Cambridge—where Alan Turing did his seminal work. Bronskill startled me: “Alvy, we don’t have to program anymore!” He had made a name for himself writing extensions for Adobe Photoshop, perhaps the most popular pixel app in the professional world.
“你是什么意思?”
“What do you mean?”
“读这个,”他边说边把一份科学论文塞到我手里。它来自加州大学伯克利分校的人工智能研究实验室。该论文描述了一个特定种类的神经网络,该网络使用 1000 张未标记和任意的马照片以及 1000 张未标记和任意的斑马照片进行训练。马的照片包含任意数量的各种颜色的马,任意排列。当然,虽然斑马颜色没有变化,但斑马照片很相似。所有这些照片都是数字的,包括像素。经过适当的训练(我不会描述),网络可以完成以下惊人的壮举:呈现任意斑马照片,经过训练的网络将返回相同的照片,但每只斑马都被替换为马(图 9.3,上对)。(实际上,每匹斑马都有马色版本,反之亦然,每匹马都被自己的斑马条纹版本所取代。)
“Read this,” he said as he thrust a scientific paper into my hands. It was from the Artificial Intelligence Research Laboratory of the University of California at Berkeley. The paper described a neural net of a certain variety that was trained with 1,000 unlabeled and arbitrary photographs of horses and 1,000 unlabeled and arbitrary photographs of zebras. The horse photographs contained any number of horses of various colors in arbitrary arrangements. The zebra photographs were similar although the zebra colors didn’t vary, of course. All these photographs were digital, comprising pixels. After suitable training (which I won’t describe), the net could do the following astonishing feat: presented with an arbitrary photograph of zebras, the trained net would return the same photograph but with every zebra replaced with a horse (figure 9.3, upper pair). (Actually, with a horse-colored version of each zebra or vice versa, each horse replaced by a zebra-striped version of itself.)
“它是如何工作的?” 我问道,并补充说:“我认为这个问题甚至没有明确定义。” 什么是计算机的马?什么是斑马?你如何将一个映射到另一个?
“How does it work?” I asked, adding, “I don’t think that problem is even well-defined.” What’s a horse to a computer? What’s a zebra? How do you map one to the other?
约翰只是忽略了这些观察:“我不知道。没有人会。它就是这样做的!逆向工程太难了。”
John just brushed past these observations: “I don’t know. Nobody does. It just does it! It’s too hard to reverse engineer.”
同一个神经网络做了其他惊人的事情。在风景照片和文森特梵高的画作上训练,它会接收任意一张风景照片并输出一幅文森特风格的画作。或相反亦然。或者以莫奈的风格。或者它将夏季景观转换为冬季景观。或相反亦然。
The same neural net did other amazing things. Trained on landscape photographs and on paintings by Vincent van Gogh, it would take in an arbitrary landscape photo and output a painting in the style of Vincent. Or vice versa. Or in the style of Monet. Or it would convert summer landscapes to winter landscapes. Or vice versa.
我本着“Digital Light 的下一步是什么?”的精神提到这一点。我承认我不明白这里发生了什么,或者从长远来看它是否重要。但让我们考虑一下。
I mention this in the spirit of “what comes next in Digital Light?” I confess that I don’t understand what’s going on here, or whether it’s even important in the long run. But let’s think about it a little.
图灵允许他的存储程序或通用图灵机在其程序上进行计算,就好像它是数据一样。这正是他发明的存储程序计算机所允许的。马到斑马的计算是对程序计算的一个例子吗?图灵对这种可能性和人工智能特别着迷。就上下文而言,现代计算机的操作系统通常不允许对程序进行计算,因为它很容易造成破坏。
Turing allowed his stored-program, or universal, Turing machine to compute on its program as if it were data. That’s exactly what his invention of the stored-program computer allowed. Is the horse-to-zebra computation an example of computing on the program? Turing was particularly fascinated by this possibility, and by artificial intelligence. For context, the operating systems of modern computers typically disallow computing on the program because it can easily create havoc.
神经网络是在普通计算机上模拟的,因此不会计算进行模拟的程序。但是假设神经网络是一个实际的神经网络,而不仅仅是一个模拟。可以理解为在自己的程序上进行计算吗?我相信如此。我们自己的大脑显然是一个神经网络,据我们所知,其中没有与数据存储分开的程序存储。除了图灵计算之外,它可能没有做任何事情。在 80 年的概念经验之后,我们还没有发现任何仔细的过程。
The neural net is simulated on a normal computer, so the program doing the simulation is not being computed on. But suppose the neural net was an actual neural net, not just a simulation. Could it be construed as computing on its own program? I believe so. Our own brain is clearly a neural net, and there’s no program store separate from a data store in it, so far as we know. And it’s probably not doing anything beyond a Turing computation. We’ve not found any careful process that does so after 80 years of experience with the concept.
图 9.3
Figure 9.3
1965 年,我开始在斯坦福大学攻读研究生,因为它是(我所知道的)提供名为人工智能的迷人新学科的两所大学之一——如今通常缩写为 AI。麻省理工学院是另一个。我从斯坦福大学的人工智能创始人约翰麦卡锡那里学到了东西。我与麻省理工学院的另一位创始人马文·明斯基进行了几次有影响的讨论。
In 1965 I began graduate studies at Stanford because it was one of two universities (that I knew of) offering the fascinating new subject called artificial intelligence—often abbreviated these days to AI. MIT was the other. I learned from John McCarthy, a founding AI father at Stanford. And I had several influential discussions with MIT’s Marvin Minsky, another founding father.
几年后,我退出了人工智能,并决定在我的有生之年不会发生这种情况。考虑到我可能还有二十年的时间,这可能是一个过早的结论,但与此同时,我帮助制作了第一部数字电影。完成这些后,我现在有时间重新思考人工智能。事实上,我从未停止过这样做。
After a couple years I dropped out of AI, having decided that it wasn’t going to happen in my lifetime. That might have been a premature conclusion given that I probably have two decades to go but, in the meantime, I helped make the first digital movie. Having accomplished that, I now have time to return to musing about AI. In fact, I’ve never stopped doing so.
约翰·布朗斯基尔的话让我措手不及。我一直认为,当人工智能最终被解释时,我就能理解这个解释。然而,这里有一个机器学习的例子——可能还不够先进,还不能被称为人工智能——我无法理解。是因为网络在自己的程序上计算吗?我们知道,一般来说,我们甚至无法判断程序是否会停止这样简单的事情,所以我们无法弄清楚这个斑马马程序做了什么也就不足为奇了。
It was John Bronskill’s remark that brought me up short. I had always assumed that when AI was finally explained, I would be able to understand the explanation. Yet here was an example of machine learning—perhaps not quite advanced enough yet to be called AI—that I couldn’t understand. Is it because the net computes on its own program? We know that, in general, we can’t even tell such a simple thing as whether a program will halt, so perhaps it’s no surprise we can’t figure out what this zebra-horse program does.
就其价值而言,从马到斑马的过程并不完美。Bronskill 向我展示的论文中展示的一个示例将弗拉基米尔·普京 (Vladimir Putin) 赤膊骑在马背上的著名照片作为输入。输出是普京和他的马融合成一个双头斑马条纹半人马(图 9.4)。10
For what it’s worth, the horse-to-zebra process isn’t perfect. One example presented in the paper Bronskill showed me has as input the famous photograph of Vladimir Putin riding shirtless on horseback. The output is both Putin and his horse melded into a two-headed, zebra-striped centaur (figure 9.4).10
当前革命的本质是我们无法预测它超过一个数量级。我们只需要乘风破浪,看看接下来会带我们去什么令人兴奋甚至神秘的地方。
The very nature of the current revolution is that we cannot predict it beyond one order of magnitude. We just have to ride the wave and see to what exciting, even mysterious, place it takes us next.
图 9.4
Figure 9.4
我们在这里做了什么?我们用一个抽象的数学对象代替了一张图片,并用它打开了一个广阔的新想象领域。该对象令人不安地重复和离散,它的每个位点都在等待应用它自己的无限小斑点。但从它而来的是世界的所有图片,或世界。我以伊塔洛·卡尔维诺(Italo Calvino)的小说《看不见的城市》( Invisible Cities)中的一段作为结尾,其中作者想象年轻的探险家马可·波罗向年迈的蒙古皇帝忽必烈描述他在尤多西亚城发现了一块魔毯。这是一场介于真实与再现之间的对话:
What have we done here? We’ve replaced a picture with an abstract mathematical object, and with it opened a vast new realm of imagination. The object is disconcertingly repetitive and discrete, with each of its loci awaiting application of its own little blob of infinity. But from it comes all the pictures of the world, or worlds. I close with a passage from Italo Calvino’s novel Invisible Cities, in which the author imagines the young explorer Marco Polo describe to Kublai Khan, the aging Mongol emperor, his discovery of a magic carpet in the city of Eudoxia. It’s a conversation at the boundary between real and represented:
欧多克西亚上下延伸,蜿蜒的小巷、台阶、死胡同、小屋,保留了一块地毯,您可以在其中观察城市的真实面貌。乍一看,似乎没有什么比 Eudoxia 更像地毯的设计了,以对称的动机布置,其图案沿着直线和圆形重复,与色彩鲜艳的尖顶交织在一起,在整个纬线上都可以遵循这种重复。但是如果你停下来仔细观察,你会相信地毯上的每个地方都对应着城市中的一个地方,城市中的所有东西都包含在设计中,按照它们的真实关系排列,这一切都逃不过你的眼睛。被喧嚣、人群、推搡弄得心烦意乱。欧多西亚的所有困惑,骡子的叫声,油烟的污渍,鱼腥味是你掌握的不完整视角中明显的东西;但地毯证明了城市在某一点上显示出它的真实比例,几何图案隐含在它的每一个最微小的细节中。. . . 一位神谕被问及地毯和城市这样不同的两个物体之间的神秘联系。两个物体中的一个——神谕回答——具有众神赋予星空的形状和世界旋转的轨道;另一个是近似反映,就像每个人类创造一样。
——伊塔洛·卡尔维诺,《看不见的城市》11
In Eudoxia, which spreads both upward and down, with winding alleys, steps, dead ends, hovels, a carpet is preserved in which you can observe the city’s true form. At first sight nothing seems to resemble Eudoxia less than the design of that carpet, laid out in symmetrical motives whose patterns are repeated along straight and circular lines, interwoven with brilliantly colored spires, in a repetition that can be followed throughout the whole woof. But if you pause and examine it carefully, you become convinced that each place in the carpet corresponds to a place in the city and all the things contained in the city are included in the design, arranged according to their true relationship, which escapes your eye distracted by the bustle, the throngs, the shoving. All of Eudoxia’s confusion, the mules’ braying, the lampblack stains, the fish smell is what is evident in the incomplete perspective you grasp; but the carpet proves that there is a point from which the city shows its true proportions, the geometrical scheme implicit in its every, tiniest detail. . . . An oracle was questioned about the mysterious bond between two objects so dissimilar as the carpet and the city. One of the two objects—the oracle replied—has the form the gods gave the starry sky and the orbits in which the worlds revolve; the other is an approximate reflection, like every human creation.
—Italo Calvino, Invisible Cities11
我最深切地感谢艾莉森·戈普尼克(Alison Gopnik),我的妻子、同伴和帮助会面。十年前,她从一开始就鼓励我写这本书,然后开始教我如何去做。我热切地听她说,因为她写了几本畅销书。“解开那些句子”是一个早期的指导,观察到我的学术句子大约有五个正常的句子。她的另一条指导智慧是:“至少要经过 50 次编辑,这些词才能开始呈现出它们从你的潜意识中自然流畅地流出的样子。” 我没有为“离开”十年而向配偶道歉,我要衷心感谢我让我与她分享写作的世界——其中的快乐和磨难。
My deepest thanks to Alison Gopnik, my wife, companion, and helpmeet. She encouraged me from the start, a decade ago, to write this book, and then proceeded to teach me how to do it. I eagerly listened to her, since she’d written several bestsellers. “Unpack those sentences,” was an early instruction, observing that my academic sentences housed about five normal ones. Another piece of her guiding wisdom was: “It’ll take at least fifty edits before the words even start to take on that appearance that they flowed naturally and smoothly from your unconscious.” Instead of an apology to a spouse for being “away” for ten years, I get to thank mine profusely for letting me share the world of writing—its joys and tribulations—with her.
我对芭芭拉·罗伯逊表示了另一种深切的感谢。芭芭拉在计算机图形学界享有数十年的获奖报道。在这本书的多年酝酿过程中,她一直是我的第一编辑。除了艾莉森之外,她是世界上少数几个可以自由批评我的作品的人之一,她知道我会善意地接受她的评论——如果可能是脾气暴躁的话——并采取行动。芭芭拉惯用的诡计是“建议”对我的句子进行简单的重新排列。几乎在所有情况下,她的重新排列都比我原来的效果更好。这些话仍然是我的,但更好。流程更流畅,逻辑更清晰,节奏更快。芭芭拉在我的计算机图形职业生涯的大部分时间里都是我的朋友,我们的友谊以这种方式得以幸存。的确,
And I give a different kind of profound thanks to Barbara Robertson. Barbara is famous in the computer graphics world for decades of prize-winning reporting. She’s worked as first editor with me on this book throughout its multiyear gestation. She’s one of the few people in the world, other than Alison, who can criticize my writing freely and know I’ll take her comments goodnaturedly—if perhaps grumpily—and act on them. Barbara’s usual devious trick was to “suggest” a simple rearrangement of my sentences. In nearly every case, her rearrangement worked better than my original. The words were still mine but better. The flow was smoother, the logic cleaner, and the rhythm snappier. Barbara has been a friend for much of my computer graphics career, and our friendship has survived working together this way. Indeed, I believe it’s better than ever before.
在这里,我挑选出几个人,他们就本书涵盖的各种主题提供了特殊的、有时是至关重要的帮助:
Here I single out several people who provided special, sometimes crucial, assistance on various topics covered in the book:
名片通用图灵机和解释,基于第 3 章(图灵)的部分内容,作为旨在欢迎他们的On the Same Page活动的一部分,已于 2013 年提供给所有进入加州大学伯克利分校的新生。向每个新生(大约 8,000 人)赠送了一张名片图灵机的卡片纸实现,并附有一个乔治戴森的副本,图灵大教堂:数字宇宙的起源(纽约:万神殿书籍,2012 年)。
The business-card universal Turing machine and explanation, based on part of chapter 3 (Turing), was given to all entering University of California at Berkeley Freshman in 2013 as part of the On the Same Page event designed to welcome them. A card-stock realization of the business-card Turing machine was presented to each Freshman—about 8,000 of them—accompanied by a copy of George Dyson, Turing’s Cathedral: The Origins of the Digital Universe (New York: Pantheon Books, 2012).
史密斯,阿尔维·雷。“A Taxonomy and Genealogy of Digital Light-Based Technologies”,Sean Cubitt、Daniel Palmer 和 Nathaniel Tkacz 编辑的第 1 章,Digital Light(伦敦:开放人文出版社,2015 年)。这篇论文于 2011 年 3 月在墨尔本发表,是本书的起源。
Smith, Alvy Ray. “A Taxonomy and Genealogy of Digital Light-Based Technologies,” chapter 1 in Sean Cubitt, Daniel Palmer, and Nathaniel Tkacz eds., Digital Light (London: Open Humanities Press, 2015). This paper, presented in Melbourne in Mar. 2011, was the origin of this book.
史密斯,阿尔维·雷。“他的正义沙漠:对四本图灵书的评论” ,美国数学会通告,第61 期,不。8 (2014): 891–895。基于第 3 章(图灵)的部分内容。
Smith, Alvy Ray. “His Just Deserts: A Review of Four Turing Books,” Notices of the American Mathematical Society 61, no. 8 (2014): 891–895. Based on part of chapter 3 (Turing).
史密斯,阿尔维·雷。“数字光的黎明”,IEEE 计算历史年鉴38,第 3 期。4 (2016): 74–91。第 4 章(黎明)的学术介绍。
Smith, Alvy Ray. “The Dawn of Digital Light,” IEEE Annals of the History of Computing 38, no. 4 (2016): 74–91. A scholarly presentation of chapter 4 (Dawn).
史密斯,阿尔维·雷。“电影为什么会动?” 在约翰·布罗克曼编着的《这解释了一切:世界如何运作的深刻、美丽和优雅的理论》(纽约:Harper Perennial,2013 年),269–272。基于第 5 章(电影)的部分内容。
Smith, Alvy Ray. “Why Do Movies Move?” in John Brockman ed., This Explains Everything: Deep, Beautiful, and Elegant Theories of How the World Works (New York: Harper Perennial, 2013), 269–272. Based on part of chapter 5 (Movies).
史密斯,阿尔维·雷。“皮克斯如何利用摩尔定律预测未来”,《连线》,2013 年 4 月 17 日,https://www.wired.com/2013/04/how-pixar-used-moores-law-to-predict-the -future/,2020 年 4 月 13 日访问。基于第 6 章(形状)的部分内容。
Smith, Alvy Ray. “How Pixar Used Moore’s Law to Predict the Future,” Wired Online, Apr. 17, 2013, https://www.wired.com/2013/04/how-pixar-used-moores-law-to-predict-the-future/, accessed Apr. 13, 2020. Based on part of chapter 6 (Shapes).
除非另有说明,否则电子邮件将发送给作者。
Emails are addressed to the author unless otherwise indicated.
引文中使用的缩写:
Abbreviations used in citations:
1 . Henri Breuil 和 Hugo Obermaier,西班牙 Santillana del Mar 的阿尔塔米拉洞穴(马德里:Junta de las Cuevas de Altamira,美国西班牙裔社会和历史学院,1935 年),图板 XLV。
1. Henri Breuil and Hugo Obermaier, The Cave of Altamira at Santillana del Mar, Spain (Madrid: The Junta de las Cuevas de Altamira, The Hispanic Society of America, and The Academia de las Historia, 1935), Plate XLV.
2 . Appletons 的美国传记百科全书,6 卷,由 James Grant Wilson 和 John Fiske 编辑(纽约:D. Appleton and Company,1887 年),1:311–312。
2. Appletons’ Cyclopaedia of American Biography, 6 vols., edited by James Grant Wilson and John Fiske (New York: D. Appleton and Company, 1887), 1:311–312.
3 . 这本书在http://alvyray.com/DigitalLight/上在线进行了完整的注释。注释按页码组织,然后键入每个段落的前三个单词,我为此提供了附加信息、源材料或数学文档。
3. This book is fully annotated online at http://alvyray.com/DigitalLight/. The annotations are organized by page number and then keyed to the first three words of each paragraph for which I provide additional information, source material, or mathematical documentation.
1 . 维克多·雨果,《悲惨世界》(波士顿:小布朗,1887 年),192。
1. Victor Hugo, Les Misérables (Boston: Little, Brown, 1887), 192.
2 . 查尔斯·珀西·斯诺(Charles Percy Snow),“两种文化”,《两种文化与科学革命:重演讲座》,1959 年(纽约:剑桥大学出版社,1961 年),1-21。
2. Charles Percy Snow, “The Two Cultures,” in The Two Cultures and the Scientific Revolution: The Rede Lecture, 1959 (New York: Cambridge University Press, 1961), 1–21.
3 . Ronald N. Bracewell,傅立叶变换及其应用(纽约:McGraw-Hill,1965 年);Jacques-Joseph Champollion-Figeac, Fourier et Napoleon, l'Egypte et les Cent Jours (Paris: 1844); Victor Cousin,Note Biographiques pour Faire Suite a l'Éloge de M. Fourier(巴黎:1831);Jean Dhombres 和 Jean-Bernard Robert, Joseph Fourier, 1768–1830: Créateur de la Physique-Mathematique (巴黎: Belin, 1998); Enrique A. González-Velasco,傅里叶分析和边值问题(圣地亚哥:学术出版社,1995 年);Ivor Grattan-Guiness (with JR Ravetz), Joseph Fourier, 1768–1830 (Cambridge, MA: MIT Press, 1972);约翰·赫里维尔,约瑟夫傅立叶:人与物理学家(牛津:牛津大学出版社,1975 年)。
3. Ronald N. Bracewell, The Fourier Transform and Its Applications (New York: McGraw-Hill, 1965); Jacques-Joseph Champollion-Figeac, Fourier et Napoleon, l’Egypte et les Cent Jours (Paris: 1844); Victor Cousin, Notes Biographiques pour Faire Suite a l’Éloge de M. Fourier (Paris: 1831); Jean Dhombres and Jean-Bernard Robert, Joseph Fourier, 1768–1830: Créateur de la Physique-Mathematique (Paris: Belin, 1998); Enrique A. González-Velasco, Fourier Analysis and Boundary Value Problems (San Diego: Academic Press, 1995); Ivor Grattan-Guiness (with J. R. Ravetz), Joseph Fourier, 1768–1830 (Cambridge, MA: MIT Press, 1972); John Herivel, Joseph Fourier: The Man and the Physicist (Oxford: Oxford University Press, 1975).
4 . William Wordsworth, The Prelude, or Growth of a Poet's Mind (text of 1805),由 Ernest de Selincourt 和 Stephen Gill 编辑,X:692 (Oxford: Oxford University Press, 1970)。
4. William Wordsworth, The Prelude, or Growth of a Poet’s Mind (text of 1805), edited by Ernest de Selincourt and Stephen Gill, X:692 (Oxford: Oxford University Press, 1970).
5 . 约瑟夫·傅立叶,1795 年 6 月/7 月给维莱塔的信,约翰·赫里维尔,约瑟夫·傅立叶:人与物理学家(牛津:牛津大学出版社,1975 年),280。
5. Joseph Fourier, letter to Villetard, June/July 1795, in John Herivel, Joseph Fourier: The Man and the Physicist (Oxford: Oxford University Press, 1975), 280.
6 . 约瑟夫·傅立叶,1795 年 6 月/7 月给维莱塔的信,在赫里维尔,约瑟夫·傅立叶,284。
6. Joseph Fourier, letter to Villetard, June/July 1795, in Herivel, Joseph Fourier, 284.
8 . Robert B. Asprey,拿破仑·波拿巴的崛起(纽约:基础书籍,2000 年);Robert B. Asprey,拿破仑·波拿巴的统治(纽约:基础书籍,2001 年)。Asprey 使用出生名拼写“Nabolione”而不是更常见的“Napoleone”。
8. Robert B. Asprey, The Rise of Napoleon Bonaparte (New York: Basic Books, 2000); Robert B. Asprey, The Reign of Napoleon Bonaparte (New York: Basic Books, 2001). Asprey uses the birth-name spelling “Nabolione” instead of the more common “Napoleone.”
9 . 安德鲁·罗宾逊,破解埃及密码:让-弗朗索瓦·商博良的革命生活(牛津:牛津大学出版社,1975 年)。
9. Andrew Robinson, Cracking the Egyptian Code: The Revolutionary Life of Jean-Francois Champollion (Oxford: Oxford University Press, 1975).
11 . Oeuvres de Fourier,由 M. Gaston Darboux 编辑,2 卷,2:97–125(巴黎:Gauthier-Villars et Fils,1888–1890);史蒂夫·琼斯(Steve Jones),《革命性科学:断头台时代的转型与动荡》(纽约:Pegasus Books,2017 年),338。
11. Oeuvres de Fourier, edited by M. Gaston Darboux, 2 vols., 2:97–125 (Paris: Gauthier-Villars et Fils, 1888–1890); Steve Jones, Revolutionary Science: Transformation and Turmoil in the Age of the Guillotine (New York: Pegasus Books, 2017), 338.
13 . Herivel, Joseph Fourier , 189, 引用 JJ Champollion-Figeac, Fourier et Napoleon, l'Egypte et les cent jours (Paris, 1844), 187。
13. Herivel, Joseph Fourier, 189, citing J. J. Champollion-Figeac, Fourier et Napoleon, l’Egypte et les cent jours (Paris, 1844), 187.
15 . Louis L. Bucciarelli 和 Nancy Dworsky,Sophie Germain:弹性理论史论文集(波士顿:D. Reidel,1980 年),第 7-8 章。
15. Louis L. Bucciarelli and Nancy Dworsky, Sophie Germain: An Essay in the History of the Theory of Elasticity (Boston: D. Reidel, 1980), chapters 7–8.
16 . 埃菲尔铁塔:埃菲尔铁塔实验室,“72 位学者”,https: //www.toureiffel.paris/en/the-monument/eiffel-tower-and-science,2020 年2 月 18 日访问。
16. The Eiffel Tower: The Eiffel Tower Laboratory, “The 72 Savants,” https://www.toureiffel.paris/en/the-monument/eiffel-tower-and-science, accessed Feb. 18, 2020.
1 . Aleksandr I. Solzhenitsyn, The Gulag Archipelago: 1918–1956: An Experiment in Literary Investigation (New York: HarperCollins, 2001), 1:590。
1. Aleksandr I. Solzhenitsyn, The Gulag Archipelago: 1918–1956: An Experiment in Literary Investigation (New York: HarperCollins, 2001), 1:590.
2 . Vladimir Aleksandrovich Kotelnikov,“O Propusknoi Sposobnosti 'Efira' i Provoloki v Elektrosvyazi [关于电气通信中'以太'和电线的传输能力]”,载于Vsesoyuznyi Energeticheskii Komitet。Materialy k I Vsesoyuznomu S'ezdu po Voprosam Tekhnicheskoi Rekonstruktsii Dela Svyazi i Razvitiya Slabotochnoi Promyshlennosti。Po Radiosektsii [全联盟能源委员会。第一次全联盟通信设施技术改造和小电流行业进展大会材料。在无线电科](莫斯科:Upravlenie Svyazi RKKA,1933 年),4。
2. Vladimir Aleksandrovich Kotelnikov, “O Propusknoi Sposobnosti ‘Efira’ i Provoloki v Elektrosvyazi [On the Transmission Capacity of the ‘Ether’ and Wire in Electrical Communications],” in Vsesoyuznyi Energeticheskii Komitet. Materialy k I Vsesoyuznomu S’ezdu po Voprosam Tekhnicheskoi Rekonstruktsii Dela Svyazi i Razvitiya Slabotochnoi Promyshlennosti. Po Radiosektsii [The All-Union Energy Committee. Materials for the 1st All-Union Congress on the Technical Reconstruction of Communication Facilities and Progress in the Low-Currents Industry. At Radio Section] (Moscow: Upravlenie Svyazi RKKA, 1933), 4.
3 . David R. Brillinger,“John W. Tukey:他的生活和专业贡献” ,统计年鉴30(2002):1569–1570;Jon Gertner,理念工厂:贝尔实验室和美国创新的伟大时代(纽约:企鹅出版社,2012 年),135;Fred R. Shapiro,“软件术语的起源:来自 JSTOR 电子期刊档案的证据”,IEEE 计算历史年鉴22(2000):69–71;John Wilder Tukey,“具体数学的教学”,美国数学月刊65(1958 年 1 月):1-9。
3. David R. Brillinger, “John W. Tukey: His Life and Professional Contributions,” The Annals of Statistics 30 (2002): 1569–1570; Jon Gertner, The Idea Factory: Bell Labs and the Great Age of American Innovation (New York: Penguin Press, 2012), 135; Fred R. Shapiro, “Origin of the Term Software: Evidence from the JSTOR Electronic Journal Archive,” IEEE Annals of the History of Computing 22 (2000): 69–71; John Wilder Tukey, “The Teaching of Concrete Mathematics,” American Mathematical Monthly 65 (Jan. 1958): 1–9.
4 . WR Bennett,“时分复用系统”,贝尔系统技术期刊20 (1941): 199–221;Denis Gabor,“通信理论” ,电气工程学院学报(伦敦)93(1946):429–457;Karl Küpfmüller,“Wellenfiltern 中的 Über Einschwingvorgänge [滤波器中的瞬态现象]”,Elektrische Nachrichten-Technik 1 (1924):141–152;Harry Nyquist,“电报传输理论中的某些主题”,AIEE 交易(AIEE冬季会议记录,1928 年 2 月 13-17 日,纽约,纽约),617-644;Herbert Raabe,“Untersuchungen an der Wechsilzeitigen Mehrfachübertragung (Multiplexübertragung)”,Elektrische Nachrichtentechnik16 (1939): 213–228; Claude E. Shannon,“A Mathematical Theory of Communication”,贝尔系统技术期刊27(1948 年 7 月,10 月):379-423、623-656;Stephen Mack Stigler,“Stigler 的同名法则”,《纽约科学院学报》 39(1980):147–158;爱德华·泰勒·惠特克(Edward Taylor Whittaker),“关于插值理论扩展所代表的功能”,载于爱丁堡皇家学会会刊35(1915):181-194;John MacNaughton Whittaker,插值函数理论(剑桥:剑桥大学出版社,1935 年)。
4. W. R. Bennett, “Time Division Multiplex Systems,” Bell Systems Technical Journal 20 (1941): 199–221; Denis Gabor, “Theory of Communication,” Journal of the Institute of Electrical Engineering (London) 93 (1946): 429–457; Karl Küpfmüller, “Über Einschwingvorgänge in Wellenfiltern [Transient Phenomena in Wave Filters],” Elektrische Nachrichten-Technik 1 (1924): 141–152; Harry Nyquist, “Certain Topics in Telegraph Transmission Theory,” Transactions of the AIEE (proceedings of the Winter Conference of the AIEE, Feb. 13–17, 1928, New York, NY), 617–644; Herbert Raabe, “Untersuchungen an der Wechsilzeitigen Mehrfachübertragung (Multiplexübertragung),” Elektrische Nachrichtentechnik 16 (1939): 213–228; Claude E. Shannon, “A Mathematical Theory of Communication,” Bell Systems Technical Journal 27 (July, Oct. 1948): 379–423, 623–656; Stephen Mack Stigler, “Stigler’s Law of Eponymy,” Transactions of the New York Academy of Sciences 39 (1980): 147–158; Edward Taylor Whittaker, “On the Functions which are Represented by the Expansions of the Interpolation-Theory,” in Proceedings of the Royal Society of Edinburgh 35 (1915): 181–194; John MacNaughton Whittaker, Interpolatory Function Theory (Cambridge: Cambridge University Press, 1935).
5 . Christopher C. Bissell,“Vladimir Aleksandrovich Kotelnikov:采样定理、密码学、最优检测、行星映射的先驱。. . ,” IEEE 通信杂志47 (2009): 32; Mikhail K. Tchobanou 和 Nikolay N. Udalov,“Vladimir Kotelnikov 和莫斯科电力工程学院——采样定理,雷达系统。. . a Fascinating and Extraordinary Life” ,2006 年国际 TICSP 频谱方法和多速率信号处理研讨会论文集,意大利佛罗伦萨,2006 年 9 月 2-3 日,第 177 页。
5. Christopher C. Bissell, “Vladimir Aleksandrovich Kotelnikov: Pioneer of the Sampling Theorem, Cryptography, Optimal Detection, Planetary Mapping . . . ,” IEEE Communications Magazine 47 (2009): 32; Mikhail K. Tchobanou and Nikolay N. Udalov, “Vladimir Kotelnikov and Moscow Power Engineering Institute—Sampling Theorem, Radar Systems . . . a Fascinating and Extraordinary Life,” Proceedings of the 2006 International TICSP Workshop on Spectral Methods and Multirate Signal Processing, Florence, Italy, Sept. 2–3, 2006, 177.
6 . John Herivel, Joseph Fourier: The Man and the Physicist (Oxford: Oxford University Press, 1975), 154, 172; Natalia Vladimirovna Kotelnikova, “Vladimir Aleksandrovich Kotel'nikov: The Life's Journey of a Scientist,” in Yu V. Gulyaev et al., “Scientific Session of the Division of Physical俄罗斯科学院科学纪念 Vladimir Aleksandrovich Kotelnikov 院士”,Physics-Uspekhi [英文版] 49 (2006): 727。
6. John Herivel, Joseph Fourier: The Man and the Physicist (Oxford: Oxford University Press, 1975), 154, 172; Natalia Vladimirovna Kotelnikova, “Vladimir Aleksandrovich Kotel’nikov: The Life’s Journey of a Scientist,” in Yu V. Gulyaev et al., “Scientific Session of the Division of Physical Sciences of the Russian Academy of Sciences in Commemoration of Academician Vladimir Aleksandrovich Kotelnikov,” Physics-Uspekhi [English version] 49 (2006): 727.
7 . 科特尔尼科娃,“弗拉基米尔·亚历山德罗维奇·科特尔尼科夫”,728-729。
7. Kotelnikova, “Vladimir Aleksandrovich Kotel’nikov,” 728–729.
8 . 科特尔尼科娃,“弗拉基米尔·亚历山德罗维奇·科特尔尼科夫”,728-729。
8. Kotelnikova, “Vladimir Aleksandrovich Kotel’nikov,” 728–729.
9 . 米哈伊尔·布尔加科夫,白卫兵(纽黑文:耶鲁大学出版社,2008 年);科特尔尼科娃,“弗拉基米尔·亚历山德罗维奇·科特尔尼科夫”,728-729。
9. Mikhail Bulgakov, White Guard (New Haven: Yale University Press, 2008); Kotelnikova, “Vladimir Aleksandrovich Kotel’nikov,” 728–729.
10 . 比塞尔,“弗拉基米尔·亚历山德罗维奇·科捷尔尼科夫”,24;科捷尔尼科娃,“弗拉基米尔·亚历山德罗维奇·科捷尔尼科夫”,729;Tchobanou 和 Udalov,“Vladimir Kotelnikov”,172。
10. Bissell, “Vladimir Aleksandrovich Kotelnikov,” 24; Kotelnikova, “Vladimir Aleksandrovich Kotel’nikov,” 729; Tchobanou and Udalov, “Vladimir Kotelnikov,” 172.
11 . 科捷尔尼科娃,“弗拉基米尔·亚历山德罗维奇·科捷尔尼科夫”,730;Tchobanou 和 Udalov,“Vladimir Kotelnikov”,172-173。
11. Kotelnikova, “Vladimir Aleksandrovich Kotel’nikov,” 730; Tchobanou and Udalov, “Vladimir Kotelnikov,” 172–173.
12 . 科捷尔尼科娃,“弗拉基米尔·亚历山德罗维奇·科捷尔尼科夫”,731;Tchobanou 和 Udalov,“Vladimir Kotelnikov”,173。
12. Kotelnikova, “Vladimir Aleksandrovich Kotel’nikov,” 731; Tchobanou and Udalov, “Vladimir Kotelnikov,” 173.
13 . Richard F. Lyon,“A Brief History of 'Pixel'”,受邀论文发表在 IS&T/SPIE 电子成像研讨会上,2006 年 1 月 15 日至 19 日,加利福尼亚州圣何塞。
13. Richard F. Lyon, “A Brief History of ‘Pixel,’” an invited paper presented at the IS&T/SPIE Symposium on Electronic Imaging, Jan. 15–19, 2006, San Jose, CA.
14 . 香农,“沟通的数学理论”;Claude E. Shannon,“存在噪音时的通信” ,IRE 37 会议记录,第 3 期。1(1949 年 1 月):10-21。
14. Shannon, “A Mathematical Theory of Communication”; Claude E. Shannon, “Communication in the Presence of Noise,” Proceedings of the IRE 37, no. 1 (Jan. 1949): 10–21.
15 . Fredrich L. Bauer,解密的秘密:密码学的方法和准则(柏林:Springer-Verlag,1997),6;大卫斯塔福德、罗斯福和丘吉尔:秘密人物(纽约:Overlook Press,1999 年),22。
15. Fredrich L. Bauer, Decrypted Secrets: Methods and Maxims of Cryptology (Berlin: Springer-Verlag, 1997), 6; David Stafford, Roosevelt and Churchill: Men of Secrets (New York: Overlook Press, 1999), 22.
17 . 比塞尔,“弗拉基米尔·亚历山德罗维奇·科捷尔尼科夫”;科捷尔尼科娃,“弗拉基米尔·亚历山德罗维奇·科捷尔尼科夫”。
17. Bissell, “Vladimir Aleksandrovich Kotelnikov”; Kotelnikova, “Vladimir Aleksandrovich Kotel’nikov.”
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23. Boris Evseevich Chertok, Rakety I lyudi: Fili Podlipki Tyuratam [Rockets and people, Vol. 2: Creating a rocket industry], 4 vols. (Moscow: Mashinostroyeniye, 1996), 2:96–108.
24 . Aleksandr I. Solzhenitsyn, In the First Circle , 修复后的文本,由 Harry T. Willetts 翻译自俄文(纽约:HarperCollins,2009 年),92。
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29. Kotelnikova, “Vladimir Aleksandrovich Kotel’nikov,” 732; Tchobanou and Udalov, “Vladimir Kotelnikov,” 173–174.
30 . 科捷尔尼科娃,“弗拉基米尔·亚历山德罗维奇·科捷尔尼科夫”,第 732、734 页。
30. Kotelnikova, “Vladimir Aleksandrovich Kotel’nikov,” 732, 734.
31 . Simon Ings,斯大林和科学家:1905-1953 年的胜利与悲剧史(纽约:大西洋月刊,2016 年),312-314。
31. Simon Ings, Stalin and the Scientists: A History of Triumph and Tragedy 1905–1953 (New York: Atlantic Monthly Press, 2016), 312–314.
32 . Keith Dexter 和 Ivan Rodionov,苏联国防工业的工厂、研究和设计机构:指南,第 13 版,华威大学经济系,2012 年 1 月;科特尔尼科娃,“弗拉基米尔·亚历山德罗维奇·科特尔尼科夫”,733-734;索尔仁尼琴,在第一圈;Marshall Winokur,“从古到今的俄罗斯建筑评论,卷。1:教堂和修道院。日本:俄罗斯东正教青年委员会,1973 年,“斯拉夫和东欧杂志26 (1982): 113。
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34 . Homer W. Dudley,“声码器”,贝尔系统技术期刊17 (1939):122–126;科捷尔尼科娃,“弗拉基米尔·亚历山德罗维奇·科捷尔尼科夫”,731;Dave Tompkins,如何破坏漂亮的海滩:从二战到嘻哈的声码器:机器说话(布鲁克林:梅尔维尔出版社,2011 年),70,122–130。
34. Homer W. Dudley, “The Vocoder,” Bell Systems Technical Journal 17 (1939): 122–126; Kotelnikova, “Vladimir Aleksandrovich Kotel’nikov,” 731; Dave Tompkins, How to Wreck a Nice Beach: The Vocoder from World War II to Hip-Hop: The Machine Speaks (Brooklyn: Melville House Publishing, 2011), 70, 122–130.
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37. Chertok, Rakety I lyudi, 2:106–108; Boris Evseevich Chertok, “V. A. Kotel’nikov and His Role in the Development of Space Radio Electronics in Our Country,” in Gulyaev et al., “Scientific Session of the Division of Physical Sciences” [English version], 761–762; Dexter and Rodionov, The Factories, Research and Design Establishments of the Soviet Defence Industry.
38 . 科特尔尼科娃,“弗拉基米尔·亚历山德罗维奇·科特尔尼科夫”,734-735。
38. Kotelnikova, “Vladimir Aleksandrovich Kotel’nikov,” 734–735.
39 . 医学数字成像和通信 (DICOM),第 14 部分:灰度标准显示功能(Rosslyn,VA:国家电气制造商协会,2004 年)。
39. Digital Imaging and Communications in Medicine (DICOM), Part 14: Grayscale Standard Display Function (Rosslyn, VA: National Electrical Manufacturers Association, 2004).
40 . E. Brad Meyer 和 David R. Moran,“插入到高分辨率音频播放中的 CD 标准 A/D/A 循环的可听性” ,音频工程学会杂志55(2007):778;Joshua D. Reiss,“高分辨率音频感知评估的元分析” ,音频工程学会杂志,第64 期,不。6(2016 年 6 月):364–379;超级音频 CD 参考,“Thread Debunking Meyer and Moran”,http://www.sa-cd.net/showthread/42987,2020年 2 月 28 日访问。
40. E. Brad Meyer and David R. Moran, “Audibility of a CD-Standard A/D/A Loop Inserted into High-Resolution Audio Playback,” Journal of the Audio Engineering Society 55 (2007): 778; Joshua D. Reiss, “A Meta-Analysis of High Resolution Audio Perceptual Evaluation,” Journal of the Audio Engineering Society 64, no. 6 (June 2016): 364–379; The Super Audio CD Reference, “Thread Debunking Meyer and Moran,” http://www.sa-cd.net/showthread/42987, accessed Feb. 28, 2020.
41 . Vladimir Aleksandrovich Kotelnikov,“无线电时代”,在二十一世纪的生活中,由 Mikhail Vassiliev 和 Sergei Gouschev 编辑,由 HE Crowcroft 和 RJ Wason 翻译(伦敦:企鹅出版社,1961 年),129。
41. Vladimir Aleksandrovich Kotelnikov, “The Age of Radio,” in Life in the Twenty-First Century, edited by Mikhail Vassiliev and Sergei Gouschev, translated by H. E. Crowcroft and R. J. Wason (London: Penguin, 1961), 129.
42 . Paul Dickson, Sputnik: The Shock of the Century (New York: Walker Publishing, 2001), 98–99, 130; NASA 的国家空间科学数据中心(Sputnik),https ://nssdc.gsfc.nasa.gov/nmc/spacecraft/display.action?id= 1957-001B,2020 年 2 月 28 日访问。
42. Paul Dickson, Sputnik: The Shock of the Century (New York: Walker Publishing, 2001), 98–99, 130; NASA’s National Space Science Data Center (Sputnik), https://nssdc.gsfc.nasa.gov/nmc/spacecraft/display.action?id=1957-001B, accessed Feb. 28, 2020.
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43. Ben Evans, At Home in Space: The Late Seventies into the Eighties (New York: Springer-Praxis, 2012), 37; Edward Clinton Ezell and Linda Newman Ezell, The Partnership: A NASA History of the Apollo-Soyuz Test Project (Mineola, NY: Dover, 2010), 182–188.
44 . Lutz D. Schmadel,小行星名称词典,第 5 版,第一卷。1 (柏林: Springer-Verlag, 2003), 231; Tchobanou 和 Udalov,“Vladimir Kotelnikov”,176-177。
44. Lutz D. Schmadel, Dictionary of Minor Planet Names, 5th ed., vol. 1 (Berlin: Springer-Verlag, 2003), 231; Tchobanou and Udalov, “Vladimir Kotelnikov,” 176–177.
45 . Andrei Sakharov 的克格勃档案,由 Joshua Rubenstein 和 Alesander Gribanov 编辑(纽黑文:耶鲁大学,2005 年),193–196。
45. The KGB File of Andrei Sakharov, edited by Joshua Rubenstein and Alesander Gribanov (New Haven: Yale University, 2005), 193–196.
46 . Vitaly Lazarevich Ginzburg,“The Sakharov Phenomenon”,载于Andrei Sakharov:生活的方方面面(Gif-sur-Yvette,法国:Editions Frontières 和 PN Lebedev 物理研究所,1991 年)。
46. Vitaly Lazarevich Ginzburg, “The Sakharov Phenomenon,” in Andrei Sakharov: Facets of a Life (Gif-sur-Yvette, France: Editions Frontières and P. N. Lebedev Physics Institute, 1991).
47 . Chertok,Rakety I lyudi,2:108;时代杂志,1957 年 7 月 22 日,“俄罗斯:快活与死者”。
47. Chertok, Rakety I lyudi, 2:108; Time Magazine, July 22, 1957, “Russia: The Quick & the Dead.”
49 . 比塞尔,“弗拉基米尔·亚历山德罗维奇·科捷尔尼科夫”;Mark Bykhovskiy,“充满认知和行动的生活(献给 VA Kotelnikov 院士诞辰 100 周年)”,IEEE 信息理论学会通讯59(2009):13-15;Kotelnikov,“O Propusknoi Sposobnosti 'Efira' i Provoloki v Elektrosvyazi”,引言;乔巴努和乌达洛夫,“弗拉基米尔·科捷尔尼科夫”。
49. Bissell, “Vladimir Aleksandrovich Kotelnikov”; Mark Bykhovskiy, “The Life Filled with Cognition and Action (dedicated to the 100th Anniversary of Academician V. A. Kotelnikov),” IEEE Information Theory Society Newsletter 59 (2009): 13–15; Kotelnikov, “O Propusknoi Sposobnosti ‘Efira’ i Provoloki v Elektrosvyazi,” the introduction; Tchobanou and Udalov, “Vladimir Kotelnikov.”
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1 . Tom Stoppard,Arcadia(伦敦:Faber 和 Faber,1993 年),51-52(摘自第 1 幕,第 4 场)。
1. Tom Stoppard, Arcadia (London: Faber and Faber, 1993), 51–52 (excerpt from act 1, scene 4).
2 . 艾伦·图灵讣告,皇家学会研究员传记回忆录,1955 年 11 月 1 日,https: //doi.org/10.1098/rsbm.1955.0019,2020 年2 月 29 日访问;Sara Turing、Alan M. Turing(剑桥:剑桥大学出版社,1959 年;代表百年纪念版,2012 年)。
2. Alan Turing obit., Biographical Memoirs of Fellows of the Royal Society, Nov. 1, 1955, https://doi.org/10.1098/rsbm.1955.0019, accessed Feb. 29, 2020; Sara Turing, Alan M. Turing (Cambridge: Cambridge University Press, 1959; repr. Centenary Edition, 2012).
3 . Harry Hinsley 爵士,“二战中 Ultra 的影响”,http://www.cix.co.uk/~klockstone/hinsley.htm,2020年 2 月 28 日访问;安德鲁·霍奇斯,艾伦·图灵:谜(纽约:西蒙和舒斯特,1983 年)。
3. Sir Harry Hinsley, “The Influence of Ultra in the Second World War,” http://www.cix.co.uk/~klockstone/hinsley.htm, accessed Feb. 28, 2020; Andrew Hodges, Alan Turing: The Enigma (New York: Simon and Schuster, 1983).
4 . B. Jack Copeland,图灵:信息时代的先驱(牛津:克拉伦登出版社,2012 年),285,n。6;霍奇斯,艾伦·图灵,149;萨拉·图灵,艾伦·M·图灵,117。
4. B. Jack Copeland, Turing: Pioneer of the Information Age (Oxford: Clarendon Press, 2012), 285, n. 6; Hodges, Alan Turing, 149; Sara Turing, Alan M. Turing, 117.
5 . 谷轮,图灵:先锋,223-234;霍奇斯,艾伦·图灵,487–492;John Dermot Turing 爵士,教授:Alan Turing Decoded(格洛斯特郡切尔滕纳姆:历史出版社,2015 年);萨拉图灵,艾伦 M. 图灵,114-121。
5. Copeland, Turing: Pioneer, 223–234; Hodges, Alan Turing, 487–492; Sir John Dermot Turing, Prof: Alan Turing Decoded (Cheltenham, Gloucestershire: The History Press, 2015); Sara Turing, Alan M. Turing, 114–121.
8 . David Leavitt,《知道太多的人:艾伦·图灵和计算机的发明》(纽约:Atlas Books,WW Norton,2006 年),18。
8. David Leavitt, The Man Who Knew Too Much: Alan Turing and the Invention of the Computer (New York: Atlas Books, W. W. Norton, 2006), 18.
9 . Seymour Papert, Mindstorms: Children, Computers, and Powerful Ideas (New York: Basic Books Inc., 1980), viii.
9. Seymour Papert, Mindstorms: Children, Computers, and Powerful Ideas (New York: Basic Books Inc., 1980), viii.
10 . Re Scrooge 会见 Baggins 参见Walt Disney 的 Uncle Scrooge(纽约:戴尔出版公司,1954 年 3 月至 5 月),第 1 期。5、11;JRR Tolkien,《指环王》(波士顿:Houghton Mifflin Harcourt,2004 年),第 1 册,第 1 章,第 1 段。
10. Re Scrooge meets Baggins see Walt Disney’s Uncle Scrooge (New York: Dell Publishing Company Inc., Mar.–May 1954), no. 5, 11; J.R.R. Tolkien, The Lord of the Rings (Boston: Houghton Mifflin Harcourt, 2004), book 1, chapter 1, paragraph 1.
11 . 托马斯·乌斯克,《爱的遗嘱》 [ca. 1375],由 Gary W. Shawver 编辑(多伦多:多伦多大学出版社,2002 年),II.7.71-73。
11. Thomas Usk, The Testament of Love [ca. 1375], edited by Gary W. Shawver (Toronto: University of Toronto Press, 2002), II.7.71–73.
12 . 杰弗里·乔叟,《星盘论》;致他的母猪,1391,由 Walter W. Skeat 编辑(伦敦:乔叟协会,1872 年,1880 年出版),I.9.3。
12. Geoffrey Chaucer, A Treatise on the Astrolabe; addressed to his Sowns, 1391, edited by Walter W. Skeat (London: The Chaucer Society, 1872, repr. 1880), I.9.3.
13 . 大卫希尔伯特和威廉阿克曼,数学逻辑原理(纽约:切尔西出版社,1950 年),112-124。
13. David Hilbert and Wilhelm Ackerman, Principles of Mathematical Logic (New York: Chelsea Publishing, 1950), 112–124.
14 . 大卫·安德森,“历史反思:马克斯·纽曼:英国早期计算中被遗忘的人” ,ACM 56 通讯,第 3 期。5(2013 年 5 月):30。
14. David Anderson, “Historical Reflections: Max Newman: Forgotten Man of Early British Computting,” Communications of the ACM 56, no. 5 (May 2013): 30.
15 . 谷轮,图灵:先锋,1-2;Brian Randell,2014 年 8 月 8 日的电子邮件;萨拉·图灵,艾伦·M·图灵,63 岁。
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1 . 列夫·托尔斯泰的《战争与和平》,路易丝和艾尔默·莫德翻译(纽约:Alfred A. Knopf,1992 年),第一行,第 3 册,第 3 部分,第 1 章。
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4. Ball, The Inventor and the Tycoon, 30; Gordon Hendricks, Eadweard Muybridge: The Father of the Motion Picture (New York: Grossman Publishers, 1975), 71; Mannoni, The Great Art of Light and Shadow, 307; Rebecca Solnit, River of Shadows: Eadweard Muybridge and the Technological Wild West (New York: Penguin Books, 2003), 139.
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23 . 霍普伍德,《活生生的图画》,226;Laurent Mannoni, Georges Demenÿ: Pionnier du Cinéma (Douai: Éditions Pagine, 1997)。
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24. Donald Crafton, Before Mickey: The Animated Film, 1898–1928 (Chicago: University of Chicago Press, 1982, repr. 1993); Hendricks, The Edison Motion Picture Myth; Hopwood, Living Pictures; Mannoni, The Great Art of Light and Shadow; Musser, The Emergence of Cinema; Paul Pottash, email Oct. 18, 2015; Jacques Rittaud-Hutinet, Letters: Auguste and Louis Lumière: Inventing the Cinema (London: Faber and Faber, 1995); Spehr, The Man Who Made Movies.
25 . Richard Brown 和 Barry Anthony,The Kinetoscope:A British History(东伯内特,赫兹,英国:John Libbey Publishing,2017 年);霍普伍德,《活生生的图画》,65、98、238、240;Musser,电影的出现,91;斯佩尔,制作电影的人,106-111。
25. Richard Brown and Barry Anthony, The Kinetoscope: A British History (East Bernet, Herts., UK: John Libbey Publishing, 2017); Hopwood, Living Pictures, 65, 98, 238, 240; Musser, The Emergence of Cinema, 91; Spehr, The Man Who Made Movies, 106–111.
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31. Hendricks, The Edison Motion Picture Myth, appendix B; Musser, The Emergence of Cinema, 63, 67.
34 . WKL Dickson 和 Antonia Dickson,Thomas Alva Edison 的生活和发明(纽约:Thomas Y. Crowell & Co.,1894 年),前言。
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41 . Paul Spehr,2015 年 6 月 15 日和 2015 年 8 月 17 日的电子邮件。
41. Paul Spehr, emails June 15, 2015 and Aug. 17, 2015.
44 . 霍普伍德,《活生生的图画》,261;Paul Spehr,2015 年 8 月 17 日,6 月 15 日的电子邮件。
44. Hopwood, Living Pictures, 261; Paul Spehr, emails June 15, Aug. 17, 2015.
46 . Charles Musser, Thomas A. Edison and His Kinetographic Motion Pictures (New Brunswick, NJ: Rutgers University Press, 1995), 20; Smith, William Kennedy Laurie Dickson,图 12;Paul Spehr,2015 年 9 月 14 日的电子邮件。
46. Charles Musser, Thomas A. Edison and His Kinetographic Motion Pictures (New Brunswick, NJ: Rutgers University Press, 1995), 20; Smith, William Kennedy Laurie Dickson, Fig. 12; Paul Spehr, email Sept. 14, 2015.
47 . 斯佩尔,电影制作人,290–294;Paul Spehr,2015 年 9 月 14 日的电子邮件。
47. Spehr, The Man Who Made Movies, 290–294; Paul Spehr, email Sept. 14, 2015.
48 . 霍普伍德,《活生生的图画》,36-39;Musser,电影的出现,145;Spehr,电影制作人,352;Paul Spehr,2015 年 8 月 17 日的电子邮件。
48. Hopwood, Living Pictures, 36–39; Musser, The Emergence of Cinema, 145; Spehr, The Man Who Made Movies, 352; Paul Spehr, email Aug. 17, 2015.
50 . 鲍尔,《发明家与大亨》,318–319、334;曼诺尼,光与影的伟大艺术,331;Musser,电影的出现,66;斯佩尔,制作电影的人,142–147。
50. Ball, The Inventor and the Tycoon, 318–319, 334; Mannoni, The Great Art of Light and Shadow, 331; Musser, The Emergence of Cinema, 66; Spehr, The Man Who Made Movies, 142–147.
51 . 斯佩尔,《电影制作人》,138-140、142-147;Paul Spehr,2015 年 8 月 17 日的电子邮件。
51. Spehr, The Man Who Made Movies, 138–140, 142–147; Paul Spehr, email Aug. 17, 2015.
54 . Rittaud-Hutinet, Letters: Auguste and Louis Lumière , 16-22, 195-200。
54. Rittaud-Hutinet, Letters: Auguste and Louis Lumière, 16–22, 195–200.
55 . 曼诺尼,光与影的伟大艺术,346-350;Spehr,制作电影的人,111-117;Paul Spehr,2015 年 9 月 5 日的电子邮件。
55. Mannoni, The Great Art of Light and Shadow, 346–350; Spehr, The Man Who Made Movies, 111–117; Paul Spehr, email Sept. 5, 2015.
57 . Thierry Lefebvre、Jacques Malthête 和 Laurent Mannoni 合编,Lettres d'Étienne-Jules Marey à Demenÿ,1880 – 1894 年(巴黎:Association française de recherche sur l'histoire du cinéma,电影图书馆,2000);Mannoni , Georges Demenÿ ; 曼诺尼,光与影的伟大艺术。
57. Thierry Lefebvre, Jacques Malthête, and Laurent Mannoni, eds., Lettres d’Étienne-Jules Marey à Demenÿ, 1880–1894 (Paris: Association française de recherche sur l’histoire du cinéma, Bibliothèque du Film, 2000); Mannoni, Georges Demenÿ; Mannoni, The Great Art of Light and Shadow.
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65. Mannoni, The Great Art of Light and Shadow, 430; Paul Spehr, email Dec. 9, 2015.
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1 . 图 7.1:GE,计算机图像生成,模拟和控制系统部,通用电气公司,佛罗里达州代托纳比奇,19 页彩色营销手册(包括封面),ca。1977;GE–NASA,最终报告,视觉三视图太空飞行模拟器,合同 NAS 9-1375,GE,国防电子部门,电子实验室,纽约州伊萨卡,1964 年 8 月 1 日。
1. For figure 7.1: GE, Computer Image Generation, Simulation and Control Systems Department, General Electric Company, Daytona Beach, Fla., 19-page color marketing pamphlet (including covers), ca. 1977; GE–NASA, Final Report, Visual Three-View Space-Flight Simulator, Contract NAS 9-1375, GE, Defense Electronics Division, Electronics Laboratory, Ithaca, NY, Aug. 1, 1964.
2 . Gene Youngblood,扩展电影(纽约:EP Dutton,1970),252。
2. Gene Youngblood, Expanded Cinema (New York: E. P. Dutton, 1970), 252.
4 . Youngblood,扩展电影,205;Gene Youngblood,2019 年 3 月 12 日的电子邮件。
4. Youngblood, Expanded Cinema, 205; Gene Youngblood, email Mar. 12, 2019.
6 . Jim Blinn,2018 年 1 月的对话,2018 年 2 月 9 日的电子邮件;Zareh Gorjian,2018 年 1 月 3 日的电子邮件。
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10. GE–NASA, Visual Three-View Space-Flight Simulator; Robert Schumacker, email Feb. 22, 2018.
11 . GE-NASA,视觉三视图太空飞行模拟器,1、3;罗伯特舒马克,2018 年 2 月 14 日,16 日的电子邮件。
11. GE–NASA, Visual Three-View Space-Flight Simulator, 1, 3; Robert Schumacker, emails Feb. 14, 16, 2018.
13 . GE-NASA,视觉三视图太空飞行模拟器,3;罗伯特舒马克,2018 年 2 月 14 日的电子邮件。
13. GE–NASA, Visual Three-View Space-Flight Simulator, 3; Robert Schumacker, email Feb. 14, 2018.
15 . Jasia Reichardt 编辑,Cybernetic Serendipity: The Computer and the Arts(Studio International 特刊,伦敦,1968 年 7 月),65;Youngblood,扩展电影,215–222。
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32. Documents in my possession: Laurin Herr, reports dated 16 Aug. 1985, 27 Sept. 1984; Shogakukan, notes 27–30 July 1985, Dec. 1985, Jan. 1986.
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36 . 作者拥有的文件:“Potential Investors III”,1985 年 6 月 21 日。
36. Document in the author’s possession: “Potential Investors III,” June 21, 1985.
37 . 作者拥有的文件:“Potential Investors I”,1985 年 6 月 21 日。
37. Document in the author’s possession: “Potential Investors I,” June 21, 1985.
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50 . Walter Isaacson, Steve Jobs(纽约:Simon & Schuster,2011),244–245。
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51 . Smith,Altamira Formation Journal,1991 年 7 月 1 日、9 月 6 日和 9 月 9 日的条目。
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2. Darcy Gerbarg (website), http://www.darcygerbarg.com/, accessed Feb. 23, 2020.
3 . Jonghyun Kim、Youngmo Jeong、Michael Stengel、Kaan Aksit、Racherl Albert、Ben Boudaoud、Trey Greer、Joohwah Kim、Ward Lopes、Zander Majercik、Peter Shirley、Josef Spjut、Morgan McGuire 和 David Luebke,“注视点 AR:动态注视点增强现实显示,” ACM Transactions on Graphics 38,第 3 期。4(2019 年 7 月):第 99 条。
3. Jonghyun Kim, Youngmo Jeong, Michael Stengel, Kaan Aksit, Racherl Albert, Ben Boudaoud, Trey Greer, Joohwah Kim, Ward Lopes, Zander Majercik, Peter Shirley, Josef Spjut, Morgan McGuire, and David Luebke, “Foveated AR: Dynamically-Foveated Augmented Reality Display,” ACM Transactions on Graphics 38, no. 4 (July 2019): Article 99.
4 . 第 68 届科学技术成就奖,1996 年 3 月 2 日,https ://www.imdb.com/event/ev0000003/1996/1,2020 年 2 月 23 日访问。
4. 68th Scientific & Technical Achievement Awards, Mar. 2, 1996, https://www.imdb.com/event/ev0000003/1996/1, accessed Feb. 23, 2020.
5 . Alvy Ray Smith,“无相机电影,或数字人类在等待中”,《科学美国人》 ,2000 年 11 月,72-78。
5. Alvy Ray Smith, “Cameraless Movies, or Digital Humans Wait in the Wings,” Scientific American, Nov. 2000, 72–78.
6 . 芭芭拉·罗伯逊(Barbara Robertson),“旧的又是新的”,《计算机图形学世界》第 32 期,第 3 期。1(2009 年 1 月),http://www.cgw.com/Publications/CGW/2009/Volume-32-Issue-1-Jan-2009-/Whats-Old-is-New-Again.aspx,访问 3 月2020 年 1 月 1 日。
6. Barbara Robertson, “What’s Old Is New Again,” Computer Graphics World 32, no. 1 (Jan. 2009), http://www.cgw.com/Publications/CGW/2009/Volume-32-Issue-1-Jan-2009-/Whats-Old-is-New-Again.aspx, accessed Mar. 1, 2020.
7 . Barbara Robertson,“Face Lift”,计算机图形世界,2019 年冬季,http ://www.cgw.com/Publications/CGW/2019/Winter-2019/Face-Lift.aspx,2020 年 3 月 1 日访问;这 10 位演员如何为他们的电影减龄,https://www.youtube.com/watch?v= twKiEzjeH-M,于2020 年 2 月 23 日访问。
7. Barbara Robertson, “Face Lift,” Computer Graphics World, Winter 2019, http://www.cgw.com/Publications/CGW/2019/Winter-2019/Face-Lift.aspx, accessed Mar. 1, 2020; How These 10 Actors Were De-Aged for Their Movies, https://www.youtube.com/watch?v=twKiEzjeH-M, accessed Feb. 23, 2020.
9 . George Dyson,Analogia:超越可编程控制的技术的出现(纽约:Farrar、Straus 和 Giroux,2020 年),184-185。
9. George Dyson, Analogia: The Emergence of Technology Beyond Programmable Control (New York: Farrar, Straus and Giroux, 2020), 184–185.
10 . Jun-Yan Zhu、Taesung Park、Phillip Isola 和 Alexei A. Efros,“Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks”,IEEE 2017 年计算机视觉国际会议 (ICCV),2223–2232。
10. Jun-Yan Zhu, Taesung Park, Phillip Isola, and Alexei A. Efros, “Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks,” IEEE 2017 International Conference on Computer Vision (ICCV), 2223–2232.
知识共享许可缩写:CC:知识共享,BY:署名,CC0:无权利保留,NC:非商业,ND:无衍生,SA:相同方式共享。
Creative Commons license abbreviations: CC: Creative Commons, BY: with Attribution, CC0: no rights reserved, NC: Non-Commercial, ND: No Derivatives, SA: Share Alike.
0.1 由西班牙裔博物馆和图书馆提供。
0.1 Courtesy of the Hispanic Museum & Library.
0.2 维基共享资源,公共领域。
0.2 Wikimedia Commons, public domain.
1.1–2, 5–6, 9, 11 作者:Alvy Ray Smith。
1.1–2, 5–6, 9, 11 By Alvy Ray Smith.
1.3 由 Ken Power 提供。
1.3 Courtesy of Ken Power.
1.4 维基共享资源,公共领域,由 Alvy Ray Smith 修改。
1.4 Wikimedia Commons, public domain, modified by Alvy Ray Smith.
1.7 Claudio Divizia,Shutterstock,1553757458。
1.7 By Claudio Divizia, Shutterstock, 1553757458.
1.8 Indiamart,https://www.indiamart.com/proddetail/gi-corrugated-sheet-4450703088.html,图片于 2020 年 2 月 9 日下载。
1.8 Indiamart, https://www.indiamart.com/proddetail/gi-corrugated-sheet-4450703088.html, image downloaded Feb. 9, 2020.
1.10 维基共享资源,公共领域。
1.10 Wikimedia Commons, public domain.
2.1-2、4-7、10-19 由 Alvy Ray Smith 撰写。
2.1–2, 4–7, 10–19 By Alvy Ray Smith.
2.3 Vladimir Aleksandrovich Kotelnikov,“O Propusknoi Sposobnosti 'Efira' i Provoloki v Elektrosvyazi [关于电气通信中“以太”和电线的传输能力]。” 在Vsesoyuznyi Energeticheskii Komitet。Materialy k I Vsesoyuznomu S'ezdu po Voprosam Tekhnicheskoi Rekonstruktsii Dela Svyazi i Razvitiya Slabotochnoi Promyshlennosti。Po Radiosektsii [全联盟能源委员会。第一次全联盟通信设施技术改造和进展情况代表大会资料低电流行业。在无线电部分]。莫斯科:Upravlenie Svyazi RKKA,1933 年,4。原始俄罗斯论文由 Christopher Bissell 提供。
2.3 Vladimir Aleksandrovich Kotelnikov, “O Propusknoi Sposobnosti ‘Efira’ i Provoloki v Elektrosvyazi [On the Transmission Capacity of the ‘Ether’ and Wire in Electrical Communications].” In Vsesoyuznyi Energeticheskii Komitet. Materialy k I Vsesoyuznomu S’ezdu po Voprosam Tekhnicheskoi Rekonstruktsii Dela Svyazi i Razvitiya Slabotochnoi Promyshlennosti. Po Radiosektsii [The All-Union Energy Committee. Materials for the 1st All-Union Congress on the Technical Reconstruction of Communication Facilities and Progress in the Low-Currents Industry. At Radio Section]. Moscow: Upravlenie Svyazi RKKA, 1933, 4. Original Russian paper courtesy of Christopher Bissell.
2.8 Richard F. Lyon,“'像素'的简史”,在 IS&T/SPIE 电子成像研讨会上发表的受邀论文,2006 年 1 月 15 日至 19 日,加利福尼亚州圣何塞,第 5 页(共 16 页)。
2.8 Richard F. Lyon, “A Brief History of ‘Pixel,’” an invited paper presented at the IS&T/SPIE Symposium on Electronic Imaging, Jan. 15–19, 2006, San Jose, CA, 5 (of 16).
2.9(左)感谢 Christopher Bissell、俄罗斯科学院和 Kotelnikov 家族。(右)照片由麻省理工学院博物馆提供。
2.9 (Left) Thanks to Christopher Bissell, the Russian Academy of Sciences, and the Kotelnikov family. (Right) Photo courtesy of MIT Museum.
2.20 在线几个地方——例如,https ://www.moscovery.com/aleksandr-solzhenitsyn/,2020年 3 月 4 日访问。
2.20 Online several places—e.g., https://www.moscovery.com/aleksandr-solzhenitsyn/, accessed Mar. 4, 2020.
2.21 俄罗斯总统:活动,http ://en.kremlin.ru/events/president/news/29520/photos ,图片下载于 2020 年 3 月 4 日。感谢克里姆林宫新闻网站。
2.21 President of Russia: Events, http://en.kremlin.ru/events/president/news/29520/photos, image downloaded Mar. 4, 2020. Thanks to the Kremlin news site.
3.1 经剑桥国王学院图书馆许可。AMT/K/7/8。
3.1 By permission of King’s College Library, Cambridge. AMT/K/7/8.
3.2 CC BY-NC-ND 3.0 未移植许可证。阿尔维·雷·史密斯(Alvy Ray Smith),2014 年。
3.2 CC BY-NC-ND 3.0 Unported license. By Alvy Ray Smith, 2014.
3.3–5, 7 阿尔维·雷·史密斯(Alvy Ray Smith)。
3.3–5, 7 By Alvy Ray Smith.
3.6 Kolb Brothers 摄,Kolb Brother's Trail Photos 的硝酸盐负片原件,Cline Library Special Collections and Archives,北亚利桑那大学。由玛丽娜惠特曼提供。
3.6 Photo by Kolb Brothers, original nitrate negative at Kolb Brother’s Trail Photos, Cline Library Special Collections and Archives, Northern Arizona University. Courtesy of Marina Whitman.
4.1(左)摄影:Christopher Riche Evans,ca。1975 年,由他的遗产提供。(右)维基共享资源,照片 © Carolyn Djanogly。
4.1 (Left) Photo by Christopher Riche Evans, ca. 1975, courtesy of his estate. (Right) Wikimedia Commons, photo © Carolyn Djanogly.
4.2–3 Tom Kilburn,“用于二进制数字计算机的存储系统”,1947 年 12 月 1 日,http://curation.cs.manchester.ac.uk/computer50/www.computer50.org/kgill/mark1 /report1947cover.html,2020 年 2 月 29 日访问,照片 1 和 2。
4.2–3 Tom Kilburn, “A Storage System for Use with Binary Digital Computing Machines,” Dec. 1, 1947, http://curation.cs.manchester.ac.uk/computer50/www.computer50.org/kgill/mark1/report1947cover.html, accessed Feb. 29, 2020, photographs 1 and 2.
4.4 由曼彻斯特大学计算机科学系提供。
4.4 Courtesy of the University of Manchester, Department of Computer Science.
4.5, 7–9 阿尔维·雷·史密斯。
4.5, 7–9 By Alvy Ray Smith.
4.6 CC BY-ND 3.0 未移植许可证。阿尔维·雷·史密斯(Alvy Ray Smith),2017 年。
4.6 CC BY-ND 3.0 Unported license. By Alvy Ray Smith, 2017.
4.10–13, 16, 21–22 经 The MITRE Corporation 许可使用和转载。©2016。
4.10–13, 16, 21–22 Used and reprinted with permission of The MITRE Corporation. ©2016.
4.14 图片由加利福尼亚州山景城的计算机历史博物馆提供,博物馆日期为 ca。1949 年,Mac McLaughlin 的礼物,对象 ID:102710661。
4.14 Image courtesy of the Computer History Museum, Mountain View, CA, dated by the museum ca. 1949, gift of Mac McLaughlin, object ID: 102710661.
4.15 Jan Rajchman/RCA 实验室,由 George Dyson 提供。
4.15 Jan Rajchman/RCA Laboratories, courtesy of George Dyson.
4.17 图片来自英国曼彻斯特科学与工业博物馆持有的出版物。
4.17 Image reproduced from a publication held by the Museum of Science and Industry, Manchester, England.
4.18 经 The Camphill Village Trust Limited 许可。
4.18 With permission of The Camphill Village Trust Limited.
4.19 AS Douglas,由 Martin Campbell-Kelly 提供。
4.19 A. S. Douglas, courtesy of Martin Campbell-Kelly.
4.20 旋风 1 编程,报告 R-196,麻省理工学院数字计算机实验室,1951 年 6 月 11 日,批准公开发布,案例 06-1104, 55。
4.20 Programming for Whirlwind 1, Report R-196, Digital Computer Laboratory, MIT, June 11, 1951, approved for public release, case 06-1104, 55.
4.23(左)经 The MITRE Corporation 许可使用和转载。© 2016。(右)Alvy Ray Smith。
4.23 (Left) Used and reprinted with permission of The MITRE Corporation. © 2016. (Right) By Alvy Ray Smith.
4.24(左)纺织品采样器,维基共享资源,公共领域。(右)意大利拉文纳 St Apollinare Nuovo 大教堂的天使之间的玛丽和耶稣马赛克,作者 wjarek,Adobe 股票,310119847,扩展许可。
4.24 (Left) Textile sampler, Wikimedia Commons, public domain. (Right) Mosaic of Mary and Jesus between Angels in Basilica of St Apollinare Nuovo in Ravenna, Italy, by wjarek, Adobe stock, 310119847, extended license.
4.25(左)麦当娜,作者 Meyer Hill,美联社运营商,马里兰州巴尔的摩,1947 年,由 Alvy Ray Smith 的文字汇编而成。(右)哈马舍尔德,1962,维基共享资源,CC BY 3.0 Unported license,照片由 Jonn Leffmann 拍摄。
4.25 (Left) Madonna, author Meyer Hill, Associated Press Operator, Baltimore, MD, 1947, assembled from text by Alvy Ray Smith. (Right) Hammarskjöld, 1962, Wikimedia Commons, CC BY 3.0 Unported license, photo by Jonn Leffmann.
4.26-27 理查德·舒普。经卡内基梅隆大学和 Nancy Dickenson Shoup 许可。
4.26–27 By Richard Shoup. With permission of Carnegie Mellon University and Nancy Dickenson Shoup.
5.1 维基共享资源,CC BY-SA 2.5 通用许可,由 Kto288 提供。
5.1 Wikimedia Commons, CC BY-SA 2.5 Generic license, by Kto288.
5.2 收藏 Cinématheque française,Stephane Dabrowski 摄。由 Laurent Mannoni 提供。
5.2 Collection Cinématheque française, photo by Stephane Dabrowski. Courtesy of Laurent Mannoni.
5.3 WKL Dickson 和 Antonia Dickson,Kinetograph、Kinetooscope 和 Kineto-Phonograph 的历史(纽约:WKL Dickson,1895,国会图书馆副本)的封底。
5.3 Back cover of W.K.L. Dickson and Antonia Dickson, History of the Kinetograph, Kinetoscope, and Kineto-Phonograph (New York: W.K.L. Dickson, 1895, Library of Congress copy).
5.4 Athanasius Kircher,Ars Magna Lucis et Umbrae(第 2 版,阿姆斯特丹,1671 年),768。
5.4 Athanasius Kircher, Ars Magna Lucis et Umbrae (rev. 2nd edition, Amsterdam, 1671), 768.
5.5 © 皮克斯。
5.5 © Pixar.
5.6(左)维基共享资源,公共领域。(右)国会图书馆,弗朗西斯·本杰明·约翰斯顿摄,约 1890 年。
5.6 (Left) Wikimedia Commons, public domain. (Right) Library of Congress, photo by Frances Benjamin Johnston, ca. 1890.
5.7-9, 15-16, 18 作者:Alvy Ray Smith。
5.7–9, 15–16, 18 By Alvy Ray Smith.
5.10 CC BY–ND 3.0 未移植许可证。阿尔维·雷·史密斯(Alvy Ray Smith),2015 年。
5.10 CC BY–ND 3.0 Unported license. By Alvy Ray Smith, 2015.
5.11(左)Getty Images,115961049。(右)戈登·亨德里克斯电影历史论文,档案中心,美国国家历史博物馆,史密森学会,AC0369-0000009。
5.11 (Left) Getty Images, 115961049. (Right) Gordon Hendricks Motion Picture History Papers, Archives Center, National Museum of American History, Smithsonian Institution, AC0369-0000009.
5.12 爱迪生国家公园,公共领域。
5.12 Edison National Park, public domain.
5.13 Étienne-Jules Marey,1887 年,公共领域。
5.13 By Étienne-Jules Marey, 1887, public domain.
5.14 维基百科,比赛削减,合理使用。
5.14 Wikipedia, Match cut, fair use.
5.17 阿尔维·雷·史密斯。图片由纽约理工学院提供。
5.17 By Alvy Ray Smith. Images courtesy of New York Institute of Technology.
5.19(左)© Sharon Green/Ultimate Sailing,Windmark Productions Inc.(右)© Doug Gifford,Doug Gifford Photography。
5.19 (Left) © Sharon Green/Ultimate Sailing, Windmark Productions Inc. (Right) © Doug Gifford, Doug Gifford Photography.
5.20 CC BY-SA-3.0 未移植许可证,由 Judy Martin(未命名)女儿拍摄。
5.20 CC BY-SA-3.0 Unported license, photo by Judy Martin’s (unnamed) daughter.
6.1 ClipArt ETC 付费商业许可。
6.1 ClipArt ETC Paid Commercial License.
6.2(左)由皮特·彼得森提供。(右)由鲍勃·佩里提供。
6.2 (Left) Courtesy of Pete Peterson. (Right) Courtesy of Bob Perry.
6.3–9、12、23–25、28、30、39 作者:Alvy Ray Smith。
6.3–9, 12, 23–25, 28, 30, 39 By Alvy Ray Smith.
6.10 维基共享资源,CC BY-SA 2.0 通用许可。通过马歇尔·阿斯特。
6.10 Wikipedia Commons, CC BY-SA 2.0 Generic license. By Marshall Astor.
6.11(右)FAVPNG 商业许可。
6.11 (Right) FAVPNG Commercial License.
6.13 CC BY–ND 3.0 未移植许可证。作者:阿尔维·雷·史密斯,2020。
6.13 CC BY–ND 3.0 Unported license. By Alvy Ray Smith, 2020.
6.14(左)维基共享资源,CC BY 2.0 通用许可。作者:伊藤乔。(右)经 The MITRE Corporation 许可使用和转载。©2016。
6.14 (Left) Wikimedia Commons, CC BY 2.0 Generic license. By Joi Ito. (Right) Used and reprinted with permission of The MITRE Corporation. ©2016.
6.15 IBM Sage 计算机广告,1960 年,https://www.youtube.com/watch?v= iCCL4INQcFo,大约在 ca。1:00。
6.15 IBM Sage Computer Ad, 1960, https://www.youtube.com/watch?v=iCCL4INQcFo, framegrab at ca. 1:00.
6.16 J. Martin Graetz,“太空战争的起源”,Creative Computing 7,第 7 期。8(1981 年 8 月):39(下载 80 个中的 41 个),https://archive.org/details/creativecomputing-1981-08/,2020年 2 月 29 日访问。
6.16 J. Martin Graetz, “The Origin of Spacewar,” Creative Computing 7, no. 8 (Aug. 1981): 39 (41 of 80 in download), https://archive.org/details/creativecomputing-1981-08/, accessed Feb. 29, 2020.
6.17 照片由 Abbott Weiss 提供,1964 年。经他许可转载。
6.17 Photo by and courtesy of Abbott Weiss, 1964. Reprinted with his permission.
6.18 CC0 1.0 通用公共领域专用许可证。作者:Wojciech Mu l a。
6.18 CC0 1.0 Universal Public Domain Dedication license. By Wojciech Muła.
6.19 经 Antony Hare PI, 2010 许可,© Antony Hare。
6.19 By and with permission of Antony Hare P.I., 2010. © Antony Hare.
6.20(左)CC BY-SA 3.0 未移植许可证。托马斯·福斯曼摄。(中)CC BY-SA 3.0 未移植许可证。查尔斯01的照片。(右)Pierre E. Bézier,“汽车行业现有系统的示例:Unisurf 系统” ,伦敦皇家学会会刊。系列 A,数学和物理科学321(1971):208,图。2.
6.20 (Left) CC BY-SA 3.0 Unported license. Photo by Thomas Forsman. (Middle) CC BY-SA 3.0 Unported license. Photo by Charles01. (Right) Pierre E. Bézier, “Examples of an Existing System in the Motor Industry: The Unisurf System,” Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences 321 (1971): 208, fig. 2.
6.21 经 Tina Merandon 许可。
6.21 By and with permission of Tina Merandon.
6.22 Hanns Peter Bieri 和 Hartmut Prautzsch,“前言”,计算机辅助几何设计16 (1999): 579。
6.22 Hanns Peter Bieri and Hartmut Prautzsch, “Preface,” Computer Aided Geometric Design 16 (1999): 579.
6.26 经戴夫·科尔曼许可。
6.26 By and with permission of Dave Coleman.
6.27 经 Michele Bosi 许可, http: //VisualizationLibrary.org。
6.27 By and with permission of Michele Bosi, http://VisualizationLibrary.org.
6.29(左)经 Daniel Pillis 许可。(中)画板,https://www.youtube.com/watch?v= hB3jQKGrJo0,大约帧抓取。2:30。(右)照片由拉里·罗伯茨提供。
6.29 (Left) By and with permission of Daniel Pillis. (Middle) Sketchpad, https://www.youtube.com/watch?v=hB3jQKGrJo0, framegrab ca. 2:30. (Right) Photo courtesy of Larry Roberts.
6.31 © 阿尔维·雷·史密斯 (Alvy Ray Smith),1973 年。
6.31 © Alvy Ray Smith, 1973.
6.32 Bernhart 和 Fetter,美国专利号 3,519,997。
6.32 Bernhart and Fetter, US Patent No. 3,519,997.
6.33 Edward E. Zajac,“计算机制作的透视电影作为一种科学和交流工具” ,ACM 7 通讯,第 7 期。3(1964 年 3 月):170,图。2. 经 ACM 许可。
6.33 Edward E. Zajac, “Computer-Made Perspective Movies as a Scientific and Communication Tool,” Communications of the ACM 7, no. 3 (Mar. 1964): 170, fig. 2. With permission of ACM.
6.34 画板 III,https://www.youtube.com/watch?v= t3ZsiBMnGSg,大约帧抓取。约 1 点 22 分 约 1 点 23 分 2:11,约。2:55。
6.34 Sketchpad III, https://www.youtube.com/watch?v=t3ZsiBMnGSg, framegrabs ca. 1:22, ca. 1:23, ca. 2:11, ca. 2:55.
6.35 Ivan Sutherland,“Sketchpad, A Man-Machine Graphical Communication System”,博士论文,麻省理工学院,EE Dept.,Cambridge,MA,1963 年 1 月,133,图。9.8,经 Ivan Sutherland 许可。
6.35 Ivan Sutherland, “Sketchpad, A Man-Machine Graphical Communication System,” PhD thesis, MIT, EE Dept., Cambridge, MA, Jan. 1963, 133, fig. 9.8, with permission of Ivan Sutherland.
6.36 © Ken Knowlton,1998,Laurie M. Young 收藏。http://knowltonmosaics.com/。
6.36 © Ken Knowlton, 1998, collection of Laurie M. Young. http://knowltonmosaics.com/.
6.37 © Cybernetic Serendipity,1968 年,由 Franciszka Themerson 设计。经 Jasia Reichardt 许可。
6.37 © Cybernetic Serendipity, 1968, design by Franciszka Themerson. With permission of Jasia Reichardt.
6.38 Ephraim Cohen 使用由 Ron Baecker 在 Eric Martin 和 Lynn Smith 的建议下设计和编程的Genesys系统制作的动画。经贝克尔和科恩许可。
6.38 Animation by Ephraim Cohen using the Genesys system designed and programmed by Ron Baecker with the advice of Eric Martin and Lynn Smith. With permission of Baecker and Cohen.
6.40 Ivan Sutherland,“头戴式三维显示器” ,1968 年 AFIPS 秋季联合计算机会议论文集,759,图。2,经 Ivan Sutherland、Bob Sproull 和 Quintin Foster 许可。
6.40 Ivan Sutherland, “A Head-Mounted Three Dimensional Display,” Proceedings of 1968 AFIPS Fall Joint Computer Conference, 759, fig. 2, with permission of Ivan Sutherland, Bob Sproull, and Quintin Foster.
7.1 GE,计算机图像生成,模拟和控制系统部,通用电气公司,佛罗里达州代托纳比奇,NASA 图像,公共领域。由吉姆·布林供稿。
7.1 GE, Computer Image Generation, Simulation and Control Systems Department, General Electric Company, Daytona Beach, FL, NASA image, public domain. Contributed by Jim Blinn.
7.2 NASA/JPL–Caltech/Dan Goods,公共领域。
7.2 NASA/JPL–Caltech/Dan Goods, public domain.
7. 3 NASA 图片,公共领域。罗纳德·帕内塔供稿。
7. 3 NASA image, public domain. Contributed by Ronald Panetta.
7. 4 NASA 图片,公共领域。由 Peter Kamnitzer 和 Gene Youngblood 提供。
7. 4 NASA image, public domain. Courtesy of Peter Kamnitzer and Gene Youngblood.
7.5–11, 14–17, 19, 28–29 作者:Alvy Ray Smith。
7.5–11, 14–17, 19, 28–29 By Alvy Ray Smith.
7.12 CC BY–ND 3.0 未移植许可证许可证。作者:阿尔维·雷·史密斯,2019。
7.12 CC BY–ND 3.0 Unported License license. By Alvy Ray Smith, 2019.
7.13(左)Edwin Catmull,“计算机生成电影系统” ,ACM 年会论文集,卷。1, 426,波士顿,马萨诸塞州,1972 年 8 月 1 日。另外https://www.youtube.com/watch?v=RBBcPeZ1rgk&feature=youtu.be 1:30。经许可埃德卡特穆尔。(中)Frederic Ira Parke,“人脸的计算机生成动画”,硕士论文,犹他大学,1972 年 6 月,17,图。2.8(d)。还有 Frederic Ira Parke,“计算机生成的人脸动画” ,ACM 年会论文集,第一卷。1, 453,波士顿,马萨诸塞州,1972 年 8 月 1 日。经 Fred Parke 许可。(右)康奈尔透视,https://www.youtube.com/watch?v= 3iQqqv_bcXs,framegrab ca。0:07。经唐格林伯格许可。
7.13 (Left) Edwin Catmull, “A System for Computer Generated Movies,” Proceedings of the ACM Annual Conference, vol. 1, 426, Boston, Mass., 1 Aug. 1972. Also https://www.youtube.com/watch?v=RBBcPeZ1rgk&feature=youtu.be, framegrab ca. 1:30. With permission of Ed Catmull. (Middle) Frederic Ira Parke, “Computer Generated Animation of Faces,” MS thesis, University of Utah, June 1972, 17, fig. 2.8(d). Also Frederic Ira Parke, “Computer Generated Animation of Faces,” Proceedings of the ACM Annual Conference, vol. 1, 453, Boston, MA, Aug. 1, 1972. With permission of Fred Parke. (Right) Cornell in Perspective, https://www.youtube.com/watch?v=3iQqqv_bcXs, framegrab ca. 0:07. With permission of Don Greenberg.
7.18 Luká š Buri č in. Wikimedia Commons,公共领域。
7.18 By Lukáš Buričin. Wikimedia Commons, public domain.
7.20 理查德·舒普。经卡内基梅隆大学和 Nancy Dickenson Shoup 许可。
7.20 By Richard Shoup. With permission of Carnegie Mellon University and Nancy Dickenson Shoup.
7.21 Preston Blair,动画(Walter T. Foster,ca. 1940s),http://www.welcometopixelton.com/downloads/Animation%20by%20Preston%20Blair.pdf,2020年 3 月 1 日下载,封面,22, 24。由普雷斯顿布莱尔庄园提供。
7.21 Preston Blair, Animation (Walter T. Foster, ca. 1940s), http://www.welcometopixelton.com/downloads/Animation%20by%20Preston%20Blair.pdf, downloaded 1 Mar. 2020, cover, 22, 24. Courtesy of the Preston Blair Estate.
7.22–23, 26–27, 33 经纽约理工学院许可。
7.22–23, 26–27, 33 With permission of New York Institute of Technology.
7.24 Wikimedia Commons,公共领域,由 Viscountrapier 提供。
7.24 Wikimedia Commons, public domain, courtesy of Viscountrapier.
7.25 Ephraim Cohen,1977 年,经他许可。
7.25 By Ephraim Cohen, 1977, and with his permission.
7.30 维基共享资源,CC BY-SA 3.0 未移植许可证。作者:Brion Vibber、McLoaf 和 GDallimore。
7.30 Wikimedia Commons, CC BY-SA 3.0 Unported license. By Brion Vibber, McLoaf, and GDallimore.
7.31 由 Jim Blinn 提供并经其许可。
7.31 Courtesy of and with permission of Jim Blinn.
7.32(左)经纽约理工学院许可。(右)太阳石,1979 年,由 Ed Emshwiller 执导,由 Alvy Ray Smith 制作纹理映射动画。
7.32 (Left) With permission of New York Institute of Technology. (Right) Sunstone, 1979, directed by Ed Emshwiller, with texture-mapped animation by Alvy Ray Smith.
8.1 阿尔维·雷·史密斯。图片由皮克斯动画工作室提供。
8.1 By Alvy Ray Smith. Images courtesy of Pixar Animation Studios.
8.2 MC Escher,带反射球的手,1935 年。 ©2020 MC Escher 公司—荷兰。版权所有。
8.2 M. C. Escher, Hand with Reflecting Sphere, 1935. ©2020 The M. C. Escher Company—The Netherlands. All rights reserved.
8.3 Turner Whitted,“一种改进的阴影显示照明模型” ,ACM 23通讯,第 6(1980 年 6 月):347,图。7. 经 ACM 和 Turner Whitted 许可。
8.3 Turner Whitted, “An Improved Illumination Model for Shaded Display,” Communications of the ACM 23, no. 6 (June 1980): 347, fig. 7. With permission of ACM and Turner Whitted.
8.4 Gilles Tran,眼镜,2006 年。经 Gilles Tran 许可。
8.4 Gilles Tran, Glasses, 2006. With permission of Gilles Tran.
8.5 JI Yellott Jr.,“恒河猴视网膜中光感受器采样的光谱后果”,Science 221(1983 年 7 月 22 日):383,图。1(B 2 )。经 AAAS 许可。
8.5 J. I. Yellott Jr., “Spectral Consequences of Photoreceptor Sampling in the Rhesus Retina,” Science 221 (July 22, 1983): 383, fig. 1(B2). With permission from AAAS.
8.6 阿尔维·雷·史密斯。
8.6 By Alvy Ray Smith.
8.7 概念和图片由 Thomas Porter 提供。©皮克斯。
8.7 Concept and images courtesy of Thomas Porter. © Pixar.
8.8 阿尔维·雷·史密斯。概念由皮克斯的 Thomas Porter 提供。
8.8 Alvy Ray Smith. Concept courtesy of Thomas Porter, Pixar.
8.9 托马斯·波特,1984 年,1984 年。© 皮克斯。
8.9 Thomas Porter, 1984, 1984. © Pixar.
8.10 阿尔维·雷·史密斯。图片由皮克斯动画工作室提供。
8.10 By Alvy Ray Smith. Images courtesy of Pixar Animation Studios.
8.11 Alvy Ray Smith 的作曲,Loren Carpenter、Tom Duff、Chris Evans 和 Thomas Porter 的组件。图片由皮克斯动画工作室提供。
8.11 Composition by Alvy Ray Smith, of components by Loren Carpenter, Tom Duff, Chris Evans, and Thomas Porter. Image courtesy of Pixar Animation Studios.
8.12 Tron (1982), https://www.youtube.com/watch?v=-BZxGhNdz1k , framegrab ca。0:29。
8.12 Tron (1982), https://www.youtube.com/watch?v=-BZxGhNdz1k, framegrab ca. 0:29.
8.13(左)照片经 Ed Catmull、Alvy Ray Smith 和 Loren Carpenter 许可使用。图片由皮克斯动画工作室提供。(右)Craig Reynolds 的概念,Alvy Ray Smith 的图形。
8.13 (Left) Photo used with permission of Ed Catmull, Alvy Ray Smith, and Loren Carpenter. Image courtesy of Pixar Animation Studios. (Right) Concept by Craig Reynolds, graphics by Alvy Ray Smith.
8.14 © 皮克斯。
8.14 © Pixar.
8.15 约翰·拉塞特。图片由皮克斯动画工作室提供。
8.15 By John Lasseter. Images courtesy of Pixar Animation Studios.
8.16 WR Purcell Jr.,了解公司财务:图形方法(旧金山:Barnes & Noble Books,1983 年)和 Richard I. Levin,低买高卖,早收晚付:财务生存经理指南(旧金山:Prentice Hall,1983 年),Alvy Ray Smith 收藏。
8.16 W. R. Purcell Jr., Understanding a Company’s Finances: A Graphic Approach (San Francisco: Barnes & Noble Books, 1983) and Richard I. Levin, Buy Low, Sell High, Collect Early and Pay Late: The Manager’s Guide to Financial Survival (San Francisco: Prentice Hall, 1983), collection of Alvy Ray Smith.
9.1 图片由 Alvy Ray Smith 拍摄。
9.1 Photo by Alvy Ray Smith.
9.2 活力带–L2–205552D2eC2,© Darcy Gerbarg,2018。
9.2 Vibrant Band–L2–205552D2eC2, © Darcy Gerbarg, 2018.
9.3–4 Jun-Yan Zhu、Taesung Park、Phillip Isola 和 Alexei A. Efros,“Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks”,IEEE 2017 年计算机视觉国际会议,意大利威尼斯,无花果。1 和 12,经作者许可。
9.3–4 Jun-Yan Zhu, Taesung Park, Phillip Isola, and Alexei A. Efros, “Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks,” IEEE 2017 International Conference on Computer Vision, Venice, Italy, figs. 1 and 12, with the authors’ permissions.
页码后跟“f”表示数字。
Page numbers followed by an “f” indicate figures.
在第一圈,67
in In the First Circle, 67
科捷利尼科夫和,67
Kotelnikov and, 67
与 Beria 一起领导 NKVD,62
led NKVD with Beria, 62
领导 SMERSH,62
led SMERSH, 62
斯大林和62
Stalin and, 62
学术奖
Academy Award
artistic (Oscar), 424, 427, 430–431
技术(科技), 301 , 368 , 409 , 427 , 460
technical (Sci-Tech), 301, 368, 409, 427, 460
王牌(电脑),132
Ace (computer), 132
Ace report (Proposed Electronic Calculator), 127, 132
Adams, Charles W. (“Charlie”), 146, 155
高级研究计划署。见 ARPA
Advanced Research Projects Agency. See ARPA
飞机模拟器。见飞行模拟器
Aircraft simulators. See Flight simulators
阿罕布拉,25
Alhambra, 25
几乎计算机, 100 , 103 , 108 , 120 , 121 , 133 , 136
Almost-computers, 100, 103, 108, 120, 121, 133, 136
Alpha (A) 通道,385
Alpha (A) channel, 385
Altamira Software 和428–429
Altamira Software and, 428–429
增强现实 (AR) 和458
augmented reality (AR) and, 458
Ed Catmull, Alvy Ray Smith, 和, 363–365 , 367–368
Ed Catmull, Alvy Ray Smith, and, 363–365, 367–368
compositing and, 363, 384, 417
framebuffers and, 365, 367, 384–385
概述,363–368
overview, 363–368
汤姆·波特、汤姆·达夫和368
Tom Porter, Tom Duff, and, 368
RGBA绘画程序和,385
RGBA paint program and, 385
painting of walking boar in, 1, 1f
阿尔塔米拉作曲家,368
Altamira Composer, 368
Altamira Software, 368, 428–429
扩增, 19 , 77 , 119–120 , 247 , 434 , 441
Amplification, 19, 77, 119–120, 247, 434, 441
Digital Light and, 83, 114, 463
fractals and, 386–387, 387f, 414
去超新星,301-304(另见摩尔定律:超新星)
goes supernova, 301–304 (see also Moore’s Law: as supernova)
Malleability and, 77, 83, 85, 88
摩尔定律和, 82 , 120 , 301–304 , 310 , 338 , 435 , 455 , 463
Moore’s Law and, 82, 120, 301–304, 310, 338, 435, 455, 463
81-82的概述和性质
overview and nature of, 81–82
超越和,81-83
transcendence and, 81–83
三角形和, 243–246 , 307 , 322 , 329 , 337 , 386–387 , 387f
triangles and, 243–246, 307, 322, 329, 337, 386–387, 387f
Amtorg 贸易公司,64–65
Amtorg Trading Corp., 64–65
作为间谍活动的温床,65
as hotbed of espionage, 65
模拟(与数字),2
Analog (vs. digital), 2
模拟和数字无穷大, 48–51 , 48f–51f , 55 , 59 , 68 , 74
analog and digital infinities, 48–51, 48f–51f, 55, 59, 68, 74
将模拟媒体类型融合到数字/通用媒体中,436
convergence of analog media types into digital/universal medium, 436
digital can faithfully represent analog, 44, 49, 70
digital is not inferior to or less than analog, 70, 438
模拟(与数字)(续)
Analog (vs. digital) (cont.)
傅立叶和, 4 , 15 , 50 , 51 , 74 , 438
Fourier and, 4, 15, 50, 51, 74, 438
大数字融合,436
Great Digital Convergence and, 436
Kotelnikov and, 5, 49–51, 70, 438
模拟的现实,328
reality as analog, 328
recovery of analog from digital, 51, 55
采样定理和, 44 , 49 , 50–51 , 59 , 64 , 74
Sampling Theorem and, 44, 49, 50–51, 59, 64, 74
模拟动画机,349
Analog animation machine, 349
模拟时钟,15
Analog clock, 15
样品,49
samples of, 49
Analog television, 138, 139, 314
André & Wally B. (电影), 412–416 , 418
André & Wally B. (film), 412–416, 418
动画技术
Animation technologies
cels(见cel 动画)
cels (see cel animation)
剪纸, 211
decoupage, 211
刀耕火种,211
slash and tear, 211
Animators and actors, same skills used by, 210, 461–462
抗锯齿, 162f , 377 , 399 , 403 , 411
Antialiasing, 162f, 377, 399, 403, 411
first explicit and full, 162, 455
水平, 161
horizontal, 161
概述和性质, 161–162
overview and nature of, 161–162
光栅图像,359
raster images, 359
采样定理和,161-163
Sampling Theorem and, 161–163
Tom Stockham and, 162–163, 259, 359
at University of Utah, 162–163, 259, 359
预期和夸张, 171 , 213 , 216–217 , 450
Anticipation and exaggeration, 171, 213, 216–217, 450
Apollo Lunar Module, 320, 322, 327, 329
阿波罗月球计划,309f , 320 , 321 , 339 , 455
Apollo Moon Project, 309f, 320, 321, 339, 455
阿波罗-联盟号测试项目,71
Apollo–Soyuz Test Project, 71
近似理论,275
Approximation theory, 275
增强现实。见 增强现实
AR. See Augmented reality
ARPA (高级研究计划署),314、454、455 。另见DARPA
ARPA (Advanced Research Projects Agency), 314, 454, 455. See also DARPA
道格·恩格尔巴特和,256
Doug Engelbart and, 256
创始, 254
founding, 254
资助计算机图形学,293–294
funding computer graphics, 293–294
NASA和254、307、314、454、455 _ _ _ _ _ _ _
NASA and, 254, 307, 314, 454, 455
拉里·罗伯茨和,294
Larry Roberts and, 294
伊万·萨瑟兰和, 294 , 296 , 355 , 454
Ivan Sutherland and, 294, 296, 355, 454
鲍勃·泰勒和,294
Bob Taylor and, 294
艺术,167、209、210、297–299、327、350、351、375、376、454。_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 另见 DiFrancesco,大卫
Art, 167, 209, 210, 297–299, 327, 350, 351, 375, 376, 454. See also DiFrancesco, David
computers and, 318, 344, 348–349
Ed Emshwiller 和,375–377
Ed Emshwiller and, 375–377
Darcy Gerbarg and, 458–459, 459f
NEA 和355–356
NEA and, 355–356
光栅图形获得了它的第一笔公共艺术资金,355–356
raster graphics gets its first public art funding, 355–356
Jasia Reichardt 和(参见Cybernetic Serendipity)
Jasia Reichardt and (see Cybernetic Serendipity)
阿尔维·雷·史密斯 (Alvy Ray Smith),344
Alvy Ray Smith’s, 344
技术,355
technology and, 355
电传打字机,161
teletype, 161
斯坦范德贝克和,355
Stan Vanderbeek and, 355
人工制品,取样。请参阅 采样工件
Artifacts, sampling. See Sampling artifacts
Artificial intelligence (AI), 441, 464–466
第三定律,463
third law of, 463
原子弹(A - bomb),73、254、256、451
Atomic bomb (A-bomb), 73, 254, 256, 451
Augmented reality (AR), 305, 458–460
混合现实 (MR) 和459–460
mixed reality (MR) and, 459–460
virtual reality (VR) and, 305, 458–459
头像,461–462
Avatars, 461–462
宝贝(电脑)。见 曼彻斯特宝贝
Baby (computer). See Manchester Baby
Baecker, Ronald Michael (“Ron”), 262 , 298–299 , 301 , 348 , 372
Baecker, Ronald Michael (“Ron”), 262, 298–299, 301, 348, 372
Genesys和299、301、348、371 _ _ _ _ _
Genesys and, 299, 301, 348, 371
TX - 2和298、299、371 _
烘焙,462
Baking, 462
Barton, Christine, 356–358, 365
在米奇(克拉夫顿)之前,206、209、210、224、225 _ _
Before Mickey (Crafton), 206, 209, 210, 224, 225
Bell Labs, 45, 52, 75. See also Dudley, Homer
克劳德·香农 (Claude Shannon),45 岁、75岁、104岁
Claude Shannon at, 45, 75, 104
在第一圈,67
in In the First Circle, 67
领导内务人民委员部,62
led NKVD, 62
贝塞尔,皮埃尔·E。
Bézier, Pierre E.
computer graphics and, 279, 453–454
Steven Coons and, 261, 263, 267, 269
Paul de Faget de Casteljau 和,270–271
Paul de Faget de Casteljau and, 270–271
罗宾福雷斯特和,275
Robin Forrest and, 275
数学和, 275
mathematics and, 275
概述,267–269
overview, 267–269
照片,270f
photograph of, 270f
作为战俘 (POW), 268
as prisoner of war (POW), 268
贝塞尔曲线, 261 , 267 , 271 , 272 , 274
Bézier curves, 261, 267, 271, 272, 274
贝塞尔补丁,267 , 271 , 274–275 , 343
Bézier patches, 267, 271, 274–275, 343
贝塞尔样条曲线,274
Bézier spline, 274
双三次吊具,57–58
Bicubic spreader, 57–58
比林斯利,弗雷德,52 岁
Billingsley, Fred, 52
传记,202–203
Biographe, 202–203
Biograph projector, 197, 204, 451
位
Bits
计算机说话和数数,69
computerspeak and counting with, 69
关于的误解,111
misconceptions about, 111
不需要计算,114
not required for computation, 114
spread pixels and, 137, 143, 246
术语,122
terminology, 122
布兰查德,马尔科姆,353、355、374、403 _ _
Blanchard, Malcolm, 353, 355, 374, 403
布莱切利公园, 92 , 102f , 103 , 111–113
Bletchley Park, 92, 102f, 103, 111–113
炸弹由102
Bombes built by, 102
马克斯·纽曼( Max Newman )在103、104、113
概述,101–102
overview, 101–102
图灵, 78 , 80 , 92 , 101–104 , 111 , 113
Turing at, 78, 80, 92, 101–104, 111, 113
Blinn , James F.(“吉姆”),304、331、369、383
Blinn, James F. (“Jim”), 304, 331, 369, 383
描述和概述,369
description and overview, 369
大卫 Em 和,349–350
David Em and, 349–350
喷气推进实验室( JPL )和350、370、383、403、404 _ _
Jet Propulsion Laboratory (JPL) and, 350, 370, 383, 403, 404
在卢卡斯影业,403
at Lucasfilm, 403
在纽约理工大学,331、369、370、403 _ _
阿尔维·雷·史密斯( Alvy Ray Smith )和369、370、383、403、404
Alvy Ray Smith and, 369, 370, 383, 403, 404
at University of Utah, 331, 369, 370
Voyager spacecraft planetary flybys and, 370, 404
布林定律,419
Blinn’s Law, 419
Blue Sky Studios, 331, 407, 431, 432
Ice Age and, 331, 407, 431, 456
卡尔路德维希和,375
Carl Ludwig and, 375
MAGI 和373 , 375 , 407 , 431 , 432 , 456
MAGI and, 373, 375, 407, 431, 432, 456
波拿巴,拿破仑。见 拿破仑·波拿巴
Bonaparte, Napoleon. See Napoleon Bonaparte
布雷斯韦尔,罗恩,42 岁
Bracewell, Ron, 42
布雷森汉姆,杰克,247、248、262 _
Bresenham, Jack, 247, 248, 262
Bresenham’s algorithm, 247–248, 289
B样条,272
B-spline, 272
布尔加科夫,米哈伊尔,47岁
Bulgakov, Mikhail, 47
布什,万尼瓦,253–254
Bush, Vannevar, 253–254
名片设备, 89–90 , 90f , 92 , 95 , 111 , 119
Business card device, 89–90, 90f, 92, 95, 111, 119
作为计算机,93、105、106、110、119、137 _ _ _ _ _ _ _ _
as a computer, 93, 105, 106, 110, 119, 137
编码,108
encoding, 108
(名片的)方向/状态,92、94、105、110、441 _
orientations/states (of the business card), 92, 94, 105, 110, 441
as universal Turing machine, 92–95, 426, 440
C (programming language), 372, 409, 426
加元。参见 计算机辅助设计
CAD. See Computer-aided design
计算器,111
Calculators, 111
书法绕道, 139–141 , 163 , 241 , 277
Calligraphic detour, 139–141, 163, 241, 277
卡尔维诺,意大利,467
Calvino, Italo, 467
无相机电影,461–462
Cameraless movie, 461–462
相机投影系统,200-201。又见电影摄影
Camera-projector system, 200–201. See also Cinématographe
CAPS (电脑动画制作系统), 219 , 223 , 296 , 411 , 424 , 450
CAPS (Computer Animation Production System), 219, 223, 296, 411, 424, 450
Carpenter, Loren, 386 , 403–405 , 409 , 415 , 425 , 427。又见无产阶级
Carpenter, Loren, 386, 403–405, 409, 415, 425, 427. See also Proletariat
fractals and, 386, 387, 404, 411
喷气推进实验室( JPL )和386、403、404
Jet Propulsion Laboratory (JPL) and, 386, 403, 404
卢卡斯影业和399 , 403 , 411 , 425 , 427
Lucasfilm and, 399, 403, 411, 425, 427
RenderMan, Reyes, and, 425, 427
阿尔维·雷·史密斯( Alvy Ray Smith )和386、387、401、411、411f
Alvy Ray Smith and, 386, 387, 401, 411, 411f
卡彭蒂埃,朱尔斯,200
Carpentier, Jules, 200
漫画方法,295
Cartooning methods, 295
阴极射线,138
Cathode ray, 138
Cathode-ray tube (CRT), 118, 145
埃德萨克和,144
Edsac and, 144
电磁偏转器,318
electromagnetic deflectors, 318
NASA-1 和318
NASA-1 and, 318
概述和性质, 138–139
overview and nature of, 138–139
存储位,149–150
storing bits on, 149–150
弗雷迪威廉姆斯和,121
Freddie Williams and, 121
Catmull, Edwin (“Ed”), 351 , 355 , 364 , 365 , 367 , 386 , 409 , 410 , 413 , 414
Catmull, Edwin (“Ed”), 351, 355, 364, 365, 367, 386, 409, 410, 413, 414
alpha channel and, 363–365, 367
动画和, 219 , 233 , 334 , 354 , 355 , 359 , 399 , 410 , 413
animation and, 219, 233, 334, 354, 355, 359, 399, 410, 413
在应用程序,355
at Applicon, 355
克里斯汀巴顿和,357
Christine Barton and, 357
马尔科姆布兰查德和,355
Malcolm Blanchard and, 355
大写字母和219
CAPS and, 219
深度缓冲和,336
depthbuffering and, 336
大卫·迪弗朗西斯科和, 374 , 383 , 384 , 402 , 409 , 417
David DiFrancesco and, 374, 383, 384, 402, 409, 417
在数字等价物上,339
on digital equivalent, 339
dissertation, 163, 317, 339, 357
219 , 354 , 355 , 368 , 369 , 374 , 383 , 402 , 409 , 419–421 , 423的就业和职位
employment and positions held by, 219, 354, 355, 368, 369, 374, 383, 402, 409, 419–421, 423
家庭, 355
family, 355
hidden-surface problem and, 364, 367
John Lasseter and, 412–414, 428
卢卡斯影业和, 219 , 355 , 374 , 382–384 , 399 , 402 , 409 , 411 , 413 , 419–423
Lucasfilm and, 219, 355, 374, 382–384, 399, 402, 409, 411, 413, 419–423
运动模糊和,399
motion blur and, 399
纽约理工大学和355、357、368、371、372、377、382、383、402、409、417 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
NYIT and, 355, 357, 368, 371, 372, 377, 382, 383, 402, 409, 417
概述,354–355
overview, 354–355
皮克斯和, 219 , 240 , 355 , 374 , 421 , 429 , 431 , 433 , 460
Pixar and, 219, 240, 355, 374, 421, 429, 431, 433, 460
编程语言,372
programming languages and, 372
鲍勃舒马克和,357
Bob Schumacker and, 357
亚历克斯·舒尔和219、354、355、378、379、402 _ _ _ _ _ _
Alex Schure and, 219, 354, 355, 378, 379, 402
阿尔维·雷·史密斯和, 219 , 223 , 240 , 284 , 351 , 353 , 354 , 363–365 , 369 , 374 , 378–379 , 382–384 , 409 , 410 , 413 , 417–423 , 428 , 46
Alvy Ray Smith and, 219, 223, 240, 284, 351, 353, 354, 363–365, 369, 374, 378–379, 382–384, 409, 410, 413, 417–423, 428, 460
Ivan Sutherland and, 261, 284, 354
补间程序和417
Tween program and, 417
犹他大学261 , 317 , 334 , 354 , 357 , 369 , 371 , 410
University of Utah and, 261, 317, 334, 354, 357, 369, 371, 410
华特迪士尼公司和219 , 223 , 378–379 , 413 , 428 , 429
Walt Disney Company and, 219, 223, 378–379, 413, 428, 429
Catmull-Rom 样条,240
Catmull-Rom spline, 240
Catmull-Rom spreader, 272, 399
塞尔动画。另请 参阅
cel animation. See also cels
Ed Catmull 和,359
Ed Catmull and, 359
经典,185
classic, 185
墨水和油漆,212–213
ink and paint, 212–213
Ub Iwerks 和, 212
Ub Iwerks and, 212
皮克斯和,450
Pixar and, 450
Celluloid film, 187, 190, 196, 199
cels(赛璐珞片),211-213,301,418 。另见cel 动画
cels (celluloid sheets), 211–213, 301, 418. See also cel animation
数量限制,213
limits on the number of, 213
中心教条,7
Central Dogma, 7
威廉·费特和,281
William Fetter and, 281
逆向计算机图形和,459
inverse computer graphics and, 459
摩尔定律和,329
Moore’s Law and, 329
牛顿物理学和, 7 , 327 , 418 , 457 , 459
Newtonian physics and, 7, 327, 418, 457, 459
not required in computer graphics, 279, 347
外面, 279 , 328 , 343 , 355 , 457
outside the, 279, 328, 343, 355, 457
概述,457
overview, 457
千禧年后的使用,458–460
postmillennial uses of, 458–460
CAD 和混合现实 (MR )中需要,279、327、459
required in CAD and mixed reality (MR), 279, 327, 459
Larry Roberts and, 281, 327–328, 457
and the Triumvirate, 314, 328, 457
Triumvirate and, 314, 328, 457
Champollion, Jean-François, 11, 34
破译象形文字,28
deciphers hieroglyphs, 28
Champollion-Figeac,雅克-约瑟夫,40
Champollion-Figeac, Jacques-Joseph, 40
角色动画, 205 , 210 , 348 , 407 , 408 , 412 , 413 , 456
Character animation, 205, 210, 348, 407, 408, 412, 413, 456
中心教条和,418
Central Dogma and, 418
第一,209
first, 209
210–211的技术
technologies of, 210–211
three-dimensional (3D), 418, 456
角色动画师, 408 , 412 , 414 , 417 , 418
Character animator(s), 408, 412, 414, 417, 418
温莎·麦凯作为第一个,209
Winsor McCay as the first, 209
切尔托克,鲍里斯
Chertok, Boris
俄罗斯火箭科学家,68 岁
Russian rocket scientist, 68
沙拉什卡,68 岁
sharashka, 68
计时码表,202–203
Chronophotographe, 202–203
计时摄影师,198
Chronophotographer, 198
庄,理查德,409–411
Chuang, Richard, 409–411
“电影。” 另请参阅 电影
“Cinema.” See also Movie(s)
术语的使用,176
use of the term, 176
电影摄影师,200–203
Cinématographe, 200–203
克拉克,詹姆斯 H.(“吉姆”),377
Clark, James H. (“Jim”), 377
Alex Schure and, 378, 379, 382
搅动马蜂窝,377–378
stirs the hornet’s nest, 377–378
克拉克,韦斯利 A.,284
Clark, Wesley A., 284
克拉克,亚瑟 C.,304
Clarke, Arthur C., 304
克劳德·E·香农奖,53
Claude E. Shannon Award, 53
Cohen, Ephraim, 299, 358f, 371
彩色像素,311
Color pixels, 311
首先, 316 , 318 , 320–322 , 432 , 455
first, 316, 318, 320–322, 432, 455
通用电气和316、320、321、323、330 _ _ _ _ _ _
GE and, 316, 320, 321, 323, 330
Lunar Module and, 309f, 320, 323
Rougelot 和 Schumacker 以及, 331 , 344 , 357
Rougelot and Schumacker and, 331, 344, 357
Gene Youngblood and, 316, 318, 455
喷气推进实验室 (JPL) 和314–316
Jet Propulsion Laboratory (JPL) and, 314–316
罗德·鲁杰洛特和321 , 331 , 344 , 357 , 455
Rod Rougelot and, 321, 331, 344, 357, 455
Bob Schumacker and, 321–322, 344
巨像, 103 , 111 , 121 , 133 , 447
Colossus, 103, 111, 121, 133, 447
as an almost-computer, 103, 121, 133
计算
Computation
as a careful process, 4, 438, 440
确定但未预先确定, 81 , 106 , 107 , 441
determined but not predetermined, 81, 106, 107, 441
历史,4
history of, 4
延展性和, 77 , 81 , 83 , 114 , 119 , 390 , 440
Malleability and, 77, 81, 83, 114, 119, 390, 440
谜底,5
mystery of, 5
不需要的速度、位和电子设备,114
speed, bits, and electronics not required for, 114
计算机辅助设计 (CAD), 252 , 265 , 271 , 443 , 453 , 457
Computer-aided design (CAD), 252, 265, 271, 443, 453, 457
车身模拟,422
auto-body simulation and, 422
皮埃尔·艾蒂安·贝塞尔和, 267 , 269 , 271 , 279
Pierre Étienne Bézier and, 267, 269, 271, 279
史蒂文·安森·库恩斯和, 263 , 264 , 279 , 285
Steven Anson Coons and, 263, 264, 279, 285
Paul de Casteljau 和, 279 , 453
Paul de Casteljau and, 279, 453
罗宾福雷斯特和,265
Robin Forrest and, 265
巴雷特哈格里夫斯和,286
Barrett Hargreaves and, 286
计算机辅助设计 (CAD)(续)
Computer-aided design (CAD) (cont.)
概述和性质,249
overview and nature of, 249
面向图片的计算机图形学和, 249 , 252 , 263 , 279 , 285 , 291 , 443 , 453
picture-oriented computer graphics and, 249, 252, 263, 279, 285, 291, 443, 453
开拓者,453
pioneers in, 453
伺服实验室和,253
Servo Lab and, 253
画板 I、画板 III 和290
Sketchpad I, Sketchpad III, and, 290
Ivan Sutherland and, 285, 289, 294
玩具总动员和,252
Toy Story and, 252
麻省理工学院的计算机辅助设计 (CAD) 项目,253
Computer-Aided Design (CAD) Project at MIT, 253
Computer Aided Operations Research Facility (CAORF), 356, 357
电脑动画制作系统 (CAPS), 219 , 223 , 296 , 411 , 424 , 450
Computer Animation Production System (CAPS), 219, 223, 296, 411, 424, 450
Computer art, 318. See also Art
出生, 281
birth, 281
定义和概述,240–242
definition and overview, 240–242
数码灯和,240
Digital Light and, 240
第一次使用该术语,281–282
first use of the term, 281–282
240–241所需的步骤
steps required for, 240–241
计算机图形和图像处理(期刊),262
Computer Graphics and Image Processing (journal), 262
Computer Graphics Lab at NYIT, 219, 278
电脑)。另请参阅特定主题
Computer(s). See also specific topics
不是数字计算者,111
aren’t number crunchers, 111
第一台(见 第一台电脑)
first (see First computer)
历史,6
history of, 6
的发明,4
invention of, 4
make computations fast, 4, 102, 438
放大的奇迹,4
miracle of Amplification, 4
misconceptions about, 440–442
关于109–112的神话
myths about, 109–112
计算机语言,69
Computerspeak, 69
征服,罗伯特,61 岁
Conquest, Robert, 61
建筑与重建,453
Construction vs. reconstruction, 453
Cook, Robert L. (“Rob”), 427
Cook, Robert L. (“Rob”), 427
as Don Greenberg’s student at Cornell, 331, 388
卢卡斯影业和, 331 , 388 , 399 , 425 , 427
Lucasfilm and, 331, 388, 399, 425, 427
塑料和,388
plastic and, 388
shading language and, 388, 425, 427
库恩斯,史蒂文·安森(“史蒂夫”),453
Coons, Steven Anson (“Steve”), 453
皮埃尔·贝塞尔和, 261 , 263 , 267 , 269
Pierre Bézier and, 261, 263, 267, 269
计算机辅助设计( CAD )和263、264、279、285 _
computer-aided design (CAD) and, 263, 264, 279, 285
Tim Johnson and, 263, 265, 290
伊万·萨瑟兰和, 263 , 265 , 269 , 276 , 284 , 285
Ivan Sutherland and, 263, 265, 269, 276, 284, 285
昆斯奖, 261 , 267 , 269 , 394 , 427
Coons Award, 261, 267, 269, 394, 427
Coons 补丁,264–267 , 271 , 275 , 290
Coons patches, 264–267, 271, 275, 290
科波拉,弗朗西斯·福特,410
Coppola, Francis Ford, 410
康奈尔 1972 年的电影, 334 , 335 , 374
Cornell movie of 1972, 334, 335, 374
罗伯·库克 (Rob Cook),388
Rob Cook at, 388
通用电气和321、330、331 _ _
唐·格林伯格,电话:321、331、334、374、388 _ _ _
Don Greenberg at, 321, 331, 334, 374, 388
马克·莱沃伊 (Marc Levoy),374
Marc Levoy at, 374
MAGI 和,374
MAGI and, 374
罗德·鲁杰洛 (Rod Rougelot),电话: 320–321 , 331 , 334
Rod Rougelot at, 320–321, 331, 334
Corrugations, 30, 32, 176, 177, 179
傅里叶波 和, 30 , 32 , 176 , 177 , 179
Fourier waves and, 30, 32, 176, 177, 179
furrows, potato chips, and, 30, 438
表弟,维克多,35 岁
Cousin, Victor, 35
Cray supercomputer, 410, 411, 415
计算机图形学和241–242
computer graphics and, 241–242
显示空间和, 63 , 64 , 240–242 , 263 , 346–347 , 369
Display Space and, 63, 64, 240–242, 263, 346–347, 369
绘画程序和347
paint programs and, 347
创造力,品种/种类,460-462。另请参阅 Tower vs. stinks
Creativity, varieties/kinds of, 460–462. See also Tower vs. stinks
artistically vs. technically creative, 8, 461
科学家与工程师,8
scientists vs. engineers, 8
技术来自于8
technologies come from the interaction of, 8
古巴,拉里,381–382
Cuba, Larry, 381–382
Curious Case of Benjamin Button, The (film), 461, 462
Cybernetic Serendipity: The Computer and the Arts (Reichardt), 296–298 , 298f , 355 , 371 , 454
Cybernetic Serendipity: The Computer and the Arts (Reichardt), 296–298, 298f, 355, 371, 454
DAC-1。参见 计算机增强的设计
DAC-1. See Design Augmented by Computers
DARPA (Defense Advanced Research Projects Agency), 454. See also ARPA
大卫, 雅克-路易, 2 , 3f , 8 , 13 , 435
David, Jacques-Louis, 2, 3f, 8, 13, 435
去老化, 462
De-aging, 462
de Casteljau, Paul de Faget, 279 , 453 , 454
de Casteljau, Paul de Faget, 279, 453, 454
computer-aided design (CAD) and, 279, 453
概述,270–271
overview, 270–271
照片,271f
photograph of, 271f
as unsung hero, 270–272, 274–275
de Casteljau 曲线, 271–272 , 274
de Casteljau curves, 271–272, 274
剪纸,211
Decoupage, 211
深度伪造,462
Deepfakes, 462
Defense Advanced Research Projects Agency (DARPA), 454. See also ARPA
Demenÿ, Georges, 199 , 203 , 450
Demenÿ, Georges, 199, 203, 450
Demenÿ-Gaumont 关系,202–203
Demenÿ–Gaumont relationship, 202–203
Demenÿ–Lumière relationship, 204, 452
Demenÿ–Yanks 关系,204
Demenÿ–Yanks relationships, 204
亨利乔利和,203
Henri Joly and, 203
Marey-Demenÿ 关系, 198 , 199 , 201–202
Marey–Demenÿ relationship, 198, 199, 201–202
德尼罗,罗伯特,462
De Niro, Robert, 462
深度缓冲区,336
Depthbuffer, 336
计算机增强设计 (DAC-1)
Design Augmented by Computers (DAC-1)
computer-aided design (CAD) and, 285, 286
创建, 285
creation of, 285
麻省理工学院,286
MIT and, 286
Sketchpad III and, 285–286, 454
迪克森,安东尼娅(威廉的妹妹),193
Dickson, Antonia (William’s sister), 193
迪克森,威廉·肯尼迪·劳瑞(“WKL”/“劳瑞”),196
Dickson, William Kennedy Laurie (“W.K.L.”/”Laurie”), 196
35 mm film system, 196, 201, 451
Biograph Company and, 195–197, 204, 451
信用(不)给予193–197 , 201 , 449 , 451
credit (not) given to, 193–197, 201, 449, 451
爱迪生和,190–199
Edison and, 190–199
家庭背景和早年生活,194
family background and early life, 194
电影, 207
films, 207
Gordon Hendricks on, 190–191, 194
Lumière 兄弟和,452
Lumière brothers and, 452
作为真正制作电影的人,193–197
as the man who really made movies, 193–197
名字,193–194
names, 193–194
个性, 194
personality, 194
投影机和, 192 , 195 , 196 , 204 , 451
projectors and, 192, 195, 196, 204, 451
克里斯汀巴顿和,357
Christine Barton and, 357
Ed Catmull和374、383、384、402、409、417 _ _ _ _ _ _ _ _
Ed Catmull and, 374, 383, 384, 402, 409, 417
computer graphics lab and, 353, 355
电影录音机项目,384
film recorder project, 384
基于激光的胶片扫描仪和384
laser-based film scanner and, 384
MAGI 和,375
MAGI and, 375
国家艺术基金会 (NEA) 赠款和348–350 , 355 , 356
National Endowment for the Arts (NEA) grants and, 348–350, 355, 356
纽约理工大学和355、375、379、383、402 _ _ _ _ _
NYIT and, 355, 375, 379, 383, 402
概述,348–350
overview, 348–350
PARC和349、350、355、356 _ _ _ _ _
迪克舒普和,349
Dick Shoup and, 349
阿尔维·雷·史密斯和348 , 350 , 351 , 353 , 355 , 356 , 358 , 358f , 374 , 375 , 379 , 383 , 402 , 409 , 417
Alvy Ray Smith and, 348, 350, 351, 353, 355, 356, 358, 358f, 374, 375, 379, 383, 402, 409, 417
数字的
Digital
历史,2
history of, 2
notion of and characteristics of, 2, 44, 436
数字文物。请参阅 采样工件
Digital artifacts. See Sampling artifacts
Digital Light, 2, 4, 5. See also First Light; specific categories
Amplification and, 83, 114, 463
阐明惠特尼王朝的贡献,318-320
clarifies the Whitney dynasty contributions, 318–320
(第一) 的黎明, 118 , 119 , 119f , 121–122 , 252
dawning of the (first), 118, 119, 119f, 121–122, 252
126–127、128f、130的流程图_
flow chart of, 126–127, 128f, 130
定义,2
defined, 2
大数字融合和, 44 , 63 , 148 , 163 , 205 , 310 , 373 , 376 , 435–436
Great Digital Convergence and, 44, 63, 148, 163, 205, 310, 373, 376, 435–436
数码灯体验,种类繁多
Digital Light experience, varieties of
analytic vs. synthetic, 347, 442–443
计算机图形学, 443
computer graphics, 443
图像处理,443
image processing, 443
交互式与非交互式,443–445
interactive vs. non-interactive, 443–445
对象与图片,443
object vs. picture, 443
面向图片的计算机图形学,443
picture-oriented computer graphics, 443
实时与非实时,443–445
real-time vs. non-real-time, 443–445
shoot vs. compute, 83, 442–443
数字电影,6-7
Digital movie(s), 6–7
首先(见 电影,The)
first (see Movie, The)
工作室(见蓝天;梦工厂;皮克斯)
studios (see Blue Sky; DreamWorks; Pixar)
数码照片。又见 第一道光
Digital pictures. See also First Light
轻浮或禁止, 2 , 119 , 125 , 256 , 318 , 452
frivolous or forbidden, 2, 119, 125, 256, 318, 452
misconceptions about, 440–442
数字制作,409–412
Digital Productions, 409–412
Dirichlet,彼得·古斯塔夫·勒琼,42 岁
Dirichlet, Peter Gustav Lejeune, 42
迪士尼(华特迪士尼公司),219、223、456 。另见大写字母
Disney (Walt Disney Company), 219, 223, 456. See also CAPS
Ub Iwerks 和, 172 , 212 , 219–225 , 379 , 450
Ub Iwerks and, 172, 212, 219–225, 379, 450
Pixar purchased by, 219, 223, 429, 433
Pixar’s relationship with, 359, 424, 428, 429
迪士尼,罗伊·爱德华(沃尔特的侄子),223 , 430 , 433
Disney, Roy Edward (Walt’s nephew), 223, 430, 433
迪斯尼,罗伊奥利弗(沃尔特的兄弟),220 , 221 , 223
Disney, Roy Oliver (Walt’s brother), 220, 221, 223
米老鼠和, 166 , 221–222 , 286 , 452
Mickey Mouse and, 166, 221–222, 286, 452
展示
Display
作为从样本中重建模拟的行为,63
as act of reconstruction of analog from samples, 63
作为现代世界的基本假设,63
as a fundamental assumption of modern world, 63
是可变的,而像素是恒定的,63
is variable, whereas pixels are constant, 63
从435–436中分离图片
separation of picture from, 435–436
启用大数字融合,436
enabled Great Digital Convergence, 436
声音是扬声器和放大器,63
of sound is speaker and amplifier, 63
显示元素。另请参阅 传播像素
Display element(s). See also Spread pixels
数字输入,模拟输出,2
digital in, analog out, 2
作为非通用且因设备而异,436
as non-universal and varying among devices, 436
平滑连续,2
smooth and continuous, 2
spread pixels and, 64, 297, 311, 436
作为微小的发光点,2 , 5 , 64 , 139 , 436
as tiny glowing spot, 2, 5, 64, 139, 436
可见, 436
visible, 436
展示空间,241–242
Display Space, 241–242
在增强现实 (AR) 中,459–460
in augmented reality (AR), 459–460
创意空间和, 63 , 64 , 240–242 , 263 , 346–347 , 369
Creative Space and, 63, 64, 240–242, 263, 346–347, 369
绘画程序和346–347
paint programs and, 346–347
像素和, 63 , 64 , 241 , 246 , 347 , 369
pixels and, 63, 64, 241, 246, 347, 369
书法,连续,139 , 163 , 241 , 246–247 , 257 , 277–278 , 277f , 318 , 381
calligraphic, continuous, 139, 163, 241, 246–247, 257, 277–278, 277f, 318, 381
calligraphic on a grid, 277–278, 277f, 285
raster, 139–141, 140f (see also Raster displays)
Douglas, Alexander Shafto “Sandy,” 153, 287
DreamWorks Animation, 331, 430, 458
Pacific Data Images (PDI) and, 373, 430
理查德·德莱福斯,460–462
Dreyfuss, Richard, 460–462
Droidmaker: George Lucas and the Digital Revolution (鲁宾), 374 , 415
Droidmaker: George Lucas and the Digital Revolution (Rubin), 374, 415
达德利,荷马 W.,67 岁
Dudley, Homer W., 67
达夫,汤姆,372–373、404、406 _
Alpha 通道和368
alpha channel and, 368
Lucasfilm and, 368, 374, 402, 403
DVD, 4
DVD, 4
戴森,乔治,463
Dyson, George, 463
巴黎综合理工学院,22
École polytechnique, 22
皇家军事学院,13
Écoles royales militaire, 13
爱迪生,托马斯
Edison, Thomas
声称他人的发明为自己的,451
claimed others’ inventions as his own, 451
WKL 迪克森和, 190–199
W.K.L. Dickson and, 190–199
投影仪和, 192 , 195–197 , 204 , 451
projectors and, 192, 195–197, 204, 451
爱德华·迈布里奇和, 165 , 192 , 193 , 450
Edward Muybridge and, 165, 192, 193, 450
Edvac 报告(Edvac 报告初稿), 127 , 130–132 , 134
Edvac report (First Draft of a Report on the Edvac), 127, 130–132, 134
爱德华兹,大卫“戴”,125
Edwards, David “Dai,” 125
鸡蛋厂(卢卡斯影业),383
Egg Factory (Lucasfilm), 383
埃及。另见 罗塞塔石碑
Egypt. See also Rosetta Stone
描述 de l'Egypte , 22
Déscription de l’Egypte, 22
埃及学,28
Egyptology, 28
拿破仑的学者,22
Napoleon’s savants, 22
埃及学,22
Egyptology, 22
general theory of relativity, 12, 42, 46
帮助赫伯弗里曼逃离纳粹德国,261–262 , 344 , 454
helped Herb Freeman escape Nazi Germany, 261–262, 344, 454
Em,大卫,349–350
Em, David, 349–350
发射光与反射光,33
Emitted light vs reflected light, 33
Emshwiller, Ed (“Emsh”), 375–377
Emshwiller, Ed (“Emsh”), 375–377
加密。见 一次性垫
Encryption. See One-time pad
恩格尔巴特,道格,255–256,293–294
Engelbart, Doug, 255–256, 293–294
作为“几乎是计算机”,100 , 103 , 108 , 120 , 136
as “almost-computer,” 100, 103, 108, 120, 136
出生, 120
birth, 120
巨像和,121
Colossus and, 121
数码灯和,100
Digital Light and, 100
as first computer, 120, 121, 447
John von Neumann and, 100, 108–109
Eniac+ (Eniac 的可编程版本), 136 , 137 , 396 , 448
Eniac+ (programmable version of Eniac), 136, 137, 396, 448
出生, 136
birth, 136
作为第一台计算机,136、396、448
as first computer, 136, 396, 448
John von Neumann and, 136, 448
Entscheidungs 问题。见 问题
Entscheidungsproblem. See eProblem
Epoch 1(计算机历史),120,310 。另见 摩尔定律
Epoch 1 (computer history), 120, 310. See also under Moore’s Law
概述,7
overview, 7
阶段,248
stages of, 248
Epoch 1 speedup, 82. See also Amplification
纪元 2(计算机历史),7,82。另见摩尔定律;摩尔定律加速
Epoch 2 (computer history), 7, 82. See also under Moore’s Law; Moore’s Law speedup
Amplification enabled by, 390, 432, 455
color pixels and, 310, 432, 455
约会和开始, 120 , 249 , 302 , 302f , 310 , 321 , 322
dating and the start of, 120, 249, 302, 302f, 310, 321, 322
时代 2 放大。见 放大
Epoch 2 Amplification. See Amplification
电子问题(Entscheidungsproblem),85-89
eProblem (Entscheidungsproblem), 85–89
Alonzo Church 的解决方案,88-89
Alonzo Church’s solution to, 88–89
Turing’s solution to, 87–89, 106, 440
以太网,294
Ethernet, 294
欧多克希亚,467
Eudoxia, 467
欧拉,莱昂哈德,46 岁
Euler, Leonhard, 46
埃文斯,大卫,261、278、294、296、354 _ _ _ _ _
Evans, David, 261, 278, 294, 296, 354
Ivan Sutherland 和, 261 , 278 , 294 , 296 , 454(另见Evans & Sutherland)
Ivan Sutherland and, 261, 278, 294, 296, 454 (see also Evans & Sutherland)
埃文斯和萨瑟兰 (E&S), 330 , 331 , 351 , 358
Evans & Sutherland (E&S), 330, 331, 351, 358
克里斯汀巴顿和,357
Christine Barton and, 357
cofounding of, 261, 278, 294, 454
Computer Aided Operations Research Facility (CAORF), 356, 357
港口模拟器,356
harbor simulator, 356
LDS-1(书法展示),278
LDS-1 (calligraphic display), 278
Rougelot 和 Schumacker 在321 , 357
Rougelot and Schumacker at, 321, 357
亚历克斯舒尔和,353–355
Alex Schure and, 353–355
约翰沃诺克和,357
John Warnock and, 357
埃弗里特,鲍勃,145 岁
Everett, Bob, 145
夸张,214
Exaggeration, 214
预期和, 171 , 213 , 216–217 , 450
anticipation and, 171, 213, 216–217, 450
扩大电影院,355
Expanded cinema, 355
扩展影院(Youngblood), 313–314 , 316 , 318–320 , 355 , 455
Expanded Cinema (Youngblood), 313–314, 316, 318–320, 355, 455
扩展现实 (XR), 460
Extended reality (XR), 460
信仰与科学,227
Faith and science, 227
范,莫琳,458
Fan, Maureen, 458
Fantasmagorie (film), 206, 209
农场, 169
Farm, The, 169
菲利克斯猫,224–225,224f
Fetter, William A., 281, 284, 298
中心教条和,281
Central Dogma and, 281
计算机图形学,281–282
on computer graphics, 281–282
透视和, 281–284
perspective and, 281–284
电影。看 电影
Film. See Movie(s)
电影帧。见框架
Film frames. See Frames
定义, 447
defined, 447
First-computer/first-light coincidence, 163, 448
第一部数字电影。看 电影,
First digital movie. See Movie, The
关于 Edvac 的报告初稿。见 Edvac 报告
First Draft of a Report on the Edvac. See Edvac report
First Light(第一张数码照片),119、158、159、243、252、452。_ _ 另见数码灯
First Light (first digital picture), 119, 158, 159, 243, 252, 452. See also Digital Light
宝贝和, 125 , 163 , 256 , 319 , 448
Baby and, 125, 163, 256, 319, 448
汤姆·基尔本和118、119f、122、125、158、448 _ _ _ _
Tom Kilburn and, 118, 119f, 122, 125, 158, 448
弗莱舍、戴夫和马克斯,218–220
Fleischer, Dave and Max, 218–220
电影和早期电影系统的诞生,187 , 188–189f , 190 , 194–196 , 198 , 201 , 204 , 205
of the birth of cinema and early cinema systems, 187, 188–189f, 190, 194–196, 198, 201, 204, 205
dawn of Digital Light, 126–127, 128f, 130
of digital movies, 330, 331, 332–333f
早期计算机图形学 (Epoch 1), 248–249 , 250–251f
of early computer graphics (Epoch 1), 248–249, 250–251f
福雷斯特,罗宾,265、269、275、297 _ _ _
Forrest, Robin, 265, 269, 275, 297
关于动画,158
on animation, 158
概述,262–263
overview, 262–263
Forrester, Jay W., 137, 144. See also Whirlwind
数字光的基本思想。另见 采样定理
Foundational ideas of Digital Light. See also Sampling Theorem
Kotelnikov’s samples, 5, 50–51
采样定理,5
Sampling Theorem, 5
图灵的计算,5
Turing’s computations, 5
visual world is a sum of waves, 50, 51f, 74
傅立叶,让·巴蒂斯特·约瑟夫,4、7-8、11、437、445 _
Fourier, Jean Baptiste Joseph, 4, 7–8, 11, 437, 445
模拟图片表示和,438
analog picture representation and, 438
1768 年12月出生于欧塞尔
born in Auxerre 1768, 12
与14 岁的罗伯斯庇尔发生冲突
comes afoul of Robespierre, 14
橱柜, 13
cupboard, 13
为奥尔良的三名公民辩护,14
defends three citizens of Orléans, 14
排干 Bourgoin 的沼泽,34
drains the swamp of Bourgoin, 34
编辑描述 de l'Egypte , 34
editing Déscription de l’Egypte, 34
埃菲尔铁塔,姓名,39
Eiffel Tower, name on, 39
羡慕牛顿,13
envies Newton, 13
颂扬克莱伯,23
eulogizes Kléber, 23
流放到格勒诺布尔,23
exiled to Grenoble, 23
French Revolution and, 7, 11, 13–15
frequencies, amplitudes, and, 437, 438
全名让·巴蒂斯特·约瑟夫·傅立叶,13 岁
full name Jean Baptiste Joseph Fourier, 13
玛丽苏菲热尔曼和,38-39
Marie-Sophie Germain and, 38–39
39岁的法兰西学院不朽者
as immortel of Académie française, 39
1794 年入狱,14
jailed in 1794, 14
加入欧塞尔大众社会,14
joins Popular Society of Auxerre, 14
生活史和概述,12-15
life history and overview, 12–15
渴望永生,12-15
lust for immortality, 12–15
数学家和实验者,12
mathematician and experimenter, 12
导师商博良,28 岁
mentors Champollion, 28
as prefect of Isère department, 23, 24, 36, 37
作为罗纳省省长,38
as prefect of Rhône department, 38
获奖论文,36-37
Prize Essay, 36–37
Theory of Propagation of Heat in Solids (“memoir”), 35, 36, 40
傅立叶波
Fourier wave(s)
角度,30
angle, 30
一个展开的圆圈(一维),15
a circle unfurled (in one dimension), 15
颜色, 32–33
color, 32–33
波纹(二维),30
a corrugation (in two dimensions), 30
波纹和, 30 , 32 , 176 , 177 , 179
corrugations and, 30, 32, 176, 177, 179
循环,17
cycle, 17
展开的圆柱体(二维),30
a cylinder unfurled (in two dimensions), 30
frequency and amplitude, 17, 18
是一个正弦波,16
is a sine wave, 16
30-32 岁的东西
the stuff of, 30–32
Fractal mountain technique, 387, 404
扩增和386–387、387f、414 _
Amplification and, 386–387, 387f, 414
Loren Carpenter 和, 386 , 387 , 404 , 411
Loren Carpenter and, 386, 387, 404, 411
帧缓冲区,348,350–351,355,362,403 _ _ _ _ _ _
Framebuffer(s), 348, 350–351, 355, 362, 403
Alpha通道和365、367、384–385 _ _
alpha channels and, 365, 367, 384–385
克里斯汀·巴顿 (Christine Barton) 连接了356–358
Christine Barton connects the, 356–358
深度缓冲区、三角形和336
depthbuffer, triangles, and, 336
数码灯和,316
Digital Light and, 316
first full-color (24-bit), 363, 374
在卢卡斯影业,384–385
at Lucasfilm, 384–385
JPL 使用的机械帧缓冲区,314–315
mechanical framebuffer used by JPL, 314–315
性质, 314
nature of, 314
像素和314–316 , 325 , 336 , 343 , 345 , 347 , 357 , 363–365
pixels and, 314–316, 325, 336, 343, 345, 347, 357, 363–365
亚历克斯舒尔和,351,363,364,374 _ _ _
Alex Schure and, 351, 363, 364, 374
SuperPaint 和343–348
SuperPaint and, 343–348
帧率,182
Frame rate, 182
相框,胶卷,182–183
Frames, film, 182–183
作为时间样本,444
as time samples, 444
弗里曼,赫伯特(“赫伯”)
Freeman, Herbert (“Herb”)
共同创办计算机图形和图像处理(期刊),262
cofounded Computer Graphics and Image Processing (journal), 262
在爱因斯坦的帮助下逃离纳粹德国,261–262 , 344 , 454
escape from Nazi Germany with help from Einstein, 261–262, 344, 454
阿尔维·雷·史密斯 (Alvy Ray Smith) 和, 261 , 344
French Revolution, 7, 13. See also Wordsworth, William
国王路易十六被斩首,14 岁
King Louis XVI beheaded, 14
欧塞尔大众社会,14
Popular Society of Auxerre, 14
15岁的罗伯斯庇尔被斩首
Robespierre beheaded, 15
频率峰值, 24 , 27 , 34 , 179 , 187
Frequencyspeak, 24, 27, 34, 179, 187
带宽,30
bandwidth, 30
象形文字和,30
hieroglyphs and, 30
高频和, 24 , 33 , 72 , 158 , 214 , 324
high frequencies and, 24, 33, 72, 158, 214, 324
性质, 30
nature of, 30
锋利的边缘意味着高频,72
sharp edges mean high frequencies, 72
Furrows, corrugations and, 30, 438
通用电气 (GE)
General Electric (GE)
Cornell University and, 321, 330, 331
和第一个颜色像素,316 , 320 , 321 , 323 , 330
and the first color pixels, 316, 320, 321, 323, 330
为 NASA 制造的飞行模拟器,314 , 316 , 319 , 320
flight simulators built for NASA, 314, 316, 319, 320
罗德·鲁热洛( Rod Rougelot) ,电话:321、322、331、334
Rod Rougelot at, 321, 322, 331, 334
Rougelot 和 Schumacker 在357 , 455
Rougelot and Schumacker at, 357, 455
鲍勃·舒马克( Bob Schumacker ) ,电话:318、321、322、331、357、455 _
Bob Schumacker at, 318, 321, 322, 331, 357, 455
General Motors (GM), 268, 285, 289
DAC - 1和285–286、289、454 _
华特迪士尼和286
Walt Disney and, 286
麻省理工学院,286
MIT and, 286
创世纪效应,404
Genesis effect, 404
天才,天性,42
Genius, nature of, 42
Gentilella, John (“Johnny Gent”), 219
Gentilella, John (“Johnny Gent”), 219
几何模型和扩展像素,241 , 242 , 245 , 246 , 256
Geometric models and spread pixels, 241, 242, 245, 246, 256
Gerbarg, Darcy, 458–459 , 459f
Germain, Marie-Sophie, 11, 38–40
金茨堡,维塔利,73
Ginzburg, Vitaly, 73
Gödel’s Incompleteness Theorem, 98, 100
护目镜,立体/智能,260 , 458。另见 头戴式显示器;体视
Goggles, stereoscopic/smart, 260, 458. See also Head-mounted display; Stereoscopy
戈卢布佐娃,瓦莱里亚
Golubtsova, Valeriya
62岁成为MEI的长期董事
became longtime director of MEI, 62
作为 MEI 的优秀学生,62 岁
as brilliant student at MEI, 62
作为 MEI 的董事,65 岁
as director of MEI, 65
她的革命血统来自列宁,62
her revolutionary pedigree via Lenin, 62
Golubtsova, Valeriya (续)
Golubtsova, Valeriya (cont.)
as Kotelnikov’s protectress, 62, 74
母亲(奥尔加·内夫佐洛娃),62 岁
mother (Olga Nevzorova), 62
保护 Kotelnikov 免受 NKVD 的伤害,65–66
protects Kotelnikov from NKVD, 65–66
以67-68第二次救下科捷利尼科夫
saved Kotelnikov a second time, 67–68
图形用户界面,289、293、294 _
Graphical user interface, 289, 293, 294
第一,255–256
first, 255–256
重力,12
Gravity, 12
大数字融合, 4 , 12 , 43 , 44 , 72 , 75 , 374
Great Digital Convergence, 4, 12, 43, 44, 72, 75, 374
放大和,120
Amplification and, 120
动画和, 205
animation and, 205
阴极射线管 (CRT) 和138
cathode-ray tube (CRT) and, 138
定义,2
definition, 2
数码灯和, 44 , 63 , 148 , 163 , 205 , 310 , 373 , 376 , 435–436
Digital Light and, 44, 63, 148, 163, 205, 310, 373, 376, 435–436
437的意思
meaning of, 437
摩尔定律和,456
Moore’s Law and, 456
电影和, 4 , 310 , 328 , 406 , 429 , 432 , 456
movies and, 4, 310, 328, 406, 429, 432, 456
overview and nature of, 2, 141, 436
像素和2 , 63 , 141 , 241 , 313 , 376 , 436
pixels and, 2, 63, 141, 241, 313, 376, 436
光栅显示和, 277
raster display and, 277
需要全局存在的显示器,63
required global existence of displays, 63
sampling, Sampling Theorem, and, 158, 163
大恐怖/大清洗,79
Great Terror/Great Purge, 79
及其暴君,61–62
and its tyrants, 61–62
Greenberg, Donald P.(“唐”),334、374、388
Greenberg, Donald P. (“Don”), 334, 374, 388
在康奈尔大学,320–321 , 331 , 334 , 374
at Cornell University, 320–321, 331, 334, 374
Rod Rougelot 和, 320–321 , 331 , 334 , 374 , 455
Rod Rougelot and, 320–321, 331, 334, 374, 455
古根海姆, 拉尔夫, 375 , 381–382 , 433
Guggenheim, Ralph, 375, 381–382, 433
Lucasfilm and, 374, 381, 382, 433
在纽约理工大学,374、381、382、433 _ _
由 Beria 和 Abakumov 经营的奴隶劳改营,62
slave labor camps run by Beria and Abakumov, 62
黑客、太空战争和第一次,257–259
Hackers, Spacewar and the first, 257–259
锤子,阿尔芒,65 岁
Hammer, Armand, 65
哈格里夫斯,巴雷特,286
Hargreaves, Barrett, 286
头戴式显示器,305、334、377、457。_ _ _ _ 另见护目镜;体视
Head-mounted display, 305, 334, 377, 457. See also Goggles; Stereoscopy
亨德里克斯,戈登,190
Hendricks, Gordon, 190
on W.K.L. Dickson, 190–191, 194
Herzog, Bertram (“伯特”), 267 , 331 , 454
Herzog, Bertram (“Bert”), 267, 331, 454
隐藏面问题,364
Hidden-surface problem, 364
高清电视 (HDTV), 4
High-definition television (HDTV), 4
希尔伯特的第二个问题,98
Hilbert’s Second Problem, 98
史学。另见 流程图;理念-混乱-暴君
Historiography. See also Flow charts; Idea–chaos–tyrant
genealogy vs. narrative, 8, 449, 463
圣徒传记,2
hagiography, 2
received-history-is-wrong motif, 8, 446–447, 453
Hitler, Adolf. See Nazi Germany; World War II
全息镜头,460
HoloLens, 460
Horizontal antialiasing, 161. See also Antialiasing
百日,37-39
Hundred Days, 37–39
氢弹(H - bomb),72、73、254、256、451 _ _
Hydrogen bomb (H-bomb), 72, 73, 254, 256, 451
John von Neumann and, 100, 254
IBM 701、135、137、142、157–158 _ _ _ _ _ _
IBM 701, 135, 137, 142, 157–158
IBM 702、157、158 _ _
冰河世纪(电影), 331 , 407 , 431 , 456
Ice Age (film), 331, 407, 431, 456
理念-混沌-暴君,三合会,7 , 432–433 , 445 , 452 , 454 , 456–457 , 463。又见 暴君
Idea–chaos–tyrant, triad of, 7, 432–433, 445, 452, 454, 456–457, 463. See also Tyrants
在计算机中,451
in computers, 451
数字电影,456–457
digital movies, 456–457
在电影中,451–452
in movies, 451–452
形状, 454
shapes, 454
图灵,79-80,120-121,446-447 _ _ _
Turing’s, 79–80, 120–121, 446–447
理想电影, 176–177 , 179–180 , 186 , 187 , 450
Ideal movie, 176–177, 179–180, 186, 187, 450
理想的电影重建,180-182
Ideal movie reconstruction, 180–182
图像处理,443
Image processing, 443
图像处理程序,241
Image processing programs, 241
无穷大,种类,48
Infinity, kinds of, 48
countable/digital, 48, 49, 137
Information International Inc.见 Triple-I
Information International Inc. See Triple-I
Information Processing Techniques Office (IPTO), 293, 294
信息论,53
Information theory, 53
Inside-the-pupil, 182–183, 450, 460
交互式渲染的计算机图形
Interactively rendered computer graphics
画板作为第一(2D),287
Sketchpad as the first (2D), 287
画板 III 作为第一个 3D,454
Sketchpad III as the first 3D, 454
互联网,
Internet, the
以太网和294
Ethernet and, 294
Larry Roberts and, 293, 294, 454
看不见的城市(卡尔维诺),467
Invisible Cities (Calvino), 467
IPTO (Information Processing Techniques Office), 293, 294
Irishman, The (film), 175, 462
欧文,林恩,113–114
Irvine, Lyn, 113–114
艾沃克斯,Ub,219–221
Iwerks, Ub, 219–221
动画和, 172 , 212 , 219–221 , 450
animation and, 172, 212, 219–221, 450
作为商人,166
as businessman, 166
罗伊迪斯尼和,223
Roy Disney and, 223
华特迪士尼和172、212、219–225、379、450 _ _ _ _ _ _
Walt Disney and, 172, 212, 219–225, 379, 450
财务,219–222
finances, 219–222
米老鼠和221–222
Mickey Mouse and, 221–222
迈布里奇栅格和172
Muybridge rasters and, 172
名字,220
names, 220
声誉和遗产,223
reputation and legacy, 223
威利汽船,225
Steamboat Willie, 225
艾沃克斯工作室,222
Iwerks Studio, 222
喷气推进实验室 (JPL), 52 , 350 , 370 , 383 , 386 , 404
Jet Propulsion Laboratory (JPL), 52, 350, 370, 383, 386, 404
吉姆·布林和350、370、383、403、404 _ _ _ _ _
Jim Blinn and, 350, 370, 383, 403, 404
Loren Carpenter 和, 386 , 403 , 404
Loren Carpenter and, 386, 403, 404
彩色像素和314–316
color pixels and, 314–316
first color image and, 314, 315f
314–315使用的机械帧缓冲区
mechanical framebuffer used by, 314–315
NASA 参与314
NASA’s involvement with and, 314
Alvy Ray Smith and, 386, 403, 404
乔布斯,史蒂夫,191
Jobs, Steve, 191
迪士尼和428
Disney and, 428
与爱迪生相比,191
Edison compared with, 191
财务, 191 , 423 , 425 , 429 , 433 , 456–457
finances, 191, 423, 425, 429, 433, 456–457
乔纳森·艾夫和,191
Jonathan Ive and, 191
杰弗里·卡岑伯格和,428
Jeffrey Katzenberg and, 428
John Lasseter and, 425, 428, 433
皮克斯和, 423 , 425 , 429 , 433 , 456–457
Pixar and, 423, 425, 429, 433, 456–457
taking credit for others’ inventions, 191, 456
约翰逊,蒂莫西·爱德华(“蒂姆”)
Johnson, Timothy Edward (“Tim”)
建筑生涯,291
architecture career, 291
Steven Coons and, 263, 265, 290
Coons 补丁和290
Coons patches and, 290
从长远来看,290
in perspective, 290
perspective and, 278–279, 281, 284
photographs of, 276f, 290, 291f
画板 III 和, 275–276 , 279 , 290–292 , 454 , 457
Sketchpad III and, 275–276, 279, 290–292, 454, 457
Larry Roberts and, 276 , 279 , 281 , 284 , 290–292(另见 Triumvirate)
Larry Roberts and, 276, 279, 281, 284, 290–292 (see also Triumvirate)
Ivan Sutherland 和, 263 , 275 , 285 , 289–291 , 294(另见 Triumvirate)
Ivan Sutherland and, 263, 275, 285, 289–291, 294 (see also Triumvirate)
Triumvirate 和276、276f、285、454(另见 Triumvirate)
Triumvirate and, 276, 276f, 285, 454 (see also Triumvirate)
viewport implemented by, 279, 290
约翰逊航天中心。见 载人航天器中心
Johnson Space Center. See Manned Spacecraft Center
“欢乐事件”,第203 页
“Joly affair,” 203
Kajiya, James T.(“吉姆”),305 , 351
Kajiya, James T. (“Jim”), 305, 351
卡岑伯格,杰弗里,428
Katzenberg, Jeffrey, 428
关键帧动画,301
Keyframe animation, 301
关键帧, 299 , 301 , 359 , 361 , 362
Keyframes, 299, 301, 359, 361, 362
基尔本,汤姆,117、133、150 。另见威廉姆斯管/Williams-Kilburn 管
Kilburn, Tom, 117, 133, 150. See also Williams tube/Williams–Kilburn tube
宝贝和, 118 , 122 , 124f , 125 , 126 , 133 , 134 , 447 , 448
Baby and, 118, 122, 124f, 125, 126, 133, 134, 447, 448
位/位和,122
bits/digits and, 122
计算机内存和122
computer memory and, 122
显示与图片元素和,122
display vs. picture elements and, 122
论文,134
dissertation, 134
Edvac 报告,134
Edvac report and, 134
First Light(第一张数码照片)由118 , 119f , 122 , 125 , 158 , 448创建
First Light (first digital picture) created by, 118, 119f, 122, 125, 158, 448
对计算机设计的影响,127
influence on computer design, 127
photographs of, 118f, 122, 124f
pixels and, 117, 118, 122, 158
采样定理和,158
Sampling Theorem and, 158
Turing and, 133, 134, 150, 158
冯诺依曼架构和,134
von Neumann architecture and, 134
弗雷迪·威廉姆斯和, 117 , 118 , 122 , 126 , 127 , 132–134 , 141 , 447
Freddie Williams and, 117, 118, 122, 126, 127, 132–134, 141, 447
动画机,192
Kinetograph, 192
W.K.L. Dickson, Edison, and, 194–196, 198
电影放映机, 192 , 195–197 , 200 , 203
Kinetoscope, 192, 195–197, 200, 203
国王学院, 剑桥, 77 , 78f , 79 , 134 , 463–464
King’s College, Cambridge, 77, 78f, 79, 134, 463–464
克勒贝尔,让·巴蒂斯特,23 岁
Kléber, Jean Baptiste, 23
诺尔顿,肯,296–298
Knowlton, Ken, 296–298
亚历山大·科捷利尼科夫(弗拉基米尔的父亲)
Kotelnikov, Aleksandr (Vladimir’s father)
举家到基辅,46
moved family to Kiev, 46
47岁举家迁往莫斯科
moved family to Moscow, 47
作为喀山大学数学家,46
as University of Kazan mathematician, 46
彼得·科捷尔尼科夫(弗拉基米尔的祖父)
Kotelnikov, Petr (Vladimir’s grandfather)
作为罗巴切夫斯基的助手和冠军,46 岁
as Lobachevsky’s assistant and champion, 46
作为喀山大学数学家,46
as University of Kazan mathematician, 46
Kotelnikov, Semyon(弗拉基米尔的曾曾曾祖父)
Kotelnikov, Semyon (Vladimir’s great-great-great-grandfather)
圣彼得堡科学院,46
St. Petersburg Academy of Sciences, 46
作为欧拉的学生,46 岁
as student of Euler, 46
科捷尔尼科夫,弗拉基米尔·亚历山德罗维奇,5岁,45 岁,73-75岁
Kotelnikov, Vladimir Aleksandrovich, 5, 45, 73–75
1932 年47岁
1932 as annus mirabilis for, 47
1908年出生于喀山,46岁
born in Kazan 1908, 46
as Chairman of Russian Supreme Soviet, 43, 73
对太空竞赛的贡献,68
contributions to space race, 68
MEI 院长,47岁
deanship at MEI, 47
死亡,76
death, 76
作为 NKS 的工程师,48岁
as engineer at NKS, 48
evacuated his lab to Ufa, 65
71岁的阿波罗-联盟号的俄罗斯一侧
headed Russian side of Apollo–Soyuz, 71
NKS的领导学院,48
heading institute at NKS, 48
听到他的第一次广播,47
hearing his first radio broadcast, 47
IEEE Alexander Graham Bell 奖章授予43
IEEE Alexander Graham Bell Medal awarded to, 43
MEI 讲师,47岁
lectureship at MEI, 47
列宁奖,71
Lenin Prize, 71
mapped Venus with digital images, 43, 71
作为 MEI 的首批毕业生之一,47
as one of MEI’s first graduates, 47
预测手机,71
predicted mobile phone, 71
保护者(见 Golubtsova,Valeriya)
protectress (see Golubtsova, Valeriya)
萨哈罗夫事件和,72
Sakharov affair and, 72
由54证明的采样定理
Sampling Theorem proved by, 54
再次被戈卢布佐娃扑出,67-68
saved by Golubtsova again, 67–68
Golubtsova 从 NKVD 中救出,65–66
saved by Golubtsova from NKVD, 65–66
第二次尝试让他进入 sharashka, 68
second attempt to put him in sharashka, 68
第二次访问美国,71
second visit to U.S., 71
斯大林奖和列宁勋章,43
Stalin Prizes and Orders of Lenin, 43
访问美国 Amtorg,64
visited Amtorg in US, 64
作为声码器专家,67
as vocoder expert, 67
warned US about Sputnik, 43, 71
科捷利尼科夫的暴君。见 阿巴库莫夫,维克多;贝利亚,拉夫伦蒂;马林科夫,乔治
Kotelnikov’s tyrants. See Abakumov, Viktor; Beria, Lavrenti; Malenkov, Georgi
克日扎诺夫斯基,格莱布
Krzhizhanovsky, Gleb
作为列宁的朋友,62 岁
as Lenin’s friend, 62
与62 岁的 Zinaida Nevzorova 结婚
married to Zinaida Nevzorova, 62
忽必烈,467
Kublai Khan, 467
Laplace, Pierre-Simon, 22, 36, 37
拉塞特,约翰,401,412–413,415 _
Lasseter, John, 401, 412–413, 415
迪斯尼和, 226 , 407 , 408 , 413 , 428 , 430 , 431
Disney and, 226, 407, 408, 413, 428, 430, 431
杰弗里·卡岑伯格和,428
Jeffrey Katzenberg and, 428
电影/玩具总动员和, 407 , 412–414 , 421 , 424 , 425 , 428
The Movie/Toy Story and, 407, 412–414, 421, 424, 425, 428
皮克斯和, 226 , 407 , 413 , 421 , 424 , 425 , 433
Pixar and, 226, 407, 413, 421, 424, 425, 433
比尔·里夫斯和416、421、424、425、428 _ _ _ _ _
Bill Reeves and, 416, 421, 424, 425, 428
阿尔维·雷·史密斯和, 226 , 412–414 , 428
Alvy Ray Smith and, 226, 412–414, 428
LDS-1(书法展示),278
LDS-1 (calligraphic display), 278
列宁
Lenin
布尔什维克财政,62
Bolshevik finances, 62
流亡西伯利亚,62
exile in Siberia, 62
作为喀山大学的学生,46 岁
as student at University of Kazan, 46
Licklider, JCR (“舔”), 255 , 293–294
Licklider, J.C.R. (“Lick”), 255, 293–294
林肯实验室(麻省理工学院林肯实验室),276,284。另见TX-2
Lincoln Lab (MIT Lincoln Laboratory), 276, 284. See also TX-2
尼古拉·洛巴切夫斯基
Lobachevsky, Nikolai
爱因斯坦使用的数学,46
math of, used by Einstein, 46
非欧几何,46
non-Euclidean geometry, 46
作为喀山大学数学家,46
as University of Kazan mathematician, 46
卢卡斯,乔治,403、405、406、415 _ _ _
Lucas, George, 403, 405, 406, 415
André & Wally B. and, 415
André & Wally B. and, 415
动画和, 413
animation and, 413
Ed Catmull 和, 383 , 413 , 419 , 421
Ed Catmull and, 383, 413, 419, 421
迪士尼和413
Disney and, 413
拉尔夫·古根海姆、鲍勃·金迪和381–382
Ralph Guggenheim, Bob Gindy, and, 381–382
项目, 381
projects, 381
抵制制作电脑动画电影,416
resistance to making a computer-animated movie, 416
阿尔维·雷·史密斯和382 , 403 , 405 , 406 , 415 , 419
Alvy Ray Smith and, 382, 403, 405, 406, 415, 419
星球大战和381
Star Wars and, 381
vision of digitizing film production, 383, 415
卢卡斯,玛西娅(乔治的妻子)
Lucas, Marcia (George’s wife)
sharing office with, 384, 409, 412
Lucasfilm Ltd.另见星球大战
Lucasfilm Ltd. See also Star Wars
和“几乎”制作电影,416
and “almost” making The Movie, 416
布拉德伯德的访问,412
Brad Bird’s visit to, 412
Loren Carpenter 和, 399 , 403 , 411 , 425 , 427
Loren Carpenter and, 399, 403, 411, 425, 427
Ed Catmull 和, 219 , 355 , 374 , 382–384 , 399 , 402 , 409 , 411 , 413 , 419–423
Ed Catmull and, 219, 355, 374, 382–384, 399, 402, 409, 411, 413, 419–423
cel动画和,219
cel animation and, 219
计算机图形学明星,403
computer graphics stars at, 403
罗伯·库克和331、388、399、425、427 _ _ _ _ _
Rob Cook and, 331, 388, 399, 425, 427
Cornell University and, 330, 331
在385设计数码光学打印机
designing digital optical printer at, 385
David DiFrancesco and, 374, 409
迪士尼和219
Disney and, 219
汤姆·达夫和368、374、402、403 _ _ _
Tom Duff and, 368, 374, 402, 403
财务,421–423
finances, 421–423
帧缓冲区,384–385
framebuffers at, 384–385
拉尔夫古根海姆和, 374 , 381 , 382 , 433
Ralph Guggenheim and, 374, 381, 382, 433
硬件, 426
hardware, 426
约翰·拉塞特和,412–413
John Lasseter and, 412–413
摩尔定律和,456
Moore’s Law and, 456
The Movie/Toy Story and, 416, 429, 433
纽约理工大学和330、331、355、373–374、402、433 _ _ _ _ _ _ _
NYIT and, 330, 331, 355, 373–374, 402, 433
卢卡斯影业的 NYIT 秘密之旅,381–384
Lucasfilm’s secret trip to NYIT, 381–384
皮克斯和, 219 , 330 , 373–374 , 416 , 423 , 425 , 427 , 429 , 456
Pixar and, 219, 330, 373–374, 416, 423, 425, 427, 429, 456
卢卡斯影业诞生皮克斯,419–423
Lucasfilm begets Pixar, 419–423
卢卡斯影业有限公司(续)
Lucasfilm Ltd. (cont.)
汤姆波特和, 231 , 241 , 368 , 385 , 399 , 403
Tom Porter and, 231, 241, 368, 385, 399, 403
RenderMan、Reyes 和425–427
RenderMan, Reyes, and, 425–427
RGBA 绘画程序,385
RGBA paint program, 385
shading language and, 425, 426
Alvy Ray Smith 和, 219 , 355 , 373–374 , 382–386 , 388 , 401–403 , 409 , 413 , 416 , 419–423
Alvy Ray Smith and, 219, 355, 373–374, 382–386, 388, 401–403, 409, 413, 416, 419–423
犹他大学,261
University of Utah, 261
Unix 和401–402
Unix and, 401–402
路德维希,卡尔,375
Ludwig, Carl, 375
Lumière, Antoine (父亲), 200
Lumière, Antoine (father), 200
Lumière 兄弟, 195 , 196 , 451–452
Lumière brothers, 195, 196, 451–452
遗产和神话, 165 , 199 , 200 , 449–452
legacy and mythology, 165, 199, 200, 449–452
作为任何语言的光的制造者,200–204
as makers of light in any language, 200–204
投影仪, 195
projectors, 195
登月舱。见 阿波罗登月舱
Lunar Module. See Apollo Lunar Module
里昂,理查德,52 岁
Lyon, Richard, 52
李森科的生物学,46
Lysenko’s biology, 46
MAGI(数学应用集团公司),407–409、431、432、456
MAGI (Mathematical Applications Group Inc.), 407–409, 431, 432, 456
蓝天工作室和, 373 , 375 , 407 , 431 , 432 , 456
Blue Sky Studios and, 373, 375, 407, 431, 432, 456
塞尔科、卡尔·路德维希和375
Celco, Carl Ludwig, and, 375
康奈尔大学,374
Cornell University and, 374
得到一个角色动画师,408
gets a character animator, 408
冰河时代,431
Ice Age and, 431
纽约理工大学和374、409、431 _
魔法飞跃,460
Magic Leap, 460
Malenkov, Georgi, 61–62, 74, 445
开始斯大林的秘密清洗,62
kicks off Stalin’s Secret Purge, 62
斯大林之后的苏联总理,62岁
Premier of the Soviet Union after Stalin, 62
二战后仅次于斯大林,62
second only to Stalin after WWII, 62
Malleability (of computers), 4, 77, 97, 440
Amplification and, 77, 83, 85, 88
计算和, 77 , 81 , 83 , 114 , 119 , 390 , 440
computation and, 77, 81, 83, 114, 119, 390, 440
390的奇迹
the miracle of, 390
80–81的概述和性质
overview and nature of, 80–81
Manchester Baby (“宝贝”), 122 , 125 , 128f , 137 , 152
Manchester Baby (“Baby”), 122, 125, 128f, 137, 152
1998 年重建/复制,125
1998 rebuild/replica of, 125
动画和, 154
animation and, 154
阴极射线管 ( CRT )和118、448、452
cathode-ray tube (CRT) and, 118, 448, 452
第一光和125 , 163 , 256 , 319 , 448
First Light and, 125, 163, 256, 319, 448
在历史背景下,117 , 120 , 128f , 133–136 , 142 , 448 , 451
in historical context, 117, 120, 128f, 133–136, 142, 448, 451
汤姆·基尔本和118、122、124f、125、126、133、134、447、448 _ _ _ _ _ _ _ _ _ _
Tom Kilburn and, 118, 122, 124f, 125, 126, 133, 134, 447, 448
内存/位, 118 , 120 , 143 , 154 , 163 , 447 , 448
memory/bits, 118, 120, 143, 154, 163, 447, 448
Max Newman and, 126, 133–134, 142
概述和性质,133–134
overview and nature of, 133–134
图片和, 125
pictures and, 125
皮克斯和125
Pixar and, 125
阿尔维·雷·史密斯 (Alvy Ray Smith) 和125
Alvy Ray Smith and, 125
Turing and, 126, 133, 447, 448
von Neumann architecture, 134, 135, 448
von Neumann team and, 135, 447–448
弗雷迪·威廉姆斯和122 , 125 , 126 , 133 , 142 , 143
Freddie Williams and, 122, 125, 126, 133, 142, 143
威廉姆斯管和, 122 , 142 , 143 , 447 , 448
Williams tube and, 122, 142, 143, 447, 448
Manchester Mark I, 134, 142, 152
疯子(电脑), 135–137 , 142 , 149 , 157
Maniac (computer), 135–137, 142, 149, 157
Manned Spacecraft Center, 316, 319
马可波罗,467
Marco Polo, 467
马雷,艾蒂安-朱尔斯
Marey, Étienne-Jules
Georges Demenÿ 和, 198 , 199 , 201–202
Georges Demenÿ and, 198, 199, 201–202
Edward Muybridge and, 175, 198
马菲诺沙拉什卡
Marfino sharashka
出现在第一圈,67
featured in In the First Circle, 67
安置 Kotelnikov 的实验室,但不是 Kotelnikov,66–67
housed Kotelnikov’s lab but not Kotelnikov, 66–67
67 岁的索尔仁尼琴
housed Solzhenitsyn, 67
在莫斯科北部,66
in northern Moscow, 66
马克一世。见 曼彻斯特马克一世
Mark I. See Manchester Mark I
麻省理工学院。见 麻省理工学院
Massachusetts Institute of Technology. See MIT
矩阵代数,293
Matrix algebra, 293
麦卡锡,约翰,465
McCarthy, John, 465
麦卡锡,约瑟夫,79 岁
McCarthy, Joseph, 79
梅。见 莫斯科电力工程学院
MEI. See Moscow Power Engineering Institute
记忆, 数字. 请参阅 帧缓冲区
Memory, digital. See Framebuffer(s)
creation and birth of, 166, 221
华特迪士尼和, 166 , 221–222 , 286 , 452
Walt Disney and, 166, 221–222, 286, 452
Ub Iwerks 和, 221–222
Ub Iwerks and, 221–222
Microsoft, 241–242, 368, 429, 460
微软字,389
Microsoft Word, 389
明斯基,马文,465
Minsky, Marvin, 465
麻省理工学院(麻省理工学院)。另见 画板;画板三;太空战争;TX-2;旋风
MIT (Massachusetts Institute of Technology). See also Sketchpad; Sketchpad III; Spacewar; TX-2; Whirlwind
人工智能中心,465
AI center, 465
罗恩·贝克尔 (Ron Baecker),298
Ron Baecker at, 298
万尼瓦·布什,253
Vannevar Bush at, 253
史蒂夫·库恩斯 (Steve Coons),263–265
Steve Coons at, 263–265
DAC-1 与 GM 合作,286
DAC-1 work with GM, 286
赫伯弗里曼,262
Herb Freeman at, 262
在156年首次验证计算机动画
first verified computer animation at, 156
黑客,258–259
hackers, 258–259
林肯实验室 (Lincoln Lab), 276 , 284
Lincoln Laboratory (Lincoln Lab), 276, 284
PDP-1 在,259
PDP-1 at, 259
辐射实验室(Rad Lab),253
Radiation Lab (Rad Lab), 253
52 岁的威廉·施赖伯
William Schreiber at, 52
罗伯特·舒马克 (Robert Schumacker),321
Robert Schumacker at, 321
Servomechanism Lab (Servo Lab), 253, 262
克劳德·香农,254
Claude Shannon at, 254
精明营销,289
smart about marketing, 289
汤姆斯托克汉姆,259
Tom Stockham at, 259
弗雷德里克·特曼 (Frederick Terman),254
Frederick Terman at, 254
Triumvirate(萨瑟兰、约翰逊、罗伯茨)在(见 Triumvirate)
Triumvirate (Sutherland, Johnson, Roberts) at (see Triumvirate)
MITRE 公司,144
MITRE Corporation, 144
孙悟空项目359 , 416 , 417 , 420 , 430 , 456
Monkey King project, 359, 416, 417, 420, 430, 456
猴子,394–396
Monkeys, 394–396
穆勒,詹姆斯 A.(“安迪”),384
Moorer, James A. (“Andy”), 384
放大82 , 120 , 301–304 , 310 , 338 , 435 , 455 , 463
Amplification and, 82, 120, 301–304, 310, 338, 435, 455, 463
和数码灯,301
and Digital Light, 301
作为工程奇迹,8、311、432、437 _ _ _
as engineering miracle, 8, 311, 432, 437
时期 1 和 2 以及7、137、248、249、301–303、305、321
Epochs 1 and 2 and, 7, 137, 248, 249, 301–303, 305, 321
explanation of suggested, 303, 448–449
and the first color pixels, 432, 455
framebuffers and, 350–351, 364
数量级版本,6、82、120、302、303、310、323、327、331、361、417、420、428、432、435、448、456、463 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
order of magnitude version, 6, 82, 120, 302, 303, 310, 323, 327, 331, 361, 417, 420, 428, 432, 435, 448, 456, 463
术语的由来,306
origin of the term, 306
设定于 1965 年, 6 , 7 , 82 , 249 , 255 , 301–305 , 310 , 311 , 313 , 432
posited in 1965, 6, 7, 82, 249, 255, 301–305, 310, 311, 313, 432
作为超新星,6 , 120 , 227 , 301–304 , 310 , 448 , 463
as supernova, 6, 120, 227, 301–304, 310, 448, 463
伊万·萨瑟兰和,306
Ivan Sutherland and, 306
摩尔定律加速,82 , 301–304 , 386 , 444
Moore’s Law speedup, 82, 301–304, 386, 444
莫斯科高等技术学校,47
Moscow Higher Technical School, 47
莫斯科动力工程学院 (MEI), 47 , 62 , 65 , 68 , 71
Moscow Power Engineering Institute (MEI), 47, 62, 65, 68, 71
“电影。” 另请参阅 电影
“Motion picture.” See also Movie(s)
术语的使用,176
use of the term, 176
电影,The(第一部数字电影),416。另见玩具总动员(电影)
Movie, The (first digital movie), 416. See also Toy Story (film)
Central Dogma and, 328, 329, 417
成为焦点,428–429
coming into focus, 428–429
competitors, 407, 409, 410, 430
电影,第一部数字电影(续)
Movie, The (first digital movie) (cont.)
大数字融合和,406
Great Digital Convergence and, 406
约翰·拉塞特和, 412–414 , 421 , 424 , 425 , 428
John Lasseter and, 412–414, 421, 424, 425, 428
卢卡斯影业和407
Lucasfilm and, 407
和千禧年,456
and the millennium, 456
摩尔定律和, 372 , 417–419 , 425 , 428 , 455 , 456
Moore’s Law and, 372, 417–419, 425, 428, 455, 456
Bill Reeves and, 421, 424, 425
软件技术,417–419
software technology for, 417–419
用于制作的技术,401
techniques used in making, 401
三维人物模型,361
three-dimensional character models, 361
电影机, 182–183 , 190 , 204 , 226 , 450。另请参阅特定主题
Movie machine, 182–183, 190, 204, 226, 450. See also specific topics
差不多,176
almost, 176
terminology and use of the term, 176, 450
电影放映机。查看 投影仪
Movie projectors. See Projectors
电影)。另请参阅特定主题
Movie(s). See also specific topics
第一个数字,4
first digital, 4
框架作为样本,6
frame as sample, 6
6–7的历史
history of, 6–7
理想(见 理想电影)
ideal (see Ideal movie)
inside-the-pupil explanation, 182–183, 450, 460
真人与动画,6
live action vs. animated, 6
not invented by Edison, Muybridge, or Lumières, 165, 449
outside-the-pupil explanation, 450, 460
实时,443–445
real-time, 443–445
术语,176
terminology, 176
电影系统。查看 理想的电影系统
Movie system. See Ideal movie system
Mutograph, 197. See also Biograph projector
爱德华·迈布里奇 (Edward James Muggeridge), 166 , 166t , 191–192 , 220
Muybridge, Edward (Edward James Muggeridge), 166, 166t, 191–192, 220
别名, 166–167 , 166t , 169 , 173
aliases, 166–167, 166t, 169, 173
165、191、198、450的表征_ _ _ _ _
characterizations of, 165, 191, 198, 450
计时摄影,198
chronophotography practiced by, 198
Edison and, 165, 192, 193, 450
帧和, 170 , 171 , 198 , 217 , 220
frames and, 170, 171, 198, 217, 220
Étienne-Jules Marey and, 175, 198
电影/电影和, 165 , 166 , 169–170 , 172 , 175 , 192 , 449
movies/cinema and, 165, 166, 169–170, 172, 175, 192, 449
谋杀案审判,167
murder trial, 167
转描和,217
rotoscoping and, 217
Leland Stanford 和, 167 , 169 , 172–175 , 198
Leland Stanford and, 167, 169, 172–175, 198
动物运动镜,192
Zoöpraxiscope, 192
Napoleon Bonaparte, 7, 8, 11, 37, 38
born Nabolione Buonaparte, 21
雅克-路易·大卫 (Jacques-Louis David) 的画作, 2 , 8
Jacques-Louis David’s painting of, 2, 8
死亡,39
death, 39
37-39年被流放到圣赫勒拿
exiled to Saint Helena, 37–39
最后的百日力量,37-39
final Hundred Days of power, 37–39
傅立叶和, 35–37
Fourier and, 35–37
傅立叶被38 岁
Fourier fired by, 38
傅立叶被38 岁重新雇用
Fourier rehired by, 38
傅立叶的舞蹈,37-38
Fourier’s dance with, 37–38
作为傅立叶的暴君,7-8
as Fourier’s tyrant, 7–8
拿破仑定理,22
Napoleon’s Theorem, 22
美国国家航空航天局(美国国家航空航天局),327
NASA (National Aeronautics and Space Administration), 327
ARPA和254、307、314、454、455 _ _ _ _ _ _ _
ARPA and, 254, 307, 314, 454, 455
彩色图形和314、316、330 _ _
color graphics and, 314, 316, 330
GE 为314 , 316 , 319 , 320制造的飞行模拟器
flight simulators that GE built for, 314, 316, 319, 320
founding/creation of, 254, 454
资金来自,454
funding from, 454
喷气推进实验室 (JPL) 和314
Jet Propulsion Laboratory (JPL) and, 314
Manned Spacecraft Center in Houston, 316, 319
PARC 和455
PARC and, 455
Rod Rougelot 和, 320–322 , 331 , 334 , 339 , 455
Rod Rougelot and, 320–322, 331, 334, 339, 455
鲍勃·舒马克和318 , 320–322 , 331 , 334 , 339 , 455
Bob Schumacker and, 318, 320–322, 331, 334, 339, 455
鲍勃·泰勒 (Bob Taylor),电话:293 , 454
NASA-1, 316–318 , 320 , 321 , 331
NASA-1, 316–318, 320, 321, 331
NASA-1 simulator, 321, 338, 339
NASA-2, 309f , 320–322 , 331 , 343–345 , 357
NASA-2, 309f, 320–322, 331, 343–345, 357
国家艺术基金会 (NEA),355–356
National Endowment for the Arts (NEA), 355–356
纳粹德国, 85 , 97 , 253 , 300 , 307 , 344 , 451 , 454
Nazi Germany, 85, 97, 253, 300, 307, 344, 451, 454
谜码,378
Enigma code, 378
神经网络,464–465
Neural nets, 464–465
Nevzorov 姐妹(Zinaida、Sophia、Avgusta、Olga),62 岁
Nevzorov sisters (Zinaida, Sophia, Avgusta, Olga), 62
纽厄尔,马丁,244、246、274、351、369 _ _ _ _ _
Newell, Martin, 244, 246, 274, 351, 369
纽曼,林恩(麦克斯的妻子),103
Newman, Lyn (Max’s wife), 103
Newman, Max, 101, 103. See also Colossus
at Bletchley Park, 103, 104, 113
生活史和概述,103
life history and overview, 103
Princeton University and, 89, 101, 103, 133
图灵和, 87–89 , 98 , 101 , 103 , 104 , 132–134
Turing and, 87–89, 98, 101, 103, 104, 132–134
威廉姆斯管和,142
Williams tube and, 142
纽曼, 威廉 (Max 的儿子), 114 , 135 , 350
Newman, William (Max’s son), 114, 135, 350
纽曼 Laugh-O-grams,220
Newman Laugh-O-grams, 220
Newton, Isaac, 12, 42. See also Royal Society
牛顿物理学和中心法则,7 , 327 , 418 , 457 , 459
Newtonian physics and Central Dogma, 7, 327, 418, 457, 459
纽约理工学院 (NYIT), 261 , 330 , 455
New York Institute of Technology (NYIT), 261, 330, 455
Ed Catmull 和355 , 357 , 368 , 371 , 372 , 377 , 382 , 383 , 402 , 409 , 417
Ed Catmull and, 355, 357, 368, 371, 372, 377, 382, 383, 402, 409, 417
cel动画和,219
cel animation and, 219
Computer Graphics Lab, 219, 278
大卫·迪弗朗西斯科和, 355 , 375 , 379 , 383 , 402
David DiFrancesco and, 355, 375, 379, 383, 402
拉尔夫·古根海姆( Ralph Guggenheim ) ,电话:374、381、382、433
Ralph Guggenheim at, 374, 381, 382, 433
卢卡斯影业的秘密旅行,381–384
Lucasfilm’s secret trip to, 381–384
NEA(国家艺术基金会)和355–356
NEA (National Endowment for the Arts) and, 355–356
马丁纽厄尔和,351
Martin Newell and, 351
亚历克斯·舒尔和219、352、354、355、363、374、378、383、385、402、417、455、456
Alex Schure and, 219, 352, 354, 355, 363, 374, 378, 383, 385, 402, 417, 455, 456
阿尔维·雷·史密斯和,352
Alvy Ray Smith and, 352
加兰斯特恩电话:359、361–363、369、376、377 _ _ _ _ _
Garland Stern at, 359, 361–363, 369, 376, 377
NKS。见 人民通讯委员会
NKS. See People’s Commissariat for Communications
NKVD(内务人民委员部),61
NKVD (People’s Commissariat for Internal Affairs), 61
作为克格勃的前身,61
as predecessor of KGB, 61
Nuclear weapons. See Atomic bomb; Hydrogen bomb
奈奎斯特, 哈里, 45–46 , 52 , 445–446
Nyquist, Harry, 45–46, 52, 445–446
奈奎斯特-香农采样定理。参见 采样定理
Nyquist–Shannon Sampling Theorem. See Sampling Theorem
官方保密法,艾伦·图灵和,78–80 , 120–121 , 446 , 451
Official Secrets Act, Alan Turing and, 78–80, 120–121, 446, 451
“关于可计算数,应用于Entsheidungsproblem ”(Turing,1936),89 , 100
“On Computable Numbers, with an Application to the Entsheidungsproblem” (Turing, 1936), 89, 100
阿朗佐教堂和88
Alonzo Church and, 88
computation and, 89, 107, 127, 438
programs, programming, and, 89, 107
存储程序计算机和107 , 117 , 127 , 447 , 451
stored-program computer and, 107, 117, 127, 447, 451
通用图灵机,96
universal Turing machine, 96
Kotelnikov 和 Shannon 证明的可靠性,65
reliability proved by Kotelnikov and by Shannon, 65
Claude Shannon and, 65, 101, 103
由 Amtorg 使用,65
used by Amtorg, 65
奥本海默,J.罗伯特,73 岁
Oppenheimer, J. Robert, 73
ORDVAC(军械离散变量自动计算机),157
ORDVAC (Ordnance Discrete Variable Automatic Computer), 157
奥斯比,埃本,402
Ostby, Eben, 402
Out of the Inkwell(电影系列),218–219
Out of the Inkwell (film series), 218–219
Pacific Data Images (PDI), 409, 456
产生梦工厂和Antz , 430–431
begets DreamWorks and Antz, 430–431
艾尔帕西诺,462
Pacino, Al, 462
油漆3、364、372、377、385、417 _ _ _ _ _ _ _ _
Paint3, 364, 372, 377, 385, 417
framebuffers and, 364, 385, 417
帕莱,约瑟夫,13 岁
Pallais, Joseph, 13
天堂岛。见 沙拉什卡
Paradise island. See Sharashka
PARC(帕洛阿尔托研究中心),258-259,455。另请参阅施乐 PARC
PARC (Palo Alto Research Center), 258–259, 455. See also Xerox PARC
断腿导致,344
a broken leg leads to, 344
中心教条和,355
Central Dogma and, 355
彩色视频系统和,343
Color Video System and, 343
大卫·迪弗朗西斯科和,356
David DiFrancesco and, 356
纽约理工学院 (NYIT) 和330
New York Institute of Technology (NYIT) and, 330
Particle systems, 402–404, 414
Patches and patchlets, 265, 266
p曲线,299
p-curves, 299
PDI。查看 太平洋数据图像
PDI. See Pacific Data Images
像素与像素,51–52
Pel vs. pixel, 51–52
人民通讯委员会(NKS),47-48
People’s Commissariat for Communications (NKS), 47–48
解散,除了科捷尔尼科夫的实验室,62
disbanded, except for Kotelnikov’s lab, 62
Pére Lachaise 公墓,39–40
Pére Lachaise Cemetery, 39–40
看法
Perspective
威廉费特和,281–284
William Fetter and, 281–284
拉里·罗伯茨和, 281 , 284 , 290 , 305 , 410
Larry Roberts and, 281, 284, 290, 305, 410
爱德华·扎雅克和,283–284
Edward Zajac and, 283–284
透视视口。见 视口
Perspective viewport. See Viewport
佩西,乔,462
Pesci, Joe, 462
彼得大帝,46 岁
Peter the Great, 46
Phantascope, 196, 197. See also Vitascope
Phong 阴影,342
Phong shading, 342
Photoshop (Adobe), 60 , 61 , 61f , 261 , 262
Photoshop (Adobe), 60, 61, 61f, 261, 262
Alpha 通道和368
alpha channel and, 368
painting metaphor in, 347, 348
钢笔工具, 272
pen tool, 272
像素和, 58 , 60 , 105 , 241 , 459 , 464
pixels and, 58, 60, 105, 241, 459, 464
图片
Picture
和显示,分离,2
and display, separation of, 2
与中等,2
vs. medium, 2
面向图片的计算机图形学,443
Picture-oriented computer graphics, 443
图片与中等,2
Picture vs. medium, 2
飞行员王牌, 132 , 142 , 143 , 148 , 152 , 447
Pilot Ace, 132, 142, 143, 148, 152, 447
皮特,布拉德,461
Pitt, Brad, 461
animation and, 359, 417–418 (see also Pixar animators)
分娩痛,421–422
birth pangs, 421–422
大写字母和219、424、450 _ _
Ed Catmull 和219 , 240 , 355 , 374 , 421 , 429 , 431 , 433 , 460
Ed Catmull and, 219, 240, 355, 374, 421, 429, 431, 433, 460
中心教条和,417–418
Central Dogma and, 417–418
Disney’s purchase of, 219, 223, 429, 433
Disney’s relationship with, 359, 424, 428, 429
理查德·德莱福斯和,460–461
Richard Dreyfuss and, 460–461
财务, 421–423 , 425 , 428 , 429 , 433
finances, 421–423, 425, 428, 429, 433
大数字融合,432
Great Digital Convergence and, 432
Ralph Guggenheim and, 374, 433
hardware, 425 (see also Pixar Image Computer)
史蒂夫乔布斯和, 423 , 425 , 429 , 433 , 456–457
Steve Jobs and, 423, 425, 429, 433, 456–457
约翰·拉塞特和, 226 , 407 , 413 , 414 , 421 , 424 , 425 , 433
John Lasseter and, 226, 407, 413, 414, 421, 424, 425, 433
卢卡斯影业和, 219 , 330 , 373–374 , 416 , 423 , 425 , 427 , 429 , 456
Lucasfilm and, 219, 330, 373–374, 416, 423, 425, 427, 429, 456
卢卡斯影业诞生,419–423
Lucasfilm begets, 419–423
组织文化, 416
organizational culture, 416
278 , 348 , 355 , 402 , 406 , 411 , 423 , 430 , 455 , 456的起源和共同创立
origin and cofounding of, 278, 348, 355, 402, 406, 411, 423, 430, 455, 456
由 Ed Catmull 和 Alvy Ray Smith 共同创立,219 , 240 , 374 , 431
cofounded by Ed Catmull and Alvy Ray Smith, 219, 240, 374, 431
founding employees, 355, 374, 402
不是由史蒂夫乔布斯共同创立的,433
not cofounded by Steve Jobs, 433
RenderMan、Reyes 和425–427
RenderMan, Reyes, and, 425–427
亚历克斯舒尔和,433
Alex Schure and, 433
阿尔维·雷·史密斯 (Alvy Ray Smith) 离开,428
Alvy Ray Smith’s departure from, 428
子样本位置,326
subsample locations, 326
玩具总动员和, 4 , 93 , 243 , 252 , 406 , 407 , 429 , 433 , 456
Toy Story and, 4, 93, 243, 252, 406, 407, 429, 433, 456
皮克斯动画师,172、210、461 _
Pixar animators, 172, 210, 461
皮克斯图像计算机, 386 , 420 , 421 , 423 , 424
Pixar Image Computer, 386, 420, 421, 423, 424
类似皮克斯的电影,242–245
Pixar-like movies, 242–245
皮克斯电影,281、290、429、430、444 。_ _ _ _ _ _ 另见电影,The ; 玩具总动员
Pixar movies, 281, 290, 429, 430, 444. See also Movie, The; Toy Story
短裤,424
shorts, 424
“Pixar,” origin/etymology of the term, 386, 421
Pixar Touch: The Making of a Company, The (Price), 374
Pixar Touch: The Making of a Company, The (Price), 374
像素)
Pixel(s)
16位灰度就够了,69
16 bits is enough for grayscale, 69
双三次像素散布器,57-58
a bicubic pixel spreader, 57–58
位和,2
bits and, 2
特征, 51
characteristics, 51
and computer born together, 6, 163
定义, 51
defined, 51
与显示元素,4
vs. display element, 4
display elements and, 2, 4, 436
没有形状,5
has no shape, 5
隐形, 2 , 4 , 5 , 63 , 74 , 311 , 436
invisible, 2, 4, 5, 63, 74, 311, 436
是一个数字化样本,68
is a digitized sample, 68
不是正方形,5
is not a square, 5
必须传播它才能看到它,60
must spread it to see it, 60
notion of and characteristics of, 436, 437
只有散布像素有形状,60
only spread pixels have shape, 60
organizing principle of Digital Light, 4, 5
术语的由来,51
origin of the term, 51
与 pel,51–52
vs. pel, 51–52
像素化是一种误解,51
pixelation is a misconception, 51
小方块错觉之源,60
source of the little square illusion, 60
术语,51-52
terminology, 51–52
universal medium and, 2, 436, 437
视觉样本,5
the visual sample, 5
像素化,51
Pixelation, 51
像素扩展器,57–60 , 138 , 180。另见 撒布机;散布像素
Pixel spreader, 57–60, 138, 180. See also Spreader(s); Spread pixels
数码灯和,63
Digital Light and, 63
理想,180
ideal, 180
Point of view, 234–237, 240, 453
像素和,31
pixels and, 31
Poisson, Simeon Denis, 36, 37, 40
托马斯·波特(“汤姆”),398f , 400f , 404 , 409 , 418
Porter, Thomas (“Tom”), 398f, 400f, 404, 409, 418
卢卡斯影业和, 231 , 241 , 368 , 385 , 399 , 403
Lucasfilm and, 231, 241, 368, 385, 399, 403
as part of The Proletariat, 399, 401, 418
RGBA 绘画程序,385
RGBA paint program, 385
Ravi Shankar and, 231, 241, 385
阿尔维·雷·史密斯 (Alvy Ray Smith) 和, 385 , 401
splines and, 231, 232, 241, 385
价格,大卫,374
Price, David, 374
John von Neumann at, 89 , 97–98 , 101 , 108 , 135 , 136(另见 Von Neumann 团队)
John von Neumann at, 89, 97–98, 101, 108, 135, 136 (see also Von Neumann team)
digital optical, 384, 385, 420
投影灯,180
Projector light, 180
投影仪,176、183、197、203、204。_ _ _ _ _ _ 另见电影摄影;幻灯
Projectors, 176, 183, 197, 203, 204. See also Cinématographe; Magic lantern
WKL 迪克森和, 192 , 195 , 196 , 204 , 451
W.K.L. Dickson and, 192, 195, 196, 204, 451
数字, 176
digital, 176
爱迪生、迪克森和, 192 , 195–197 , 204 , 451
Edison, Dickson, and, 192, 195–197, 204, 451
帧和, 180–183
frames and, 180–183
它们是如何工作的,183
how they work, 183
理想,180–182
ideal, 180–182
Athanasius Kircher 和,170
Athanasius Kircher and, 170
电影机,450
movie machines as, 450
Year of the Projector (1895), 190, 195, 198
Proletariat, The (Cook, Carpenter, and Porter), 399 , 401 , 418
Proletariat, The (Cook, Carpenter, and Porter), 399, 401, 418
普京, 弗拉基米尔, 43 , 75 , 466 , 466f
Putin, Vladimir, 43, 75, 466, 466f
Quickening, 120. See also Moore’s Law speedup
R-1(导弹)
R-1 (missile)
作为俄罗斯版的德国 V-2, 68
as Russian version of German V-2, 68
使用 MEI-Kotelnikov 无线电系统,68
used MEI-Kotelnikov radio system, 68
R-7(导弹)
R-7 (missile)
作为第一个俄罗斯洲际导弹,68
as first Russian ICBM, 68
使用 MEI-Kotelnikov 遥测系统,68
used MEI-Kotelnikov telemetry system, 68
拉贝,赫伯特,45 岁
Raabe, Herbert, 45
雷达,386
Radar, 386
光栅显示,277
Raster displays, 277
扩展像素和, 139 , 141 , 247–248 , 278
spread pixels and, 139, 141, 247–248, 278
RCA Laboratories (RCA Labs), 149, 447
实时计算机图形/实时渲染。请参阅 交互式渲染的计算机图形
Real-time computer graphics/real-time rendering. See Interactively rendered computer graphics
“实时”,该术语的含义,259–260
“Real time,” meanings of the term, 259–260
Reconstruction filter, 44. See also Spreader(s)
Reeves , William T.(“比尔”),402、403、406
Reeves, William T. (“Bill”), 402, 403, 406
约翰·拉塞特和, 416 , 421 , 424 , 425 , 428
John Lasseter and, 416, 421, 424, 425, 428
particle systems and, 402–404, 414
相对论,爱因斯坦的广义理论,12
Relativity, Einstein’s general theory of, 12
渲染人,425–427
RenderMan, 425–427
雷耶斯渲染,425–427
Reyes rendering, 425–427
RGBA,放大,385–386
RGBA, amplifying, 385–386
RGBA漆,385
RGBA paint, 385
RGBA画图程序,第一,385
RGBA paint program, first, 385
RGBA 像素,365–367
RGBA pixels, 365–367
RGB 滑块,345
RGB sliders, 345
罗伯茨,劳伦斯·吉尔曼(“拉里” ),276、291-292、327-328 。又见三驾马车
Roberts, Lawrence Gilman (“Larry”), 276, 291–292, 327–328. See also Triumvirate
ARPA、IPTO 和294
ARPA, IPTO, and, 294
Central Dogma and, 281, 327–328, 457
蒂姆·约翰逊和, 276 , 279 , 281 , 284 , 290–292
Tim Johnson and, 276, 279, 281, 284, 290–292
透视和, 281 , 284 , 290 , 305 , 410
perspective and, 281, 284, 290, 305, 410
294人担任的职位
positions held by, 294
作为文艺复兴时期的人,291–293
as renaissance man, 291–293
画板III和276、279、292、457 _ _ _ _
Sketchpad III and, 276, 279, 292, 457
Ivan Sutherland and, 290–292, 305, 454
Triumvirate and, 276, 276f, 410
罗森达尔,卡尔,409
Rosendahl, Carl, 409
Rougelot, Rodney S.(“罗德”)
Rougelot, Rodney S. (“Rod”)
颜色像素和321 , 331 , 344 , 357 , 455
color pixels and, 321, 331, 344, 357, 455
color renderings and, 322, 334, 455
计算机辅助运筹学设施 (CAORF) 和357
Computer Aided Operations Research Facility (CAORF) and, 357
在康奈尔大学,320–321
at Cornell University, 320–321
在埃文斯和萨瑟兰,321
at Evans & Sutherland, 321
由321创建的飞行模拟器
flight simulators created by, 321
唐·格林伯格和, 320–321 , 331 , 334 , 374 , 455
Don Greenberg and, 320–321, 331, 334, 374, 455
NASA - 1和320、331、339 _
鲍勃·舒马克和321 , 322 , 331 , 334 , 339 , 344 , 357 , 455
Bob Schumacker and, 321, 322, 331, 334, 339, 344, 357, 455
three-dimensional renderings and, 322, 331, 334
卢梭,让-雅克,13 岁
Rousseau, Jean-Jacques, 13
皇家学会, 39 , 77 , 122 , 174 , 234
Royal Society, 39, 77, 122, 174, 234
鲁宾,迈克尔,373–374
Rubin, Michael, 373–374
俄罗斯科学院,46
Russian Academy of Sciences, 46
俄罗斯内战,47
Russian Civil War, 47
Sage (计算机), 256–257 , 261 , 289
Sage (computer), 256–257, 261, 289
萨哈罗夫,安德烈·德米特里耶维奇,72岁
Sakharov, Andrei Dmitrievich, 72
样本与像素,318
Sample vs. pixel, 318
采样,历史,5
Sampling, history of, 5
high frequencies and, 71–72, 187, 326
采样定理,43。另见 Shannon, Claude Elwood
Sampling Theorem, 43. See also under Shannon, Claude Elwood
模拟与数字和, 44 , 49 , 50–51 , 59 , 64 , 74
analog vs. digital and, 44, 49, 50–51, 59, 64, 74
抗锯齿和161–163
antialiasing and, 161–163
索赔人,43
claimants, 43
取决于傅立叶, 5 , 74 , 235 , 438 , 445
depends on Fourier, 5, 74, 235, 438, 445
首次亮相(1933 年),45
first appearance (1933), 45
Kotelnikov,不是奈奎斯特,445–446
by Kotelnikov, not Nyquist, 445–446
Kotelnikov,不是香农,43 , 52–53 , 75 , 445–446
by Kotelnikov, not Shannon, 43, 52–53, 75, 445–446
数学奇迹,437
mathematical miracle, 437
不是真的什么都没有,59
not really something for nothing, 59
像素分布和添加每,76
pixels spread and added per, 76
1933 年被 Kotelnikov 证明,5 , 53 , 98 , 105 , 158 , 437
proved 1933 by Kotelnikov, 5, 53, 98, 105, 158, 437
恢复、扩展像素并添加,55
to recover, spread pixels and add, 55
重新包装无限,59
repackages infinity, 59
反过来(惠特克),306
in reverse (Whittaker), 306
以最高频率的两倍采样,50–51
sample at twice the highest frequency, 50–51
样本是离散的、不连贯的、分离的、50–51
samples are discrete, disjointed, separated, 50–51
sampling artifacts and, 72, 326
something from nothing, 47, 50, 55, 64
扫描,349
Scanimate, 349
辛德勒的名单(电影),300
Schindler’s List (film), 300
施赖伯,威廉,52 岁
Schreiber, William, 52
Schumacker, Robert A. (“Bob”), 321–322 , 455
Schumacker, Robert A. (“Bob”), 321–322, 455
Ed Catmull 和,357
Ed Catmull and, 357
color pixels and, 321–322, 344
color renderings and, 322, 331
计算机辅助运筹学设施 (CAORF) 和357
Computer Aided Operations Research Facility (CAORF) and, 357
教育, 321
education, 321
在 Evans & Sutherland (E&S), 321 , 357
at Evans & Sutherland (E&S), 321, 357
由321创建的飞行模拟器
flight simulators created by, 321
在通用电气,318、321、322、331、357、455 _ _ _ _ _ _ _
at GE, 318, 321, 322, 331, 357, 455
NASA - 1和318、321、331、339 _ _ _
NASA-1 and, 318, 321, 331, 339
NASA-2 和320–322
NASA-2 and, 320–322
罗德·鲁格洛和,321 , 322 , 331 , 334 , 339 , 344 , 357 , 455
Rod Rougelot and, 321, 322, 331, 334, 339, 344, 357, 455
Alvy Ray Smith and, 318, 320–322
three-dimensional renderings and, 321, 322, 331, 334
亚历山大·舒尔(“亚历克斯叔叔”),381
Schure, Alexander (“Uncle Alex”), 381
Alpha 通道和363
alpha channel and, 363
Ed Catmull 和, 219 , 354 , 355 , 378 , 379 , 402
Ed Catmull and, 219, 354, 355, 378, 379, 402
351的表征
characterizations of, 351
计算机图形学和353–354
computer graphics and, 353–354
康奈尔大学,374
Cornell University and, 374
埃文斯和萨瑟兰 (E&S) 和353–355
Evans & Sutherland (E&S) and, 353–355
finances, 351–354, 363, 374, 378
framebuffers and, 351, 363, 364, 374
约翰尼根特和,219
Johnny Gent and, 219
纽约理工大学和219、352、354、355、363、374、378、383、385、402、417、455、456 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _
NYIT and, 219, 352, 354, 355, 363, 374, 378, 383, 385, 402, 417, 455, 456
绘画程序和385
paint programs and, 385
personality, 351, 378, 383, 402
照片,352f
photograph of, 352f
皮克斯和,433
Pixar and, 433
光栅图形和351–354
raster graphics and, 351–354
阿尔维·雷·史密斯和, 219 , 351 , 363 , 378 , 379 , 383 , 385
Alvy Ray Smith and, 219, 351, 363, 378, 379, 383, 385
Tubby the Tuba和219 , 353 , 354 , 417 , 456
Tubby the Tuba and, 219, 353, 354, 417, 456
Scientific American (magazine), 334, 461
半自动地面环境。见 鼠尾草
Semi-Automatic Ground Environment. See Sage
麻省理工学院伺服机构实验室 (Servo Lab), 253 , 262
Servomechanism Lab (Servo Lab) at MIT, 253, 262
作为概念上的飞跃,388–390
as a conceptual leap, 388–390
RenderMan, 425–427
RenderMan’s, 425–427
术语, 427
terminology, 427
尚卡尔,拉维
Shankar, Ravi
描述和概述,231
description and overview, 231
香卡,拉维(续)
Shankar, Ravi (cont.)
Alvy Ray Smith 的样条演示,用于231–234 , 236–238 , 240 , 241 , 243 , 265 , 272 , 306 , 307 , 348 , 385
Alvy Ray Smith’s spline demo for, 231–234, 236–238, 240, 241, 243, 265, 272, 306, 307, 348, 385
Shannon, Claude Elwood, 43, 45, 46
分析了二战中的 X 系统,53
analyzed the X System in WWII, 53
背景和早年生活,53
background and early life, 53
出生于密歇根州,53 岁
born in Michigan, 53
characterizations of, 45, 46, 104
密码学和53
cryptography and, 53
没有提到科捷利尼科夫,53
didn’t mention Kotelnikov, 53
第一个在打印中使用字位, 45
first to use the word bit in print, 45
Kotelnikov 和, 53 , 54 , 54f , 75–76 , 101 , 235 , 445
Kotelnikov and, 53, 54, 54f, 75–76, 101, 235, 445
密码大师,53 岁
master cryptographer, 53
在麻省理工学院,254
at MIT, 254
从未声称过采样定理,43 , 53 , 75 , 445–446
never claimed Sampling Theorem, 43, 53, 75, 445–446
哈里奈奎斯特和,45–46
Harry Nyquist and, 45–46
one-time pad and, 65, 101, 103
与科捷利尼科夫的成就相似,54
parallels Kotelnikov’s achievements, 54
作为一个顽皮的天才,53
as a playful genius, 53
采样定理和,53-54
Sampling Theorem and, 53–54
Sampling Theorem attributed to, 43, 52, 445
158推广的采样定理
Sampling Theorem popularized by, 158
Sampling Theorem re-proved by, 52–53, 235
Sampling Theorem stated/taught by, 52, 75, 105
传播理论,53
theory of communication, 53
图灵和, 77–78 , 104 , 111 , 152 , 158
Turing and, 77–78, 104, 111, 152, 158
图灵机和,111
Turing machine and, 111
语音加扰器和104
voice scramblers and, 104
获得最高奖项,54
won top awards, 54
著作,52-53
writings, 52–53
沙拉什卡,43 岁,66-68岁。另请参阅 Marfino sharashka
Sharashka, 43, 66–68. See also Marfino sharashka
Shesternin, Sergei (Sophia Nevzorova 的丈夫), 62
Shesternin, Sergei (Sophia Nevzorova’s husband), 62
小学馆, 416
Shogakukan, 416
Shoup, Richard G. (“迪克”), 248 , 343–345
Shoup, Richard G. (“Dick”), 248, 343–345
电脑鼠标和, 347
computer mice and, 347
David DiFrancesco and, 349, 350
第一次完全抗锯齿,162
first full antialiasing, 162
阿尔维·雷·史密斯( Alvy Ray Smith )和344、350、363、378
Alvy Ray Smith and, 344, 350, 363, 378
SuperPaint, 345, 348, 349, 363
马车车轮图片,162
wagon wheel pictures, 162
Xerox PARC and, 343, 344, 350, 363, 403
Siggraph (计算机图形和交互技术特别兴趣小组)会议,305、394、400、415。又见浣熊奖
Siggraph (Special Interest Group on Computer Graphics and Interactive Techniques) conference, 305, 394, 400, 415. See also Coons Award
André & Wally B. and, 414 , 415
André & Wally B. and, 414, 415
吉姆·布林,370
Jim Blinn and, 370
Loren Carpenter、Ed Catmull 和386
Loren Carpenter, Ed Catmull, and, 386
成立, 267
founding of, 267
伯特·赫尔佐格和,267
Bert Herzog and, 267
比尔·里夫斯和,402
Bill Reeves and, 402
Alvy Ray Smith and, 386, 413, 460
动画和294–295
animation and, 294–295
史蒂夫库恩斯和,285
Steve Coons and, 285
电影演示,289
film demos of, 289
通用汽车和285
GM and, 285
图形显示,285
graphic display, 285
in historical context, 275, 285
交互式渲染的 2D 计算机图形,287–289
interactively rendered 2D computer graphics, 287–289
伊万·萨瑟兰和, 261 , 275–277 , 284–290 , 294–295 , 453–454
Ivan Sutherland and, 261, 275–277, 284–290, 294–295, 453–454
Tim Johnson 经常与 Sutherland 混淆,275 , 290
Tim Johnson often confused with Sutherland, 275, 290
TX - 2和284、287–289
Sketchpad III (3D version of Sketchpad), 292, 294
中心教条和305
Central Dogma and, 305
DAC - 1和285–286、454
交互式渲染 3D 计算机图形,287–289
interactively rendered 3D computer graphics, 287–289
蒂姆·约翰逊和, 275–276 , 279 , 290–292 , 454 , 457
Tim Johnson and, 275–276, 279, 290–292, 454, 457
拉里·罗伯茨和, 276 , 279 , 292 , 457
Larry Roberts and, 276, 279, 292, 457
史密斯,林恩,299
Smith, Lynn, 299
SoftCel(“扫描和绘制”系统),362
SoftCel (“scan-and-paint” system), 362
索尔仁尼琴,亚历山大,43 岁
Solzhenitsyn, Aleksandr, 43
在 sharashkas 上,66
on sharashkas, 66
染谷功,45岁
Someya, Isao, 45
声音样本。见 索克塞尔
Sound sample. See Soxel(s)
前苏联。见莫斯科
Soviet Union. See Moscow
关于足够位数的争论,69-70
argument about sufficient bit count, 69–70
定义, 52
defined, 52
数字声音和,63
Digital Sound and, 63
词源,52
etymology of the term, 52
必须传播它才能听到它,63
must spread it to hear it, 63
像素和, 55 , 57 , 59 , 105 , 165 , 166 , 235
pixels and, 55, 57, 59, 105, 165, 166, 235
spreading and adding soxels, 57, 59
太空战争(游戏), 257–259 , 261 , 299 , 343
Spacewar (game), 257–259, 261, 299, 343
Speedup. See Moore’s Law speedup; Quickening
样条,239f
Spline(s), 239f
Loren Carpenter 的多维,405
Loren Carpenter’s multidimensional, 405
computer graphics and, 240, 307
曲线和, 232 , 237–238 , 240 , 242 , 243 , 265 , 272 , 274
curves and, 232, 237–238, 240, 242, 243, 265, 272, 274
数码灯和,239
Digital Light and, 239
geometry and, 241, 243, 306, 348
插值、近似和231 , 234 , 240 , 265 , 272 , 274 , 306–307 , 342
interpolation, approximation, and, 231, 234, 240, 265, 272, 274, 306–307, 342
隐形, 241
invisible, 241
overview and nature of, 231–234, 453
它通过的点, 232–234 , 238–239 , 239f , 272 , 274 , 306
points through which it passes, 232–234, 238–239, 239f, 272, 274, 306
Tom Porter and, 231, 232, 241, 385
在实践中,239–240
in practice, 239–240
Sampling Theorem and, 234, 306, 453
Ravi Shankar 的样条演示, 231–234 , 236–238 , 240 , 241 , 243 , 265 , 272 , 306 , 307 , 348 , 385
spline demo for Ravi Shankar, 231–234, 236–238, 240, 241, 243, 265, 272, 306, 307, 348, 385
spreaders and, 239–240, 272, 399
点和散布像素,122 , 137 , 139 , 145 , 148
Spots and spread pixels, 122, 137, 139, 145, 148
吊具,44–46
Spreader(s), 44–46
在展示行为中,63
in act of display, 63
一团无穷大,59
a blob of infinity, 59
最早的照片,44-45
earliest picture of, 44–45
理想, 56 , 58 , 59 , 63 , 180 , 235 , 239–240
ideal, 56, 58, 59, 63, 180, 235, 239–240
是模拟的,59
is analog, 59
现实世界与理想世界,56
real-world vs ideal, 56
作为工程师的重建滤波器,44
as reconstruction filter to engineers, 44
数学家的 sinc 函数,44
sinc function to mathematicians, 44
Spread pixels, 59–61. See also Pixel spreader
Bresenham 算法和247–248
Bresenham’s algorithm and, 247–248
书法展示,书法设备,以及,139 , 141 , 148 , 247 , 278
calligraphic displays, calligraphic devices, and, 139, 141, 148, 247, 278
60 , 64 , 122 , 143 , 436的特征和性质
characteristics and nature of, 60, 64, 122, 143, 436
彩色像素和311
color pixels and, 311
display elements and, 64, 297, 311, 436
First Light(第一张数码照片)、Kilburn和118、122
First Light (first digital picture), Kilburn, and, 118, 122
几何模型和, 241 , 242 , 245 , 246 , 256
geometric models and, 241, 242, 245, 246, 256
扩展像素(续)
Spread pixels (cont.)
肯·诺尔顿和,296–297
Ken Knowlton and, 296–297
光枪和,145
light gun and, 145
光栅动画和,156
raster animation and, 156
光栅显示和, 139 , 141 , 247–248 , 278
raster displays and, 139, 141, 247–248, 278
Sampling Theorem and, 139, 141
点和, 122 , 137 , 139 , 145 , 148
spots and, 122, 137, 139, 145, 148
Sproull,罗伯特(“鲍勃”),321
Sproull, Robert (“Bob”), 321
壁球和拉伸,213–216
Squash and stretch, 213–216
216-217年阿尔维·雷·史密斯 (Alvy Ray Smith) 的洗礼
Alvy Ray Smith’s baptism in, 216–217
圣彼得堡科学院,46
St. Petersburg Academy of Sciences, 46
Stalin, Joseph, 43. See also Great Terror/Great Purge
在第一圈,67
in In the First Circle, 67
马林科夫、贝利亚和61–62
Malenkov, Beria, and, 61–62
偏执狂,要求声码器,67
paranoia of, demanding vocoder, 67
秘密清洗,61
the Secret Purge, 61
斯坦福,利兰,166
Stanford, Leland, 166
农场,169
The Farm, 169
财务,175
finances, 175
艾蒂安-朱尔斯·马雷和,198
Étienne-Jules Marey and, 198
爱德华·迈布里奇和, 167 , 169 , 172–175 , 198
Edward Muybridge and, 167, 169, 172–175, 198
trotters (horses) and, 167, 169
Stanford Research Institute, 255, 293, 294
斯坦福大学, 167 , 169 , 254 , 382 , 384 , 465
Stanford University, 167, 169, 254, 382, 384, 465
阿尔维·雷·史密斯 (Alvy Ray Smith) 在, 42 , 45 , 262 , 344 , 465
Alvy Ray Smith at, 42, 45, 262, 344, 465
星际迷航 II:可汗之怒(电影),403–406。另见 创世纪演示
Star Trek II: The Wrath of Khan (film), 403–406. See also Genesis Demo
星球大战 (电影), 381 , 382 , 384 , 411 , 415 , 456
Star Wars (film), 381, 382, 384, 411, 415, 456
立体视觉,242、260、305、432、458。_ _ _ _ _ _ 另见头戴式显示器
Stereoscopy, 242, 260, 305, 432, 458. See also Head-mounted display
动画和, 359 , 361–362 , 376 , 377
animation and, 359, 361–362, 376, 377
在纽约理工大学,359 , 361–363 , 369 , 376 , 377
at NYIT, 359, 361–363, 369, 376, 377
paint programs and, 361–363, 377
Unix 和373
Unix and, 373
斯蒂格勒的同名法,45
Stigler’s Law of Eponymy, 45
臭味与塔。参见 Tower vs. stinks
Stinks vs. tower. See Tower vs. stinks
斯托克汉姆,托马斯(“汤姆”),162–163 , 259 , 359
Stockham, Thomas (“Tom”), 162–163, 259, 359
Stored-program computers, universal, 440, 447
Strachey, 克里斯托弗, 113 , 152 , 287
Strachey, Christopher, 113, 152, 287
子像素,325
Subpixels, 325
子样本,325
Subsamples, 325
帧缓冲区和343–348
framebuffers and, 343–348
萨瑟兰,伊万·爱德华,278、296、305、306、354、453、454。_ _ _ _ _ _ _ 另见头戴式显示器;三驾马车
Sutherland, Ivan Edward, 278, 296, 305, 306, 354, 453, 454. See also Head-mounted display; Triumvirate
成就,284–289
accomplishments, 284–289
动画和294–295
animation and, 294–295
ARPA和294、296、355、454 _ _ _ _ _
增强现实 (AR) 和305
augmented reality (AR) and, 305
奖项, 269
awards, 269
以及虚拟现实 (VR) 的诞生,304–305、306f(另见 头戴式显示器)
and the birth of virtual reality (VR), 304–305, 306f (see also Head-mounted display)
Bresenham 算法求解,289
Bresenham’s algorithm solved by, 289
关于漫画方法,295
on cartooning methods, 295
计算机辅助设计 (CAD) 和285 , 289 , 294
computer-aided design (CAD) and, 285, 289, 294
史蒂文·库恩斯和, 263 , 265 , 269 , 276 , 284 , 285
Steven Coons and, 263, 265, 269, 276, 284, 285
描述, 284
description of, 284
David Evans and, 261 , 278 , 294 , 296 , 454(另见Evans & Sutherland)
David Evans and, 261, 278, 294, 296, 454 (see also Evans & Sutherland)
闪烁和, 278
flickering and, 278
head-mounted display, 305, 334, 377, 457
integrated circuit chips and, 305, 306
interactively rendered computer graphics and, 287, 289
IPTO 和294
IPTO and, 294
蒂姆·约翰逊和, 263 , 275 , 285 , 289–291 , 294
Tim Johnson and, 263, 275, 285, 289–291, 294
摩尔定律和,306
Moore’s Law and, 306
290张照片
photographs of, 290
Larry Roberts and, 290–292, 305, 454
画板和, 261 , 275–277 , 284–290 , 294–295 , 453–454
Sketchpad and, 261, 275–277, 284–290, 294–295, 453–454
1963 年写生论文,294-295
1963 Sketchpad thesis, 294–295
阿尔维·雷·史密斯和, 284 , 289 , 305 , 321 , 354
Alvy Ray Smith and, 284, 289, 305, 321, 354
TX - 2和277、284–285、287–289、299 _ _ _
TX-2 and, 277, 284–285, 287–289, 299
on the ultimate display, 304, 305
犹他大学和, 117 , 261 , 294 , 296 , 454
University of Utah and, 117, 261, 294, 296, 454
Taylor, Robert “Bob,” 293–294, 350
ARPA、IPTO 和294
ARPA, IPTO, and, 294
纽约理工大学和355
NYIT and, 355
阿尔维·雷·史密斯和,294
Alvy Ray Smith and, 294
施乐PARC和294、343、355、454 _ _ _ _
Xerox PARC and, 294, 343, 355, 454
Teapot, classic, 244–246, 244f, 261
computer graphics and, 244, 266
Martin Newell’s, 244–246, 274, 351
照片,244f
photograph of, 244f
triangles and, 245–247, 266, 335
在自由卷, 386
in Vol Libre, 386
Teapot shards as display elements, 297, 297f
电传打字机,160
Teleprinter, 160
电传艺术时代,161
Teletype art era, 161
电传图片,160–161
Teletype pictures, 160–161
电传打字机,160
Teletypewriter, 160
电视,186
Television, 186
特曼,弗雷德里克,254
Terman, Frederick, 254
35 毫米电影胶片, 196 , 201 , 203 , 384
35 mm movie film, 196, 201, 203, 384
W.K.L. Dickson and, 196, 201, 451
Three-dimensional systems. See Design Augmented by Computers; Sketchpad III
三维 (3D) 查看器。见 立体镜
Three-dimensional (3D) viewers. See Stereoscopy
倾斜刷(谷歌),459
Tilt Brush (Google), 459
托尔斯泰,狮子座,165
Tolstoy, Leo, 165
作为喀山大学的学生,46 岁
as student at University of Kazan, 46
塔与臭味,8 , 88 , 126 , 132 , 133 , 175 , 202 , 225–226 , 461
Tower vs. stinks, 8, 88, 126, 132, 133, 175, 202, 225–226, 461
宝贝和,133
Baby and, 133
赫伯弗里曼和,344
Herb Freeman and, 344
ideal/concept vs. actual/engineering and, 132, 175, 226
王子学院和, 135–136
Princetitute and, 135–136
技术上与艺术创意的人,8
technically vs. artistically creative people and, 8
约翰·冯·诺依曼和,136
John von Neumann and, 136
玩具总动员(电影), 4 , 6–7 , 252 , 429。另见 电影,
Toy Story (film), 4, 6–7, 252, 429. See also Movie, The
角色动画,210
character animation and, 210
computers and, 93, 331, 447, 461
作为第一部数字电影,4、6、429、456 _
as first digital movie, 4, 6, 429, 456
拉尔夫古根海姆和,433
Ralph Guggenheim and, 433
皮克斯和, 4 , 93 , 243 , 252 , 406 , 407 , 429 , 433 , 456
Pixar and, 4, 93, 243, 252, 406, 407, 429, 433, 456
创和,407
Tron and, 407
三角形
Triangles
扩增和243–246 , 307 , 322 , 329 , 337 , 386–387 , 387f
Amplification and, 243–246, 307, 322, 329, 337, 386–387, 387f
teapots and, 245–247, 266, 335
Triple-I (Information International Inc.), 407 , 409–411
Triple-I (Information International Inc.), 407, 409–411
三巨头(萨瑟兰、约翰逊和罗伯茨),276f、281、285、294、314、454
Triumvirate (Sutherland, Johnson, and Roberts), 276f, 281, 285, 294, 314, 454
Central Dogma and, 314, 328, 457
以及被遗忘的计算机图形学历史,275–276
and the forgotten history of computer graphics, 275–276
TX-2 和277
TX-2 and, 277
Tron (film), 406–409, 413, 431
Tubby the Tuba (电影), 354 , 379
Tubby the Tuba (film), 354, 379
亚历克斯·舒尔和219、353、354、417、456 _ _ _ _
Alex Schure and, 219, 353, 354, 417, 456
Turing, Alan, 4. See also “On Computable Numbers”; Universal Turing machine
artificial intelligence (AI) and, 441, 464
在布莱切利公园, 78 , 80 , 92 , 101–104 , 111 , 113
at Bletchley Park, 78, 80, 92, 101–104, 111, 113
计算,446
computations, 446
创造力和, 461
creativity and, 461
与莫里斯·威尔克斯的敌意,134
enmity with Maurice Wilkes, 134
以及计算机的发明,447、448、451、461 _ _
and the invention of the computer, 447, 448, 451, 461
汤姆·基尔本和133、134、150、158 _ _
Tom Kilburn and, 133, 134, 150, 158
在国王学院,463–464
at King’s College, 463–464
马克斯纽曼和, 87–89 , 98 , 101 , 103 , 104 , 132–134
Max Newman and, 87–89, 98, 101, 103, 104, 132–134
原谅,79
pardon, 79
飞行员王牌, 132 , 142 , 143 , 148 , 152 , 447
Pilot Ace, 132, 142, 143, 148, 152, 447
克劳德·香农和, 77–78 , 104 , 111 , 152 , 158
Claude Shannon and, 77–78, 104, 111, 152, 158
eProblem 的解决方案, 87–89 , 106 , 440
solution to eProblem, 87–89, 106, 440
约翰·冯·诺依曼和, 98 , 100 , 101 , 118 , 119 , 131 , 134 , 135 , 446 , 448 , 451
John von Neumann and, 98, 100, 101, 118, 119, 131, 134, 135, 446, 448, 451
Turing machine, 111, 464. See also Universal Turing machine
business card device as a, 92–95, 426, 440
动画,Ron Baecker,以及,298、299、371
animation, Ron Baecker, and, 298, 299, 371
网格上的书法展示,277–278
calligraphic display on a grid, 277–278
伊万·萨瑟兰和, 277 , 284–285 , 287–289 , 299
Ivan Sutherland and, 277, 284–285, 287–289, 299
暴君,428。另见理念-混乱-暴君
Tyrants, 428. See also Idea–chaos–tyrant
跳舞,72-74
dancing around, 72–74
大恐怖及其,61-62
the Great Terror and its, 61–62
Ub Iwerks 工作室,222
Ub Iwerks Studio, 222
Universal medium, 74, 436, 437
环球影城,205
Universal Studios, 205
Universal Turing machine, 96, 440, 464
business card device as, 92–95, 426, 440
加州大学伯克利分校,294
University of California at Berkeley, 294
人工智能研究实验室,464
Artificial Intelligence Research Laboratory, 464
犹他大学, 261 , 330 , 331 , 351 , 359 , 369 , 455
University of Utah, 261, 330, 331, 351, 359, 369, 455
动画和, 296
animation and, 296
吉姆·布林(Jim Blinn) ,电话:331、369、370
Ed Catmull 和, 261 , 317 , 334 , 354 , 357 , 369 , 371 , 410
Ed Catmull and, 261, 317, 334, 354, 357, 369, 371, 410
computer graphics department, 334, 454
由大卫·埃文斯 (David Evans) 创立,294 , 296 , 454
founded by David Evans, 294, 296, 454
Tom Stockham 在259年教图形师
Tom Stockham teaching graphicists at, 259
伊万·萨瑟兰和, 117 , 261 , 294 , 296 , 454
Ivan Sutherland and, 117, 261, 294, 296, 454
使用采样定理进行空间抗锯齿,162-163
use of Sampling Theorem for spatial antialiasing at, 162–163
Unix, 372
Unix, 372
加拿大人,372–373
Canadians and, 372–373
卢卡斯影业和,401–402
Lucasfilm and, 401–402
Unix 专家。另见 达夫,汤姆
Unix experts. See also Duff, Tom
成为图形向导,401–402
becoming graphics wizards, 401–402
不可知性、计算和107
Unknowability, computation and, 107
范德贝克,斯坦,355–356
Vanderbeek, Stan, 355–356
Venture capitalists (VCs), 422, 423
视口,278–279
Viewport, 278–279
Virtual reality (VR), 306f, 457–459
augmented reality (AR) and, 305, 458–459
猴面包树工作室和458
Baobab Studios and, 458
启用摩尔定律,305
Moore’s Law enabled, 305
stereo/3D effect and, 242, 260
Ivan Sutherland and the birth of, 304–305, 306f
Vitascope, 190 , 196 , 204。另见 幻影镜
Vitascope, 190, 196, 204. See also Phantascope
声码器
Vocoder
由虚构的 Abakumov 描述,67
described by fictional Abakumov, 67
作为语音扰频器,67
as voice scrambler, 67
索尔仁尼琴在 Marfino 工作,67
worked on by Solzhenitsyn at Marfino, 67
自由卷(短片),386
Vol Libre (short film), 386
冯·诺依曼,约翰(“约翰尼”),126。另见 Edvac 报告
Von Neumann, John (“Johnny”), 126. See also Edvac report
数码光和,98
Digital Light and, 98
和哥德尔,100
and Gödel, 100
IBM 和142
IBM and, 142
约翰梅纳德凯恩斯和,113
John Maynard Keynes and, 113
life history and overview, 97–98, 100–101
威廉纽曼和,113
William Newman and, 113
在 Princetitute, 89 , 97–98 , 101 , 108 , 135 , 136(另见 冯诺依曼队)
at Princetitute, 89, 97–98, 101, 108, 135, 136 (see also Von Neumann team)
programming/”setting up” and, 108–109, 141, 446
图灵和, 98 , 100 , 101 , 118 , 119 , 131 , 134 , 135 , 446 , 448 , 451
Turing and, 98, 100, 101, 118, 119, 131, 134, 135, 446, 448, 451
威廉姆斯管和,142
Williams tube and, 142
冯诺依曼架构, 98 , 130 , 131 , 134 , 135 , 448
Von Neumann architecture, 98, 130, 131, 134, 135, 448
冯诺依曼团队,118、131、135、137、141、447。_ _ _ _ _ _ 另见Edvac 报告
Von Neumann team, 118, 131, 135, 137, 141, 447. See also Edvac report
Williams tube and, 141, 142, 448
虚拟现实。见 虚拟现实
VR. See Virtual reality
华特迪士尼公司。见 迪士尼
Walt Disney Company. See Disney
傅里叶开, 4 , 7 , 18 , 30 , 31 , 33 , 35 , 50 , 74 , 177 , 179 , 437
Fourier on, 4, 7, 18, 30, 31, 33, 35, 50, 74, 177, 179, 437
热流作为 a, 35
heat flow as a, 35
感官世界作为一个,4
sensory world as a, 4
visual flow as, 165–166, 176–180, 443
视觉世界 a, 4 , 7 , 23–25 , 30 , 31 , 33–34 , 50 , 177 , 179 , 437
visual world as a, 4, 7, 23–25, 30, 31, 33–34, 50, 177, 179, 437
韦恩,马塞利,262、300、301、359、454 _ _ _ _ _
Wein, Marceli, 262, 300, 301, 359, 454
韦恩,狼,300
Wein, Wolf, 300
查理斯·亚当斯和,154–155
Charlies Adams and, 154–155
动画和, 154–156 , 155f , 256 , 282 , 449 , 452
animation and, 154–156, 155f, 256, 282, 449, 452
Whirlwind 上显示的第一部计算机动画,157
first computer animation displayed on Whirlwind, 157
编程手册中的“弹跳球显示”,154
“bouncing ball display” in programming manual, 154
书法展示,158
calligraphic displays and, 158
书法图片来自,150–151,150f
calligraphic picture from, 150–151, 150f
cathode-ray tube (CRT) and, 144, 145
发展, 253
development, 253
数码灯和,144
Digital Light and, 144
digital picture, 144–145, 145f
赫伯弗里曼和,262
Herb Freeman and, 262
在历史背景下,256
in historical context, 256
显示的数学曲线,252
mathematical curves displayed on, 252
内存和, 144
memory and, 144
oscilloscope display, 154–155, 154f
编程,156
programming, 156
速度要求,144
speed demands, 144
spread pixels and, 156, 252, 256
拨动开关和, 144
toggle switches and, 144
版本,137
versions, 137
威廉姆斯管和,144
Williams tube and, 144
旋风–(“旋风减”),137 , 144–146 , 155 , 156
Whirlwind– (“Whirlwind minus”), 137, 144–146, 155, 156
Whirlwind– pictures, 146, 147f, 148
旋风摄影档案,144
Whirlwind photographic archives, 144
白卫兵(布尔加科夫),47
White Guard (Bulgakov), 47
Whitney, John, Jr., 318 , 407 , 409–411
Whitney, John, Jr., 318, 407, 409–411
家庭, 318
family, 318
惠特克, 埃德蒙·泰勒, 45 , 234–236 , 239 , 240 , 275 , 453
Whittaker, Edmund Taylor, 45, 234–236, 239, 240, 275, 453
Wilkes, Maurice V., 134–135, 143
威廉姆斯,弗雷德里克卡兰(“弗莱迪”)。另见 威廉姆斯管/Williams-Kilburn 管
Williams, Frederic Calland (“Freddie”). See also Williams tube/Williams–Kilburn tube
Baby and, 122 , 125 , 126 , 133 , 142 , 143(另见 曼彻斯特宝贝)
Baby and, 122, 125, 126, 133, 142, 143 (see also Manchester Baby)
背景,121
background, 121
cathode-ray tube (CRT) and, 121, 141
on computers, 117, 133, 142, 143
由118创建的第一台数码灯
first Digital Light created by, 118
荣誉, 122
honors, 122
对计算机设计的影响,127
influence on computer design, 127
汤姆·基尔伯恩和, 117 , 118 , 122 , 126 , 127 , 132–134 , 141 , 447
Tom Kilburn and, 117, 118, 122, 126, 127, 132–134, 141, 447
关于马克斯纽曼,133
on Max Newman, 133
智胜 IBM,142–143
outwits IBM, 142–143
照片,118f
photograph of, 118f
在曼彻斯特大学, 121 , 122 , 132 , 133
at University of Manchester, 121, 122, 132, 133
冯诺依曼架构和,134
von Neumann architecture and, 134
威廉姆斯,兰斯,369
Williams, Lance, 369
和抗锯齿光栅图像,359
and antialiasing raster images, 359
在纽约理工大学,369、376、416、418 _ _
阿尔维·雷·史密斯 (Alvy Ray Smith) 和, 358–359 , 416
Alvy Ray Smith and, 358–359, 416
Garland Stern and, 358, 369, 376
Williams tube memory, 143, 148, 158
威廉姆斯管/Williams-Kilburn 管, 137 , 143 , 148
Williams tube/Williams–Kilburn tube, 137, 143, 148
宝贝和, 122 , 142 , 143 , 447 , 448
Baby and, 122, 142, 143, 447, 448
朱利安毕格罗和,142
Julian Bigelow and, 142
阴极射线管 ( CRT )和137、141–144、448
cathode-ray tube (CRT) and, 137, 141–144, 448
棋盘显示在,152
checkerboard displayed on, 152
埃德萨克和,143
Edsac and, 143
电子存储器和, 447
electronic memory and, 447
对计算机设计的影响,127
influence on computer design, 127
invention/design/creation of, 122, 141
汤姆·基尔本,122
Tom Kilburn and, 122
奥德瓦克和,157
Ordvac and, 157
Selectron 和141–142
Selectron and, 141–142
术语,122
terminology, 122
von Neumann team and, 141, 142
旋风和,144
Whirlwind and, 144
赢得记忆竞赛,141–142
winning the memory race, 141–142
早期计算机图形学中的女性,357,403。另见巴顿,克里斯汀
Women in early computer graphics, 357, 403. See also Barton, Christine
第一次世界大战,46
World War I, 46
German invasion of Soviet Union, 62, 65
Xerox PARC(帕洛阿尔托研究中心),330、344、374、375、455。_ 另见PARC
Xerox PARC (Palo Alto Research Center), 330, 344, 374, 375, 455. See also PARC
迪克舒普和, 343 , 344 , 350 , 363 , 403
Dick Shoup and, 343, 344, 350, 363, 403
鲍勃·泰勒 (Bob Taylor),343
Bob Taylor at, 343
Bob Taylor 的实验室,电话:294 , 355 , 454
Bob Taylor’s lab at, 294, 355, 454
XR(扩展现实),460
XR (extended reality), 460
Year of the Projector (1895), 190, 195, 198
Youngblood, 基因, 313 , 314 , 318–320。另请参阅扩展影院
Youngblood, Gene, 313, 314, 318–320. See also Expanded Cinema
and the first color pixels, 316, 318, 455
Zajac, Edward, 283–284, 296, 298
Zephyr(计算机)。见 斯瓦克
Zephyr (computer). See Swac